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Usability evaluation of university website: a case study

P Sukmasetya 1 , A Setiawan 1 and E R Arumi 1

Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series , Volume 1517 , 2019 1st Borobudur International Symposium on Applied Science and Engineering (BIS-ASE) 2019 16 October 2019, Magelang, Indonesia Citation P Sukmasetya et al 2020 J. Phys.: Conf. Ser. 1517 012071 DOI 10.1088/1742-6596/1517/1/012071

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1 Department of Informatics Engineering, Universitas Muhammadiyah Magelang, Magelang, Indonesia.

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Web-based public services become an important part in supporting the success of a university, but there are still many difficulties to use it. This study was conducted to evaluate whether Muhammadiyah Magelang University website has had the acceptability criteria of usability testing. The study was conducted using a questionnaire as a research instrument that consisted of 17 questions and filled by 95 respondents. Those questions grouped into five variables usability, there are learnability, efficiency, memorability, error, and satisfaction. Based on analysis, the result said that the mean score of overall usability testing to measure website usage Muhammadiyah Magelang University website was 2.77, for each variable the Learnability aspects have the overall score of 2.83, the efficiency was 2.73, memorability was 2.82, an error was 2.65 and 2.79 for satisfaction by respondents. From these results indicate that the website of Muhammadiyah Magelang University already Quite Easy to use. However, there are still many things that need to be fixed, especially in case of errors, focused on the availability of the feature and efficiency aspect in the speed of accessing the feature for getting information.

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Assessing the quality of academic websites: a case study

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A Framework for Evaluating the Quality of Academic Websites

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• Sairam Vakkalanka 19 ,
• Reddi Prasadu 19 ,
• V. V. S. Sasank 19 &
• A. Surekha 19  

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1090))

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The main goal of this paper is to design a tool for the evaluation of academic website, taking into account perspectives of different user groups. A literature review was conducted on the existing models, and a list of the factors affecting the quality of academic websites was identified. A framework was developed based on the identified quality factors, to evaluate the new framework, a questionnaire was devised, and a survey was conducted on the reliability of this questionnaire. To assess the effectiveness of the framework, an experiment was conducted, considering six academic websites and 6300 people from different user groups. The threats encountered during the study were also discussed with recommendations for future work.

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Acknowledgements

We thank all the numerous participants who participated in evaluating the different websites, and thank those reviewers for suggesting changes to the questionnaires. No data was collected regarding the details of participants for website evaluations and all of the participants were anonymous.

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Vakkalanka, S., Prasadu, R., Sasank, V.V.S., Surekha, A. (2020). A Framework for Evaluating the Quality of Academic Websites. In: Raju, K., Govardhan, A., Rani, B., Sridevi, R., Murty, M. (eds) Proceedings of the Third International Conference on Computational Intelligence and Informatics . Advances in Intelligent Systems and Computing, vol 1090. Springer, Singapore. https://doi.org/10.1007/978-981-15-1480-7_44

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Top 40 Most Popular Case Studies of 2021

Two cases about Hertz claimed top spots in 2021's Top 40 Most Popular Case Studies

Two cases on the uses of debt and equity at Hertz claimed top spots in the CRDT’s (Case Research and Development Team) 2021 top 40 review of cases.

Hertz (A) took the top spot. The case details the financial structure of the rental car company through the end of 2019. Hertz (B), which ranked third in CRDT’s list, describes the company’s struggles during the early part of the COVID pandemic and its eventual need to enter Chapter 11 bankruptcy. 

The success of the Hertz cases was unprecedented for the top 40 list. Usually, cases take a number of years to gain popularity, but the Hertz cases claimed top spots in their first year of release. Hertz (A) also became the first ‘cooked’ case to top the annual review, as all of the other winners had been web-based ‘raw’ cases.

Besides introducing students to the complicated financing required to maintain an enormous fleet of cars, the Hertz cases also expanded the diversity of case protagonists. Kathyrn Marinello was the CEO of Hertz during this period and the CFO, Jamere Jackson is black.

Sandwiched between the two Hertz cases, Coffee 2016, a perennial best seller, finished second. “Glory, Glory, Man United!” a case about an English football team’s IPO made a surprise move to number four.  Cases on search fund boards, the future of malls,  Norway’s Sovereign Wealth fund, Prodigy Finance, the Mayo Clinic, and Cadbury rounded out the top ten.

Other year-end data for 2021 showed:

• Online “raw” case usage remained steady as compared to 2020 with over 35K users from 170 countries and all 50 U.S. states interacting with 196 cases.
• Fifty four percent of raw case users came from outside the U.S..
• The Yale School of Management (SOM) case study directory pages received over 160K page views from 177 countries with approximately a third originating in India followed by the U.S. and the Philippines.
• Twenty-six of the cases in the list are raw cases.
• A third of the cases feature a woman protagonist.
• Orders for Yale SOM case studies increased by almost 50% compared to 2020.
• The top 40 cases were supervised by 19 different Yale SOM faculty members, several supervising multiple cases.

CRDT compiled the Top 40 list by combining data from its case store, Google Analytics, and other measures of interest and adoption.

All of this year’s Top 40 cases are available for purchase from the Yale Management Media store .

And the Top 40 cases studies of 2021 are:

1.   Hertz Global Holdings (A): Uses of Debt and Equity

2.   Coffee 2016

3.   Hertz Global Holdings (B): Uses of Debt and Equity 2020

4.   Glory, Glory Man United!

5.   Search Fund Company Boards: How CEOs Can Build Boards to Help Them Thrive

6.   The Future of Malls: Was Decline Inevitable?

7.   Strategy for Norway's Pension Fund Global

8.   Prodigy Finance

9.   Design at Mayo

10. Cadbury

11. City Hospital Emergency Room

13. Volkswagen

14. Marina Bay Sands

15. Shake Shack IPO

16. Mastercard

17. Netflix

18. Ant Financial

19. AXA: Creating the New CR Metrics

20. IBM Corporate Service Corps

21. Business Leadership in South Africa's 1994 Reforms

22. Alternative Meat Industry

23. Children's Premier

24. Khalil Tawil and Umi (A)

25. Palm Oil 2016

26. Teach For All: Designing a Global Network

27. What's Next? Search Fund Entrepreneurs Reflect on Life After Exit

28. Searching for a Search Fund Structure: A Student Takes a Tour of Various Options

30. Project Sammaan

31. Commonfund ESG

32. Polaroid

33. Connecticut Green Bank 2018: After the Raid

34. FieldFresh Foods

35. The Alibaba Group

36. 360 State Street: Real Options

37. Herman Miller

38. AgBiome

39. Nathan Cummings Foundation

40. Toyota 2010

Organizing Your Social Sciences Research Assignments

• Annotated Bibliography
• Analyzing a Scholarly Journal Article
• Group Presentations
• Dealing with Nervousness
• Using Visual Aids
• Grading Someone Else's Paper
• Types of Structured Group Activities
• Group Project Survival Skills
• Leading a Class Discussion
• Multiple Book Review Essay
• Reviewing Collected Works
• Writing a Case Analysis Paper
• Writing a Case Study
• About Informed Consent
• Writing Field Notes
• Writing a Policy Memo
• Writing a Reflective Paper
• Writing a Research Proposal
• Generative AI and Writing
• Acknowledgments

A case study research paper examines a person, place, event, condition, phenomenon, or other type of subject of analysis in order to extrapolate  key themes and results that help predict future trends, illuminate previously hidden issues that can be applied to practice, and/or provide a means for understanding an important research problem with greater clarity. A case study research paper usually examines a single subject of analysis, but case study papers can also be designed as a comparative investigation that shows relationships between two or more subjects. The methods used to study a case can rest within a quantitative, qualitative, or mixed-method investigative paradigm.

Case Studies. Writing@CSU. Colorado State University; Mills, Albert J. , Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research . Thousand Oaks, CA: SAGE Publications, 2010 ; “What is a Case Study?” In Swanborn, Peter G. Case Study Research: What, Why and How? London: SAGE, 2010.

How to Approach Writing a Case Study Research Paper

General information about how to choose a topic to investigate can be found under the " Choosing a Research Problem " tab in the Organizing Your Social Sciences Research Paper writing guide. Review this page because it may help you identify a subject of analysis that can be investigated using a case study design.

However, identifying a case to investigate involves more than choosing the research problem . A case study encompasses a problem contextualized around the application of in-depth analysis, interpretation, and discussion, often resulting in specific recommendations for action or for improving existing conditions. As Seawright and Gerring note, practical considerations such as time and access to information can influence case selection, but these issues should not be the sole factors used in describing the methodological justification for identifying a particular case to study. Given this, selecting a case includes considering the following:

• The case represents an unusual or atypical example of a research problem that requires more in-depth analysis? Cases often represent a topic that rests on the fringes of prior investigations because the case may provide new ways of understanding the research problem. For example, if the research problem is to identify strategies to improve policies that support girl's access to secondary education in predominantly Muslim nations, you could consider using Azerbaijan as a case study rather than selecting a more obvious nation in the Middle East. Doing so may reveal important new insights into recommending how governments in other predominantly Muslim nations can formulate policies that support improved access to education for girls.
• The case provides important insight or illuminate a previously hidden problem? In-depth analysis of a case can be based on the hypothesis that the case study will reveal trends or issues that have not been exposed in prior research or will reveal new and important implications for practice. For example, anecdotal evidence may suggest drug use among homeless veterans is related to their patterns of travel throughout the day. Assuming prior studies have not looked at individual travel choices as a way to study access to illicit drug use, a case study that observes a homeless veteran could reveal how issues of personal mobility choices facilitate regular access to illicit drugs. Note that it is important to conduct a thorough literature review to ensure that your assumption about the need to reveal new insights or previously hidden problems is valid and evidence-based.
• The case challenges and offers a counter-point to prevailing assumptions? Over time, research on any given topic can fall into a trap of developing assumptions based on outdated studies that are still applied to new or changing conditions or the idea that something should simply be accepted as "common sense," even though the issue has not been thoroughly tested in current practice. A case study analysis may offer an opportunity to gather evidence that challenges prevailing assumptions about a research problem and provide a new set of recommendations applied to practice that have not been tested previously. For example, perhaps there has been a long practice among scholars to apply a particular theory in explaining the relationship between two subjects of analysis. Your case could challenge this assumption by applying an innovative theoretical framework [perhaps borrowed from another discipline] to explore whether this approach offers new ways of understanding the research problem. Taking a contrarian stance is one of the most important ways that new knowledge and understanding develops from existing literature.
• The case provides an opportunity to pursue action leading to the resolution of a problem? Another way to think about choosing a case to study is to consider how the results from investigating a particular case may result in findings that reveal ways in which to resolve an existing or emerging problem. For example, studying the case of an unforeseen incident, such as a fatal accident at a railroad crossing, can reveal hidden issues that could be applied to preventative measures that contribute to reducing the chance of accidents in the future. In this example, a case study investigating the accident could lead to a better understanding of where to strategically locate additional signals at other railroad crossings so as to better warn drivers of an approaching train, particularly when visibility is hindered by heavy rain, fog, or at night.
• The case offers a new direction in future research? A case study can be used as a tool for an exploratory investigation that highlights the need for further research about the problem. A case can be used when there are few studies that help predict an outcome or that establish a clear understanding about how best to proceed in addressing a problem. For example, after conducting a thorough literature review [very important!], you discover that little research exists showing the ways in which women contribute to promoting water conservation in rural communities of east central Africa. A case study of how women contribute to saving water in a rural village of Uganda can lay the foundation for understanding the need for more thorough research that documents how women in their roles as cooks and family caregivers think about water as a valuable resource within their community. This example of a case study could also point to the need for scholars to build new theoretical frameworks around the topic [e.g., applying feminist theories of work and family to the issue of water conservation].

Eisenhardt, Kathleen M. “Building Theories from Case Study Research.” Academy of Management Review 14 (October 1989): 532-550; Emmel, Nick. Sampling and Choosing Cases in Qualitative Research: A Realist Approach . Thousand Oaks, CA: SAGE Publications, 2013; Gerring, John. “What Is a Case Study and What Is It Good for?” American Political Science Review 98 (May 2004): 341-354; Mills, Albert J. , Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research . Thousand Oaks, CA: SAGE Publications, 2010; Seawright, Jason and John Gerring. "Case Selection Techniques in Case Study Research." Political Research Quarterly 61 (June 2008): 294-308.

Structure and Writing Style

The purpose of a paper in the social sciences designed around a case study is to thoroughly investigate a subject of analysis in order to reveal a new understanding about the research problem and, in so doing, contributing new knowledge to what is already known from previous studies. In applied social sciences disciplines [e.g., education, social work, public administration, etc.], case studies may also be used to reveal best practices, highlight key programs, or investigate interesting aspects of professional work.

In general, the structure of a case study research paper is not all that different from a standard college-level research paper. However, there are subtle differences you should be aware of. Here are the key elements to organizing and writing a case study research paper.

I.  Introduction

As with any research paper, your introduction should serve as a roadmap for your readers to ascertain the scope and purpose of your study . The introduction to a case study research paper, however, should not only describe the research problem and its significance, but you should also succinctly describe why the case is being used and how it relates to addressing the problem. The two elements should be linked. With this in mind, a good introduction answers these four questions:

• What is being studied? Describe the research problem and describe the subject of analysis [the case] you have chosen to address the problem. Explain how they are linked and what elements of the case will help to expand knowledge and understanding about the problem.
• Why is this topic important to investigate? Describe the significance of the research problem and state why a case study design and the subject of analysis that the paper is designed around is appropriate in addressing the problem.
• What did we know about this topic before I did this study? Provide background that helps lead the reader into the more in-depth literature review to follow. If applicable, summarize prior case study research applied to the research problem and why it fails to adequately address the problem. Describe why your case will be useful. If no prior case studies have been used to address the research problem, explain why you have selected this subject of analysis.
• How will this study advance new knowledge or new ways of understanding? Explain why your case study will be suitable in helping to expand knowledge and understanding about the research problem.

Each of these questions should be addressed in no more than a few paragraphs. Exceptions to this can be when you are addressing a complex research problem or subject of analysis that requires more in-depth background information.

II.  Literature Review

The literature review for a case study research paper is generally structured the same as it is for any college-level research paper. The difference, however, is that the literature review is focused on providing background information and  enabling historical interpretation of the subject of analysis in relation to the research problem the case is intended to address . This includes synthesizing studies that help to:

• Place relevant works in the context of their contribution to understanding the case study being investigated . This would involve summarizing studies that have used a similar subject of analysis to investigate the research problem. If there is literature using the same or a very similar case to study, you need to explain why duplicating past research is important [e.g., conditions have changed; prior studies were conducted long ago, etc.].
• Describe the relationship each work has to the others under consideration that informs the reader why this case is applicable . Your literature review should include a description of any works that support using the case to investigate the research problem and the underlying research questions.
• Identify new ways to interpret prior research using the case study . If applicable, review any research that has examined the research problem using a different research design. Explain how your use of a case study design may reveal new knowledge or a new perspective or that can redirect research in an important new direction.
• Resolve conflicts amongst seemingly contradictory previous studies . This refers to synthesizing any literature that points to unresolved issues of concern about the research problem and describing how the subject of analysis that forms the case study can help resolve these existing contradictions.
• Point the way in fulfilling a need for additional research . Your review should examine any literature that lays a foundation for understanding why your case study design and the subject of analysis around which you have designed your study may reveal a new way of approaching the research problem or offer a perspective that points to the need for additional research.
• Expose any gaps that exist in the literature that the case study could help to fill . Summarize any literature that not only shows how your subject of analysis contributes to understanding the research problem, but how your case contributes to a new way of understanding the problem that prior research has failed to do.
• Locate your own research within the context of existing literature [very important!] . Collectively, your literature review should always place your case study within the larger domain of prior research about the problem. The overarching purpose of reviewing pertinent literature in a case study paper is to demonstrate that you have thoroughly identified and synthesized prior studies in relation to explaining the relevance of the case in addressing the research problem.

III.  Method

In this section, you explain why you selected a particular case [i.e., subject of analysis] and the strategy you used to identify and ultimately decide that your case was appropriate in addressing the research problem. The way you describe the methods used varies depending on the type of subject of analysis that constitutes your case study.

If your subject of analysis is an incident or event . In the social and behavioral sciences, the event or incident that represents the case to be studied is usually bounded by time and place, with a clear beginning and end and with an identifiable location or position relative to its surroundings. The subject of analysis can be a rare or critical event or it can focus on a typical or regular event. The purpose of studying a rare event is to illuminate new ways of thinking about the broader research problem or to test a hypothesis. Critical incident case studies must describe the method by which you identified the event and explain the process by which you determined the validity of this case to inform broader perspectives about the research problem or to reveal new findings. However, the event does not have to be a rare or uniquely significant to support new thinking about the research problem or to challenge an existing hypothesis. For example, Walo, Bull, and Breen conducted a case study to identify and evaluate the direct and indirect economic benefits and costs of a local sports event in the City of Lismore, New South Wales, Australia. The purpose of their study was to provide new insights from measuring the impact of a typical local sports event that prior studies could not measure well because they focused on large "mega-events." Whether the event is rare or not, the methods section should include an explanation of the following characteristics of the event: a) when did it take place; b) what were the underlying circumstances leading to the event; and, c) what were the consequences of the event in relation to the research problem.

If your subject of analysis is a person. Explain why you selected this particular individual to be studied and describe what experiences they have had that provide an opportunity to advance new understandings about the research problem. Mention any background about this person which might help the reader understand the significance of their experiences that make them worthy of study. This includes describing the relationships this person has had with other people, institutions, and/or events that support using them as the subject for a case study research paper. It is particularly important to differentiate the person as the subject of analysis from others and to succinctly explain how the person relates to examining the research problem [e.g., why is one politician in a particular local election used to show an increase in voter turnout from any other candidate running in the election]. Note that these issues apply to a specific group of people used as a case study unit of analysis [e.g., a classroom of students].

If your subject of analysis is a place. In general, a case study that investigates a place suggests a subject of analysis that is unique or special in some way and that this uniqueness can be used to build new understanding or knowledge about the research problem. A case study of a place must not only describe its various attributes relevant to the research problem [e.g., physical, social, historical, cultural, economic, political], but you must state the method by which you determined that this place will illuminate new understandings about the research problem. It is also important to articulate why a particular place as the case for study is being used if similar places also exist [i.e., if you are studying patterns of homeless encampments of veterans in open spaces, explain why you are studying Echo Park in Los Angeles rather than Griffith Park?]. If applicable, describe what type of human activity involving this place makes it a good choice to study [e.g., prior research suggests Echo Park has more homeless veterans].

If your subject of analysis is a phenomenon. A phenomenon refers to a fact, occurrence, or circumstance that can be studied or observed but with the cause or explanation to be in question. In this sense, a phenomenon that forms your subject of analysis can encompass anything that can be observed or presumed to exist but is not fully understood. In the social and behavioral sciences, the case usually focuses on human interaction within a complex physical, social, economic, cultural, or political system. For example, the phenomenon could be the observation that many vehicles used by ISIS fighters are small trucks with English language advertisements on them. The research problem could be that ISIS fighters are difficult to combat because they are highly mobile. The research questions could be how and by what means are these vehicles used by ISIS being supplied to the militants and how might supply lines to these vehicles be cut off? How might knowing the suppliers of these trucks reveal larger networks of collaborators and financial support? A case study of a phenomenon most often encompasses an in-depth analysis of a cause and effect that is grounded in an interactive relationship between people and their environment in some way.

NOTE:   The choice of the case or set of cases to study cannot appear random. Evidence that supports the method by which you identified and chose your subject of analysis should clearly support investigation of the research problem and linked to key findings from your literature review. Be sure to cite any studies that helped you determine that the case you chose was appropriate for examining the problem.

IV.  Discussion

The main elements of your discussion section are generally the same as any research paper, but centered around interpreting and drawing conclusions about the key findings from your analysis of the case study. Note that a general social sciences research paper may contain a separate section to report findings. However, in a paper designed around a case study, it is common to combine a description of the results with the discussion about their implications. The objectives of your discussion section should include the following:

Reiterate the Research Problem/State the Major Findings Briefly reiterate the research problem you are investigating and explain why the subject of analysis around which you designed the case study were used. You should then describe the findings revealed from your study of the case using direct, declarative, and succinct proclamation of the study results. Highlight any findings that were unexpected or especially profound.

Explain the Meaning of the Findings and Why They are Important Systematically explain the meaning of your case study findings and why you believe they are important. Begin this part of the section by repeating what you consider to be your most important or surprising finding first, then systematically review each finding. Be sure to thoroughly extrapolate what your analysis of the case can tell the reader about situations or conditions beyond the actual case that was studied while, at the same time, being careful not to misconstrue or conflate a finding that undermines the external validity of your conclusions.

Relate the Findings to Similar Studies No study in the social sciences is so novel or possesses such a restricted focus that it has absolutely no relation to previously published research. The discussion section should relate your case study results to those found in other studies, particularly if questions raised from prior studies served as the motivation for choosing your subject of analysis. This is important because comparing and contrasting the findings of other studies helps support the overall importance of your results and it highlights how and in what ways your case study design and the subject of analysis differs from prior research about the topic.

Consider Alternative Explanations of the Findings Remember that the purpose of social science research is to discover and not to prove. When writing the discussion section, you should carefully consider all possible explanations revealed by the case study results, rather than just those that fit your hypothesis or prior assumptions and biases. Be alert to what the in-depth analysis of the case may reveal about the research problem, including offering a contrarian perspective to what scholars have stated in prior research if that is how the findings can be interpreted from your case.

Acknowledge the Study's Limitations You can state the study's limitations in the conclusion section of your paper but describing the limitations of your subject of analysis in the discussion section provides an opportunity to identify the limitations and explain why they are not significant. This part of the discussion section should also note any unanswered questions or issues your case study could not address. More detailed information about how to document any limitations to your research can be found here .

Suggest Areas for Further Research Although your case study may offer important insights about the research problem, there are likely additional questions related to the problem that remain unanswered or findings that unexpectedly revealed themselves as a result of your in-depth analysis of the case. Be sure that the recommendations for further research are linked to the research problem and that you explain why your recommendations are valid in other contexts and based on the original assumptions of your study.

V.  Conclusion

As with any research paper, you should summarize your conclusion in clear, simple language; emphasize how the findings from your case study differs from or supports prior research and why. Do not simply reiterate the discussion section. Provide a synthesis of key findings presented in the paper to show how these converge to address the research problem. If you haven't already done so in the discussion section, be sure to document the limitations of your case study and any need for further research.

The function of your paper's conclusion is to: 1) reiterate the main argument supported by the findings from your case study; 2) state clearly the context, background, and necessity of pursuing the research problem using a case study design in relation to an issue, controversy, or a gap found from reviewing the literature; and, 3) provide a place to persuasively and succinctly restate the significance of your research problem, given that the reader has now been presented with in-depth information about the topic.

Consider the following points to help ensure your conclusion is appropriate:

• If the argument or purpose of your paper is complex, you may need to summarize these points for your reader.
• If prior to your conclusion, you have not yet explained the significance of your findings or if you are proceeding inductively, use the conclusion of your paper to describe your main points and explain their significance.
• Move from a detailed to a general level of consideration of the case study's findings that returns the topic to the context provided by the introduction or within a new context that emerges from your case study findings.

Note that, depending on the discipline you are writing in or the preferences of your professor, the concluding paragraph may contain your final reflections on the evidence presented as it applies to practice or on the essay's central research problem. However, the nature of being introspective about the subject of analysis you have investigated will depend on whether you are explicitly asked to express your observations in this way.

Problems to Avoid

Overgeneralization One of the goals of a case study is to lay a foundation for understanding broader trends and issues applied to similar circumstances. However, be careful when drawing conclusions from your case study. They must be evidence-based and grounded in the results of the study; otherwise, it is merely speculation. Looking at a prior example, it would be incorrect to state that a factor in improving girls access to education in Azerbaijan and the policy implications this may have for improving access in other Muslim nations is due to girls access to social media if there is no documentary evidence from your case study to indicate this. There may be anecdotal evidence that retention rates were better for girls who were engaged with social media, but this observation would only point to the need for further research and would not be a definitive finding if this was not a part of your original research agenda.

Failure to Document Limitations No case is going to reveal all that needs to be understood about a research problem. Therefore, just as you have to clearly state the limitations of a general research study , you must describe the specific limitations inherent in the subject of analysis. For example, the case of studying how women conceptualize the need for water conservation in a village in Uganda could have limited application in other cultural contexts or in areas where fresh water from rivers or lakes is plentiful and, therefore, conservation is understood more in terms of managing access rather than preserving access to a scarce resource.

Failure to Extrapolate All Possible Implications Just as you don't want to over-generalize from your case study findings, you also have to be thorough in the consideration of all possible outcomes or recommendations derived from your findings. If you do not, your reader may question the validity of your analysis, particularly if you failed to document an obvious outcome from your case study research. For example, in the case of studying the accident at the railroad crossing to evaluate where and what types of warning signals should be located, you failed to take into consideration speed limit signage as well as warning signals. When designing your case study, be sure you have thoroughly addressed all aspects of the problem and do not leave gaps in your analysis that leave the reader questioning the results.

Case Studies. Writing@CSU. Colorado State University; Gerring, John. Case Study Research: Principles and Practices . New York: Cambridge University Press, 2007; Merriam, Sharan B. Qualitative Research and Case Study Applications in Education . Rev. ed. San Francisco, CA: Jossey-Bass, 1998; Miller, Lisa L. “The Use of Case Studies in Law and Social Science Research.” Annual Review of Law and Social Science 14 (2018): TBD; Mills, Albert J., Gabrielle Durepos, and Eiden Wiebe, editors. Encyclopedia of Case Study Research . Thousand Oaks, CA: SAGE Publications, 2010; Putney, LeAnn Grogan. "Case Study." In Encyclopedia of Research Design , Neil J. Salkind, editor. (Thousand Oaks, CA: SAGE Publications, 2010), pp. 116-120; Simons, Helen. Case Study Research in Practice . London: SAGE Publications, 2009;  Kratochwill,  Thomas R. and Joel R. Levin, editors. Single-Case Research Design and Analysis: New Development for Psychology and Education .  Hilldsale, NJ: Lawrence Erlbaum Associates, 1992; Swanborn, Peter G. Case Study Research: What, Why and How? London : SAGE, 2010; Yin, Robert K. Case Study Research: Design and Methods . 6th edition. Los Angeles, CA, SAGE Publications, 2014; Walo, Maree, Adrian Bull, and Helen Breen. “Achieving Economic Benefits at Local Events: A Case Study of a Local Sports Event.” Festival Management and Event Tourism 4 (1996): 95-106.

Writing Tip

At Least Five Misconceptions about Case Study Research

Social science case studies are often perceived as limited in their ability to create new knowledge because they are not randomly selected and findings cannot be generalized to larger populations. Flyvbjerg examines five misunderstandings about case study research and systematically "corrects" each one. To quote, these are:

Misunderstanding 1 :  General, theoretical [context-independent] knowledge is more valuable than concrete, practical [context-dependent] knowledge. Misunderstanding 2 :  One cannot generalize on the basis of an individual case; therefore, the case study cannot contribute to scientific development. Misunderstanding 3 :  The case study is most useful for generating hypotheses; that is, in the first stage of a total research process, whereas other methods are more suitable for hypotheses testing and theory building. Misunderstanding 4 :  The case study contains a bias toward verification, that is, a tendency to confirm the researcher’s preconceived notions. Misunderstanding 5 :  It is often difficult to summarize and develop general propositions and theories on the basis of specific case studies [p. 221].

While writing your paper, think introspectively about how you addressed these misconceptions because to do so can help you strengthen the validity and reliability of your research by clarifying issues of case selection, the testing and challenging of existing assumptions, the interpretation of key findings, and the summation of case outcomes. Think of a case study research paper as a complete, in-depth narrative about the specific properties and key characteristics of your subject of analysis applied to the research problem.

Flyvbjerg, Bent. “Five Misunderstandings About Case-Study Research.” Qualitative Inquiry 12 (April 2006): 219-245.

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Harvard Business Publishing makes a great deal of money selling these for business school course packs and will not make them available to libraries. You can, however, order them directly from HBS, around $8.95 each How to find them:

• Harvard Business Review publishes one case study per issue. These generally deal with fictitious companies but are very good studies of current problems faced by companies.
• Harvard Business School Publishing Search by company name or topic. Abstracts are usually included. Harvard also sells cases from Babson College and Northwestern's Kellogg School of Management, among others.

Use keyword searches in article databases . For example: "case studies and airlines" or "case  studies and management". Full-text articles and abstracts are available, depending on the journal.

Tip: Use the subject heading "case studies" in ABI/INFORM and Business Source Complete

Article database that indexes academic journals, trade publications, newspapers and magazines in business and economics. Full text is often available. Use the FindIt links to locate full text of articles that are not included in the database.

• Business Source Complete This link opens in a new window & more less... Article database that includes trade publications, academic journals, industry profiles, country information and company profiles, which include SWOT analyses. Full text is often available. Use the FindIt links to locate full text of articles that are not included in the database.
• EconLit with Full Text This link opens in a new window & more less... EconLit indexes articles from economics journals, books, book chapters, dissertations and working papers. It is a very good source for empirical studies on economics and finance. Use the FindIt links to locate full text of articles that are not included in the database.

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Frontiers in Educational Research , 2023, 6(9); doi: 10.25236/FER.2023.060920 .

Contrastive Analysis of American and Chinese University Websites—A Case Study of Tsinghua and Harvard University

Yongping Li

Xi’an International Studies University, Xi'an, Shaanxi, China, 710110

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With the improvement of China’s national strength, more and more institutions of higher learning begin to seek international development, and the willingness of overseas institutions of higher learning to conduct international exchanges and cooperation with Chinese institutions of higher learning is also increasing. In the era of increasingly fierce competition in the world of higher education, colleges and universities are trying to seek higher level of cooperation institutions, which can not only train their students into more international talents, but also improve their own international image. For this reason, many Chinese colleges and universities’ web pages are made in both Chinese and English, and the English profile of the university plays an important role in providing foreign scholars and students with a better understanding of the university. In recent years, the number of Chinese students who go aboard for further study has risen sharply, however, the number of students coming to China to study grow slowly, one of the reasons is that the publicity of  Chinese colleges and universities foreign propaganda is not enough, or the web site home page introduction in English does not accord with international friends of reading and thinking habit, which leads to the lack of the understanding of foreign students in Chinese universities, and then they don’t come to study in China.By comparing the differences between the website of Harvard University in the United States and the English version of the website of Tsinghua University in China, this thesis makes a comparative analysis of the differences between English and Chinese languages, hoping to give an in-depth thought on the comparative study of English and Chinese languages and the English translation of the websites of Chinese universities.

University and college website; English translation; Comparative study of English and Chinese

Cite This Paper

Yongping Li. Contrastive Analysis of American and Chinese University Websites—A Case Study of Tsinghua and Harvard University. Frontiers in Educational Research (2023) Vol. 6, Issue 9: 119-128. https://doi.org/10.25236/FER.2023.060920.

[1] Gu Yizhou, Yang Yuanying, Jia Hui. Corpus-based research on the core theme words of the English profile of Chinese and American university websites [J]. Journal of Kaifeng Vocational College of Culture & Art, 2014(6): 86-87.

[2] Li Yanhong, Wang Qi. A comparative study of web design of Chinese and British universities from the perspective of cultural dimension of Hofstede - A case study of Tsinghua University and Cambridge University [J]. Overseas English, 2017(24): 160-161.

[3] Li Yuanqing. A Comparative Study on the Content of the Introduction Text of English Websites in Chinese and American Universities [J]. Journal of Taiyuan Urban Vocational College, 2009(4): 157-159.

[4] Li Qian. A Comparison of Teaching Models in Chinese and American Universities [J]. Knowledge Economy, 2014(8):172-173.

[5] Zhang Sainan, Shi Gengshan. A comparative study of English profiles of Chinese and American college web pages—Taking a famous 985 university in China and Harvard University as an example [J]. Overseas English, 2018, (18):58-60.

[6] Shuneng Lian. A Contrastive Study of English and Chinese [M]. Beijing: Higher Education Press, 1993.

[7] Song Chuting, Zhao Xiaowen. A corpus-based comparison of English language differences between Chinese and American college websites [J]. Comparative Study of Cultural Innovation, 2020, (27): 142-144.

[8] Yin Liaofei. Comparison and Reflection on Undergraduate Education in Chinese and American Universities [J]. Education and teaching forum, 2019(48): 216-217.

Case studies

A case study is used to explore a problem or issue in a specific real world context. You are usually asked to apply wider reading or theory to analyse what is happening in the case. They are often used in subjects such as business or healthcare.

There are two main ways you might encounter case studies in your assignments:

• You are given a case study and you are asked to analyse it. 
• You decide to use case studies as a method for your research, and you gather information on a specific situation to produce a case study as your findings. 

Scroll down for our recommended strategies and resources. 

Answering a case study assignment usually involves analysing the case, researching and linking to theories, and then making recommendations. This useful resource takes you through these steps with example cases from Management and Nursing: 

Writing a case study (RMIT University)

Case study report (e.g. Nursing)

In Healthcare professions you may be asked to write a case study report on a specific client or patient. This resource shows you how to keep your writing relevant and focused on the patient:

Case study report on a patient [video] (RMIT University)

Research method

If you are conducting your own research, you need to understand whether a case study is the most suitable method for answering your research question(s). Look at this introduction to case studies in research and their strengths and weaknesses: 

Case study as a research method (University of Melbourne)

Time to think about theory

Case studies often take time to analyse carefully. What is presented on the surface may have deeper, or less obvious, causes underneath. This is where your wider reading and theory may help, as it can provide frameworks or models for explaining complex and unclear behaviour. For example, theories on group dynamics might help us understand why a specific project team is failing to meet its targets.

Problem-solving

Case studies are a way of exploring a real world problem. You are usually asked to propose recommendations or solutions to the issue presented in the case. Don’t just stop at analysing what is happening and why it is happening, remember to also consider ‘so what can we do about this?’

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Article Contents

Lay summary, introduction, the ‘fastest feasible’ transition path, innovation during rapid growth, estimation of the optimal parallelisation: case study of nuclear fusion, summary and discussion, acknowledgements, conflict of interest, authors' contributions, credit author statement, data availability.

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The interplay of the innovation cycle, build time, lifetime, and deployment rate of new energy technologies: a case study of nuclear fusion energy

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Niek J Lopes Cardozo, Samuel H Ward, The interplay of the innovation cycle, build time, lifetime, and deployment rate of new energy technologies: a case study of nuclear fusion energy, Oxford Open Energy , Volume 3, 2024, oiae005, https://doi.org/10.1093/ooenergy/oiae005

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This article analyses how a forced transition to low-carbon energy impacts the innovation of new energy technologies. We apply the insights to nuclear fusion, potentially a large provider of carbon-free energy currently attracting billions in private investments. We discuss the ‘fastest-feasible-growth (FFG)’ curve for transitions: exponential growth followed by linear growth, where the rate of latter is limited by the inverse lifetime of the installation. We analyse how innovation is affected if, during rapid deployment, a technology progresses through several generations. We identify key timescales: the learning time, the generation time, the build time, and the exponential growth time of the early deployment phase and compare these for different energy technologies. We distinguish learning rate-limited and generation-time-limited innovation. Applying these findings to fusion energy, we find that a long build time may slow deployment, slow learning, and promote early technology lock-in. Slow learning can be remedied by developing multiple concepts in parallel. Probabilistic analysis of value implies that the optimal strategy is to parallelize the development of many concepts. This concurs with the present surge in private investment in multiple concepts. For this strategy to be successful, the build time of the power plant must be minimized. This requirement favours concepts that lend themselves to modularization and parallelization of production and assembly.

The energy transition must be realized fast compared to the lifetime of energy systems. Innovation often comes as a sequence of generations: wind turbines become larger in steps. But if the build time of a single unit is many years, the upscaling cannot wait for lessons learned, resulting in poor innovation. To accelerate learning, multiple concepts must therefore be developed in parallel. That is expensive, but it is the economically rational approach. For nuclear fusion, this means that instead of ‘picking the winner’, five to ten concepts must be developed in parallel. Fusion start-ups, with private investments, collectively do that.

The world is in the early phase of the transition from a fossil fuel-driven economy to one based on low-carbon power generation. The question if the world is going to meet the goals of the Paris agreement [ 1 ] of 2015 becomes more urgent with every year that passes without the required action and progress in decarbonization (The impact of climate change is in the news every day. To give one official quote: In his closing speech at the COP27 conference (Nov 2022, Sharm el Sheikh) UN secretary-General stated: “But let’s be clear. Our planet is still in the emergency room. We need to drastically reduce emissions now—and this is an issue this COP did not address. A fund for loss and damage is essential—but it’s not an answer if the climate crisis washes a small island state off the map—or turns an entire African country to desert. The world still needs a giant leap on climate ambition. The red line we must not cross is the line that takes our planet over the 1.5° temperature limit. To have any hope of keeping to 1.5, we need to massively invest in renewables and end our addiction to fossil fuels.). Whereas the important role foreseen for photo-voltaic (PV) and wind is undisputed [ 2 ], that of nuclear fission remains a subject of debate. Independence of other nations or blocs for the energy supply has moved to the top of the political agenda and its value to society is evidenced by the premium price paid for it (See e.g. the unprecedented hike of the gas price following the start of the Russian invasion of Ukraine.). In this context, it is meaningful that the USA, by speech of special envoy Kerry at the COP28 summit, has announced it foresees an important role for nuclear fusion and that it wants to lead that development [ 3 ].

Unlike nuclear fission, nuclear fusion is a still undemonstrated energy source. While it has the theoretical potential to provide a sizeable share of the global energy demand [ 4 ], it has played a minor role in the scenarios for the decarbonization of the energy system, being projected too far into the future. This is a valid reasoning for the government-sponsored programmes, that plan for demonstrator projects by mid-century [ 5 ], despite recent scientific breakthroughs (On March 9, 2022 the EUROfusion organization announced a new record of fusion energy generated in the Joint European Torus, which received worldwide media coverage: see https://euro-fusion.org/eurofusion-news/european-researchers-achieve-fusion-energy-record/ retrieved 26 April 2024; On 13 Dec 2022, Lawrence Livermore National Lab announced to have achieved fusion ignition in the National Ignition Facility: see https://www.llnl.gov/news/lawrence-livermore-national-laboratory-achieves-fusion-ignition retrieved 26 April 2024, and Zylstra, A. B., Hurricane, O. A., Callahan, D. A., Kritcher, A. L., Ralph, J. E., Robey, H. F., … Zimmerman, G. B. (2022). Burning plasma achieved in inertial fusion. Nature, 601(7894), 542–548. doi: 10.1038/s41586-021-04281-w ; See also e.g. Wurzel, S.E. and Scott, C.H. Progress toward fusion energy breakeven and gain as measured against the Lawson criterion, Physics of Plasmas 29, 062103 (2022)). But today we see an upsurge of private companies that promise to commercialize fusion power on a much shorter timescale [ 6 ]. The private funding of these companies now exceeds that by governments, with several companies having raised hundreds of millions of dollars, some in excess of a billion [ 7 ]. Following suit, several governments, including the USA, the UK, and Germany, have recently announced significant steps to accelerate the introduction of fusion power ( https://www.whitehouse.gov/ostp/news-updates/2023/12/02/international-partnerships-in-a-new-era-of-fusion-energy-development/ ; https://assets.publishing.service.gov.uk/media/65301b78d06662000d1b7d0f/towards-fusion-energy-strategy-2023-update.pdf ; https://www.bmbf.de/SharedDocs/Publikationen/de/bmbf/7/775804_Positionspapier_Fusionsforschung.html ).

These developments raise the question if a technology that is still pre-demonstrator can be scaled up fast enough to make a meaningful contribution to the energy transition. And more in particular, how it can still learn and innovate during such rapid upscaling.

When a new technology enters the market, it must grow fast and innovate at the same time. An interesting example is the introduction of the smartphone: there are generations (Apple conveniently numbers them: I-phone 1, I-phone 2, ...) that got more advanced while the market was rapidly expanding. Three characteristic times in this process are (i) the time between two generations ; (ii) the doubling time during the early exponential growth at the start of the S-curve; and (iii) the lifetime of the product . In the case of the smartphone these times are all similar, at 1–2 years. That means that if every year a more advanced generation is launched, custom is guaranteed because the previous generation is about to retire.

There is a fourth determining timescale, and that is the learning time , i.e. the time needed, after the launch of generation N, to develop new ideas, prototype them, and evaluate an improved concept. For smartphones, the innovation cycle time is 4–6 weeks [ 8 ], hence an improved model can be developed and taken into production in time for the launch of the next generation. This situation is ideal to spur on innovation as well as commercial success. How does this work out for energy technologies and the energy transition?

It is sometimes suggested that a new energy technology, such as solar PV, once it reaches grid parity, will conquer the market as fast as the smartphone did. But if we look at the characteristic times, these situations are not comparable at all. Energy technologies—wind turbines, solar panels, hydro-, or nuclear power plants—typically have a long lifetime. This implies that, eventually, the replacement market is limited, which places an upper bound on the required industrial capacity, and therefore on the speed with which the transition can be realized. This limit does not play up in the case of the smartphone, owing to its short lifetime.

Looking at the other determinants, we see that the time between generations varies greatly between energy technologies. For PV, generations form almost a continuum. Wind has stepped up the unit size of series-produced turbines every few years. Generally, small unit size is conducive for efficient learning [ 9 ]. Fission, on the other hand, characterized by large unit size and bespoke power plant designs, has seen only three generations in 70 years [ 10 ], the ubiquitous Gen2 having dominated the production between 1965 and 2000. Hence, for several decades in essence, the same reactor concepts have been used, and this technology exhibited little learning [ 11 , 12 ].

The innovation cycle time, too, differs greatly between the technologies. For PV incremental improvements of the production method can be tested on a batch-to-batch basis. For nuclear technologies, the long build time and the large unit size (and hence small numbers) mean that innovations can only be tested when a new model has been built, commissioned and operated for a few years, which severely limits the pace of innovation [ 13 ]. As we saw, fission Gen2 has been the industry standard for decades.

The aim of this article is to analyze what a good innovation strategy is for nuclear fusion. Fusion is an energy technology of which the inter-generation time and the lifetime are long, while yet there is a need to scale up fast enough to realize the roughly 10 000 plants needed for a significant contribution to the energy system, in a reasonable time. How can the looming risk of technology lock-in in such a scenario be mitigated? How, in such a situation, do ‘platform’ innovation strategies (such as Space-X) compare to ‘bespoke’ [ 14 ] innovation processes typical of government-run development?

This question is particularly relevant now, because of the upsurge of private parties who—using a wide spectrum of different approaches—aim to bring fusion energy to the market within a decade. Should governments and private industry work together in a mission-driven program [ 15 ], as advocated by Mazzucato [ 16 ]? Should the governments ‘pick the winner’, as has been the strategy for the past decades, or rather work together with private initiatives in a portfolio management approach—a strategy that appears to have been embraced by the USA and UK, in 2023.

To answer these questions, this article is structured as follows. In ‘ The fastest feasible transition path ’ section, we discuss the shape of the S-curve that describes the introduction and deployment of new energy sources. We show that the total industrial capacity places constraints on the shape of the S-curve of deployment, and we describe the fastest feasible transition curve. This shows exponential growth over several orders of magnitude before the deployment becomes linear and eventually saturates. Importantly, the initial exponential growth phase is when—according to Wright’s law—most of the learning needs to happen. This then raises the question how innovation during rapid exponential growth can best be realized.

In ‘Innovation during rapid growth’ section, we consider how the different time scales that characterize the development of a new technology. This provides a basis for a systematic comparison of technologies such as Wind, PV and nuclear, and indeed others such as the smartphone. We observe that, depending on the relative time scales, learning can be limited by the generation time (if that is long, as it was for e.g. fission); or by the learning rate itself (e.g. if the innovation cycle takes long).

In ‘Estimation of the optimal parallelisation: Case study of nuclear fusion’ section, we apply this analysis to the case of nuclear fusion. Using the fastest feasible growth curve as guideline, we optimize the value of fusion power as function of the number of different technological concepts that are being explored in parallel. This results in a value-driven rather than a science-driven strategy.

In the discussion, we reflect on the assumptions underlying the analysis and on the consequences of our findings for the strategy of fusion deployment.

Forced transition

Climate change asks for the transition to low-carbon energy to be realized by 2050. In that time fossil fuel needs to be phased out by force, while all required low-carbon energy technologies need to be deployed at the fastest possible rate. This creates a situation of a virtual ‘infinite market pull’: no regular market dynamics, society will buy the product in the quantity that is made available until the transition is realized. It is a transition from one quasi-steady state to another, in the sense that all time derivatives before and after are much smaller than during the transition. The transition must be faster than the typical lifetime of the existing energy infrastructure, which means that natural replacement will not meet the required pace.

To illustrate this, we refer to the pledge, at COP28, by 20 countries, to triple the total installed nuclear (fission) power by 2050 [ 17 ]. That would entail bringing ~1000 new fission power plants online within 25 years, an average production rate of 40 per year, and well in excess of that by the end of the 2030s. The present capacity of the nuclear industry is about five plants per year, hence this industry needs to grow an order of magnitude in the coming decade. But the industrial capacity that has been built up by that time is large enough to, in steady state, maintain a fleet of thousands of power plants. If these are not realized, then the industry will have to fold back again, only to be rebuild a few decades later.

Generic ‘S-curve’ growth will lead to oscillating industrial capacity after a forced transition

The introduction of a new product or technology is commonly described by a so-called S-curve: a slow start, followed by a linear growth phase that rolls over into a steady state. Indeed, S-curves have been used widely in the literature to describe and analyze the energy transition (see e.g. [ 18 ]). These analyses consider factors that influence the speed of the transition—and there can be many, such as the market demand, the availability of raw materials, the workforce, legislation, etc—and sometimes take an empirical and/or probabilistic approach to account for the uncertainty of such factors [ 2 , 19 ].

The logistic function (black dashed line) describes an S-curve type transition. The industrial capacity (the other curves) required to realize it depends on the lifetime of the product. Due to the shape of the S-curve, the industrial capacity will go into oscillation with a period equal to the product lifetime. The faster the transition is compared to the product lifetime, the larger the oscillation will be. The ‘fastest feasible growth curve’ discussed in ‘The fastest transition path that avoids oscillation’ section realizes the transition fastest without resulting in oscillating production.

However, when it comes to a forced transition, we can also ask the much simpler question ‘how fast can we make the transition happen if all these factors can be neglected?’ Because, as we saw in the example of the pledged tripling of fission power above, there are still limiting factors having to do with the speed at which an industry can grow. And with the anticipated industrial capacity needed after the transition.

Figure 1 shows the industrial capacity as derived from a generic S-curve, for which we took the logistic function, factoring in the lifetime of the product. We compare three different conditions: the product lifetime shorter than the transition time; similar to; or two times longer. We see that if the transition time is two times longer than the lifetime the required industrial capacity grows smoothly to the saturation level, with a small residual oscillation. However, if the transition time is similar to or shorter than the lifetime, large-amplitude oscillations result with a period equal to the lifetime. Which stands to reason, as after the transition has been achieved the demand for new products will wane and only pick up when the oldest products need replacement. Such oscillations are undesirable; fluctuating demand, at this scale, would destabilize an industry that employs tens of millions of people.

The capacity of the fission industry initially grew to >30 plants per year, sufficient to build and sustain about 2000 plants at a lifetime of 60 years. But when the demand abruptly fell in the 1980s the industry had to scale down to almost zero. Today the world capacity of the fission industry is barely sufficient to keep the number of operational plants constant. Data: IAEA [ 20 ].

The development of nuclear fission illustrates this pattern. Figure 2 shows the historical development of the number of fission power plants construction starts, as a proxy of the industrial capacity. The total installed fission power flatlined around 1980. This was not planned: it was forced upon the industry as a consequence of the accident at Three Miles Island (1979), followed by the Chernobyl disaster (1986). The graph shows that the industrial capacity scaled back after this plateau was reached, in agreement with the 50–60 year lifetime of the power plants. Today, the fission industry can build about five power plants per year. To realize the COP28 pledge, this capacity has to grow to a level well above that of the 1970s and we see the oscillation appear, with a period which approximates the lifetime of the power plants.

The fastest transition path that avoids oscillation

We addressed the question how fast a new technology can be introduced while avoiding the oscillatory behaviour in [ 21 , 22 ]. It led to the mathematical description of what we will call the ‘fastest feasible growth (FFG)’ curve. The model starts from the observation that the rate of deployment, e.g. the number of solar panels installed, globally, each year, is equivalent to the industrial capacity, i.e. the number of solar panels the industry can produce, and transport and install per year. It is important to note here that our definition of ‘industrial capacity’ includes the production of raw materials, the workforce, logistics, installation etc. The model then makes one Ansatz:

Continuous, i.e. without jumps, because it is not possible to create industrial capacity overnight. Monotonical, because it is economically undesirable to build up an industrial capacity only to make it shrink again. In other words: we require that the aforementioned oscillations are avoided.

In a situation characterized by a fast growth towards a quasi-steady state (market saturation), the fastest growth trajectory is a linear growth towards saturation with a rate that is equivalent to the replacement rate in the saturated state. For energy infrastructure, with a typical lifetime of 25–50 years, that corresponds to an industrial capacity capable of replacing 2–4% of the infrastructure annually. Hence, the duration of the linear growth is equal to the lifetime of the installation—any faster growth will result in the oscillations described above. However, this industrial capacity will not be available at the start of the development. It needs to be built up before the linear growth can start. For this build-up phase, exponential growth is assumed. Figure 3 provides a graphical explanation of the FFG curve. The mathematical formulation reads as follows (see [ 21 ]):

In the FFG model, the fundamental pattern is a linear growth with slope that equals the industrial capacity needed to sustain the final installation. This industrial capacity needs to be built first, in a phase of exponential growth. The soft start is reflected in the soft roll-over.

P  =  P sat τ exp /τ life {exp[(t − t trans )/τ exp ] – exp[(t − t trans − τ life )/τ exp ]} for t  <  t trans

P  =  P sat τ exp /τ life {1 + (t-t trans )/τ exp – exp[( t − t trans − τ life )/τ exp ]} for t trans  ≤  t  ≤  t sat

P  =  P sat for t  >  t sat

where P denotes the total effective installed power in the case of power technology, or more generally the total number of a product that is operational, P sat the asymptotic value in the saturated state, τ exp the characteristic time of the exponential growth, τ life the lifetime of the power-generating installations, t the time, and t trans the time at which the transition from exponential to linear growth occurs.

The mathematical consequences of the Ansatz are that

i) the linear growth rate is limited by the replacement rate in the final, saturated, state; and

ii) the transition from exponential to linear growth occurs when the installed power has reached a fraction of the final level given by the ratio of the characteristic time for the exponential growth and the lifetime of the infrastructure.

For energy technologies, exponential growth is typically seen with a doubling time of 2–4 years. Combining that with a lifetime of 25–50 years shows that the transition to linear growth occurs at a few percent of the saturated level to be reached, in agreement with observations made by Kramer and Haigh [ 23 ].

The FFG curve is limiting curve, not a prediction of a likely evolution

The FFG curve is a limiting curve in the sense that it is unlikely that a transition will proceed faster. Whether this fastest transition path is realized or not depends entirely on investments, policy measures, geopolitical factors, and the market. All of these external factors can slow down or even halt the transition. But they are unlikely to boost the transition rate beyond the FFG curve.

We stress that the Ansatz is not a law of nature. In a ‘war economy’ it is possible to scale up faster, but society then has to accept post-war overcapacity. Below we’ll discuss the example of the introduction of LED lighting. This was managed in such a way that the transition happened on the time scale of the lifetime of the incoming, not the outgoing, technology: incandescent lamps could have been, but were not, banned overnight.

Two growth phases during the transition: First exponential, then linear

The exponential phase is required to build industrial capacity, to learn how to build in large volume and at reasonable cost. Energy technologies must typically grow several orders of magnitude during this phase, with a corresponding drop of cost, according to Wright’s law. Wind and PV are pertinent examples of this exponential growth and cost reduction. In comparison, the linear growth that follows only spans ~1 order of magnitude, hence the learning and cost reduction is limited in that phase. Therefore, it is early in the exponential growth phase when investments should go to maximizing learning. We’ll return to this important point in ‘Estimation of the optimal parallelisation: Case study of nuclear fusion’ Section.

Application to non-energy cases: LED lighting and smartphones

The replacement of incandescent lamps with LED lighting is interesting, because the outgoing technology was characterized by a short lifetime (<1 year) whereas the incoming technology has a long lifetime (~10 years). Figure 4a shows a fit of the FFG curve to the data of the LED market share. The fit corresponds to a LED lifetime of 12 years, which seems reasonable. This case study shows that in a replacement transition, with in good approximation infinite market pull, the replacement still takes a lifetime of the new technology, not the replaced technology. Which is important to keep in mind for the energy transition. We also note that, in the case of LED lighting, the exponential growth was fast, which combined with the long lifetime, resulted in an early transition to linear growth, all in agreement with the FFG model. This, too, is a characteristic that we must expect in the energy transition.

(a) The replacement of incandescent light by LED lighting is well described by the FFG curve, in both the exponential and the linear phases. This observation shows that the transition is dominated by the lifetime of the replacing, not that of the replaced technology. [Data source: Goldman Sachs]; (b) The introduction of the smartphone showed exponential growth of the industrial capacity (sales) followed by a sudden levelling off, in agreement with the FFG model: here it is the short lifetime of the product that allows the industrial capacity to grow exponentially until saturation is reached. [Data retrieved from https://www.statista.com/statistics/263437/global-smartphone-sales-to-end-users-since-2007/ ].

We chose the introduction of the smartphone as another interesting case, as here the lifetime of the product is short. In the FFG logic, this would allow exponential growth nearly all the way until the plateau is reached. Figure 4b shows that this behaviour is indeed observed: smartphone sales first grew exponentially until there was an almost abrupt stagnation in the growth of the sales (hence, industrial capacity). With the short lifetime of a smartphone, this would imply that a fully developed market was reached a few years later.

In summary, we have observed that the logistic function, often used to describe S-curves, does not satisfy the requirement of a smooth and monotonical development of industrial capacity during a transition. The FFG curve is a special S-curve constructed in such a way that it does satisfy this requirement. It shows that the fastest pace of a transition is determined by the lifetime of the incoming technology. Next, we’ll use this model to find the limiting curve for the energy transition, restricting the analysis to wind and PV.

(a) Application of the FFG model to onshore wind and PV. The same data is plotted on a log-scale (left axis) as well as a linear scale (right axis) to better bring out the two growth phases. The historical data of both wind and PV appear to follow an FFG curve. Wind appears to have transitioned to linear growth in 2012, PV shows signs of such a roll-over from 2016. If this trend is not broken, saturation will occur at a level of 350–400 GW, due to the finite lifetime. This is almost an order of magnitude too low to achieve the energy transition. (b) Reversing the logic, we take the IEA net zero emission (NZE) scenario and make the FFG model match the 2050 target, taking the present installed power as starting point and keeping the same values for the exponential growth rate and lifetime. The IEA scenario is compatible with the FFG logic but does require the industry to resume exponential growth on short term, during a few more years. (c) Application of the model to the exponential phase and matching it to the NZE values in 2050 shows that until the exponential growth slowed in 2012 and 2016 the deployment of wind and PV appeared to follow an FFG curve that would bring them to the NZE targets in time. (graphs based on historic data from the IEA data explorer, reworked by the authors (see ref [ 25 ]))

The FFG curve applied to on-shore wind and solar PV

We applied the FFG curve to the development of on-shore wind and solar PV, taking three different approaches. In the first, we fit the model to the historical data. Figure 5 shows that a fair description of the data is obtained for both the exponential growth and the transition to linear growth. The fit is obtained with 25 years for the lifetime of the installed systems and 1.9 and 3.2 years for the doubling time of PV and wind, respectively. Both appear to have transitioned to linear growth, in 2012 and 2016 for wind and PV, respectively, where it is noted that the transition is clear for Wind, while for PV it could be argued that there is still exponential growth, albeit slowing down (Footnote: these fits have four parameters, of which one, the lifetime of the wind turbines or solar installations represents a physical property of the technology. For both wind and PV, it is around 20–25 years. As metric for the goodness of the fit the sum of squared differences in the log plot was used, to obtain a balance between the exponential and linear phases. The fits are robust for the exponential growth phase, for which the data spans 2–3 orders of magnitude. The transition time, too, has an uncertainty of less than 0.5 year. The linear phase is well determined for Wind, but for PV the few data points leave room for variation: varying the lifetime between the reasonable bounds of 20–25 years results in corresponding saturation levels between 300 and 400 GW, respectively.) We note that the investments in Wind and PV have also stalled at an almost constant level between 2012 and 2020 (see e.g. investment data at IRENA [ 24 ]). The fact that both wind and PV appear to have reached a linear growth, coupled to the fact that after one lifetime all industrial capacity is needed for the replacement, results in a saturation level—if no policy changes are implemented to change this—of 300–400 GW. This is almost an order of magnitude too low to achieve the energy transition.

As said, the FFG model is not predictive other than providing a limiting growth curve. Therefore, the fact that the deployment data of PV and wind to date appear to exhibit the characteristics of the model, does not mean that this trend cannot be broken. In fact, it must be broken to realize the energy transition in time.

It is therefore interesting to analyse if, following the FFG logic, the transition goals of 2050 can be reached provided there are no other factors limiting deployment the deployment. To that end, we fill in the installed power to be reached by 2050 according to the IEA NZE2050 scenario and construct the FFG curve leading to that goal, starting from the actual installed power today, while keeping the characteristic times for wind and PV the same as in the fit to historic data. Figure 5b shows that with these parameters the 2050 goals are feasible but require a radical increase in the deployment rate. This calls for a strong increase of investments in the coming years. Such an increase can indeed be observed for PV, with annual investments almost doubling from 2021 to 2023. For wind, such a pronounced upturn of investments is not yet observed. Finally, in Fig. 5c the FFG curve is again made to fit the NZE 2050 target, but here we only matched the exponential phases. This plot illustrates how, by departing from the FFG curve, time is lost that cannot recovered.

Conclusion: energy deployment has a long exponential phase

The most important aspect of the FFG curve for the analysis in this paper is that the transition from exponential to linear growth happens at a level—relative to the final market share—that is given by the ratio of the exponential and linear growth times. For energy technologies, which have a lifetime of decades while the exponential growth should be fast, this is typically when the contribution to the energy market reaches the percent level. This means that one the one hand the phase in which a meaningful contribution to the energy system is being built up takes about a lifetime of the installation. On the other hand, as we have seen in the case of PV and wind, this linear growth is preceded by decades of exponential growth. To take the example of nuclear fusion, which we’ll discuss in ‘Estimation of the optimal parallelisation: Case study of nuclear fusion’ section, it means that the exponential growth phase should take it from the first few power plants to hundreds of power plants. This requires more than 20 years at a doubling time of 3 years. It is during this exponential phase when the largest relative growth takes place, and since according to Wright’s law learning is proportional to the logarithm of the cumulative production, most learning will happen during that phase, too. Therefore, we must address the question how learning, or innovation, is best organized during exponential growth. That is not obvious, as during the fast scale-up there is little time to learn, invent, try out and implement innovations. This is especially the case if the innovation cycle is longer than the exponential growth time.

Growth and learning by generation

It can be useful to think of an innovation process as a sequence of generations, similar to the launch of the generations of smartphones, or PC operating systems, or of a particular model car. Innovation is then measured as progress from generation to generation.

In analogy to natural evolution [ 26 ], the dynamic of innovation is governed by two processes: learning , i.e. the spawning of new ideas followed by prototyping, testing and evaluation, which is then followed by the implementation of the innovations in a new generation of the product. After the new generation of a product has been launched, a new round of learning starts. Learning needs time, but it also saturates after some time, when all that could be learned from model N has been learned and the time is ripe for a new version to be launched as generation N + 1. We’ll assume, for the sake of argument, that we can characterize the learning process with a characteristic time constant, τ L .

If the time between generations (τ G ) is long compared to τ L , the sequence of generations is slowing down the evolution/innovation. We’ll call the innovation ‘generation time-limited’ in that case. If, on the other hand, the generation time is too short compared to the learning time, the innovation is ‘learning rate-limited’. If a new generation is started before learning could take place, it is essentially the same as the previous and we would not call it a new generation. Therefore, the natural ordering is τ L  ≤ τ G .

If an innovation process is learning rate-limited , the rate of innovation can only be increased by speeding up the learning. Which may not always be possible, especially if the learning leans on external technology developments. If an innovation process is generation time-limited , then the frequency of the generations must be increased to speed up innovation. Whether this is possible or not depends on the build time.

The role of the build time

An important addition to this logic is that it takes time (τ B ) to build a new model or generation. Once the design of a device has been frozen and construction started, learning will not impact its performance anymore. Learning during the construction phase will feed into the design of the next generation. However, the integration of all the components into the new device, followed by its operation, is essential to complete the learning process. For these lessons to feed into the design and construction of the next generation, there must be time between the start of operation and the start of construction of the next generation, and naturally the generation time has to be longer than the build time: τ B  < τ L  ≤ τ G . This underlines the importance of minimizing the build time.

Figure 6 categorizes different technologies by their lifetime and build time, including LED lighting and smartphones for context. Effective learning can only be achieved when the build time is much shorter than the generation time. A long lifetime hampers the maximum rate of deployment. The generation time must be longer than the build time to allow learning to have an effect on the next generation, but ideally should be kept short to allow for a smooth building up of the industry. Technologies in the lower left quadrant, with the smartphone as the example, have ideal conditions for fast learning and swift deployment. The technologies that have long build time and long lifetime are constrained by both the generation time and the learning rate. Unless strategies are applied aimed at abating exactly those unfavourable conditions, these technologies will show slow deployment and little learning. The present development of the small modular fission reactor is an example of such a strategy.

Different technologies can be categorized by their lifetime and build time. A short lifetime allows swift deployment, a short build time allows quick exploration of innovative ideas. Technologies that are characterized by a long build time, such as nuclear fission, face unfavourable conditions for learning.

Learning during exponential growth

The difference between learning-rate-limited or generation-limited innovation fundamentally changes under rapid exponential growth. If the growth factor from one generation to the next is large—say two orders of magnitude, as was the case in fission deployment—it is clear that it pays to get as much learning as possible from the first generation. Better to invest in 10 different concept developments in Gen1, of which only few make it to Gen 2, than to risk building 100 reactors of a type that isn’t as good as it might have been.

Taking as starting point that, in order to have effective learning, τ G must be greater than τ L , we see that innovation is hampered when τ L /τ exp is too large: when fast growth is required, the learning time and hence the build time, must be reduced.

Cost of accelerated learning and de-risking by parallelisation of concept trials

The learning rate can only be increased by trying out multiple concepts in parallel. The faster learning, or a greater probability that at least one successful concept or improvement is found within a generation time, comes the cost of increased spending. There is, however, a finite number of ideas that can be tested, and if each of them a have equal probability ( p ) of success, the probability that at least one successful innovation will be found will typically have a functional profile as depicted in Fig. 7 . Here the number of ideas tried in parallel is a proxy for the required investment. For the trial of each individual concept, the probability of success itself will depend on the time available. This relation is non-linear: in practice there is a minimum time within which a project can be realized even with unlimited budget. But if there is sufficient reward for achieving success earlier, it can be worth the extra spending. On the other end of the scale, dragging out a project will increase the cost without increasing the probability of success.

Sketch of the generic relationships between the investment in learning and the reward: The expected reward increases in value if the probability that it will be realized is increased, but there is a limit to the amount of risk reduction money can buy; likewise, reducing the time of the R&D program will increase the value of the expected reward, but there is a limit to the acceleration that can be achieved by increased spending. The optimum (reward–Cost) is indicated by arrows and depends, apart from the shape of the curves, on the absolute values. Both the risk-reduction curve and the (future) reward can only be estimated, using assumptions. In sec. 4 this is done for the case of nuclear fusion.

The rapid development of vaccines during the Covid pandemic may serve illustration of these generic principles: many concepts were developed and tried in parallel (with only a few winners), and the companies and governments involved were willing to spend the budget needed for maximum acceleration of the development programs because the benefits of reaching success were clear. The reward warranted the spend. All of these arguments hold a fortiori for the climate crisis and the need to accelerate the transition to clean energy.

The optimum parallelization will depend on several factors. These include factors that we can use as input, such as the desired exponential growth rate and the cost of trying a single concept; and factors that must be estimated, most notably the expected future revenues and the discount rate. In ‘Estimation of the optimal parallelisation: Case study of nuclear fusion’ section, we shall carry out this optimization for the case of nuclear fusion, in an effort to understand why there is such a surge of private investment in fusion start-ups.

The multitude of private companies: parallel exploration of concepts

Nuclear fusion is characterized by a long build time and high cost of prototyping: the experimental reactor ITER costs more than 20 billion Euro and will take more than 35 years for construction and commissioning until full performance [ 27 ]. While future commercial fusion power plants are projected to be less costly, the construction cost of a fusion powerplant will be an important component of the cost of electricity [ 28 , 29 ].

The roadmap of the government sponsored R&D program foresees the start of the construction of a demonstrator, DEMO, after ITER has reached full performance. This puts full performance operation of DEMO towards 2060. The initial exponential growth only starts after DEMO has established a sufficiently mature technology basis.

These long timelines have motivated private parties to propose faster tracks towards the realisation of fusion power. In the past few years that their number has grown to >40 worldwide, with an accumulated private investment in excess of $6 billion as of 2022 [ 6 ]. These companies typically promise to deliver a demonstrator within a decade. And, whereas the government sponsored R&D program has largely focussed on a single concept (the so-called tokamak, a machine in which a hot plasma is confined by strong magnetic fields), the private companies together explore a wide variety of concepts. These include more compact versions of the tokamak, but also fundamentally different concepts.

As a result, the private companies taken together represent an innovation path in which several concepts are tried out in parallel, while at the same time a large effort is being made at reducing the build time. As we saw in Sec.3, this is an effective way to accelerate learning. However, exploring different concepts in parallel is expensive.

This brings us back to the question if there is an optimum parallelization and how it depends on factors such as the build time, the growth rate and the projected revenues and discount rate.

Accelerated learning by parallel trials: The cost, the gain, the optimum

To model the learning in the prototyping generation of fusion power plants and its consequences for the first generation of commercial plants, we take a probabilistic approach. We consider a fixed time t 0 in which N concepts are tried simultaneously. We’ll call this Gen0, and we assume that Gen0 will not generate revenues. We denote by I 0 the investment needed to realize revenues (R 1 ) in Gen1. The function to optimize therefore is

where <. > denotes the expectation value.

Trying out more concepts in parallel goes at the cost of a larger I 0 but will increase the probability of success, and therefore increase the expectation value <R 1 >. In this idealized model, we assume that there is initially a large number of independent concepts to choose from, which have a probability p to succeed, each; and we assume that the probabilities of success of the different concepts are uncorrelated. We’ll examine and discuss the validity of this approach later. Within this frame of assumptions, I 0 is proportional to N:

where C 0,s denotes the cost of trying out a single concept, and the probability to find a successful concept in a batch of N parallel tests is given by

The expectation value <R 1  >  in Gen1 is proportional to the number (M) of reactors in that generation, the expected revenue of a single plant ( R 1,s ), and the probability that they will be realized at all, P N . Moreover, the costs and revenue in the future must be discounted by the factor exp(−t/τ disc ) where τ disc is the e-folding time of the discounting (Footnote: The discount factor is commonly expressed as an annual percentage (x 0.100%). This is related to the e-folding time by (1 + x) t  = e t/τ ➔ τ = 1/ln(1 + x). For x ≪ 1 this can be approximated by τ ≈ 1/x.)

Next, we must make an assumption about the number of active reactors as function of time. For this, we’ll stay with the logic developed earlier in this paper and assume that the deployment proceeds according to the FFG curve.

With these elements we can estimate the future revenues. In a first approach, we can integrate the discounted cash flow over time, equating the annual revenue of a single reactor to R 1,s /τ life . This integral converges due to the discounting. In particular, due to the long lifetime of fusion power plants, the linear growth phase, which in FFG model has a duration of τ life , is much longer than the discount time constant τ disc . In that case, the integrated cash flow is largely determined by this linear growth phase, the integral over which can be approximated by

where M sat denotes the eventual saturation level of the FFG curve, which should be of order 10 4 for fusion to make a sizable contribution to the energy mix. In this approach, however, we make no distinction between generations, while in the linear growth phase the number of reactors already runs into the thousands.

We therefore propose a different estimation, in which we consider a finite number (M) of plants which we may think of as one generation. Instead of integrating the cash flow, we estimate the total revenues over the lifetime of these M power plants. Since we are looking at the early phase of deployment, this implies that the number of operational reactors grows exponentially, with characteristic time τ exp . Hence, the number of plants M and the time needed to realize those, and therefore the time over which the discounting is to be applied, are dependent. In other words, the exponentially growing number of plants must be multiplied by a—less steep—decreasing exponential function that represents the discounting. The result is still exponential but with a reduced rate.

The exponential growth only starts after t 0 , the time used to select the best concept and build the first batch of power plants, which brings in an additional discounting factor exp (−t 0 /τ disc ) .

Next, we express the net revenue R 1,s of a single reactor in terms of the cost of the reactor at the time it is built, using the economic payback time τ pb :

We chose to express the revenues in terms of the payback time, because this is more robust than an estimation of the competitive cost of electricity—made up of both the intrinsic cost and the market—decades into the future. Upon introduction, a new energy source will generally not be competitive, if only because it hasn’t gone through its learning curve yet. This market failure can be fixed by government intervention—if the new source features in their policy—by subsidies or other policy measures, in such a way that the new source is interesting for investors. That means that the payback time must be much shorter than the lifetime, typically 1–2 decades. It does not need to be shorter than that—once that is the case, government support is no longer needed.

With this assumption, the lifetime revenue is related to the initial cost of the reactor and need not be discounted over the lifetime. The factor K.C 0,s expresses the cost of the reactor in terms of the cost C 0,s of building and evaluating a prototype, which connects the future revenues to the cost of development today, in money of today. The expectation is that the cost of power plants is less than that of the demonstrator, i.e. K < 1.

The expectation value (in a statistical sense) of the future revenues of a generation comprising of M power plants then takes the generic form

Since we are interested in the value ( N opt ) of N for which the function F  = <R 1  > − N.C 0,s reaches its optimum ( F opt ), we express the expectation value of the revenue in units of the cost of a single concept trial as

where all input variables have been absorbed in the numerical constant k :

The numbers of interest are the value N opt for which this function reaches its optimum and its value at that optimum. N opt is found by differentiating the following expression:

where p denotes the probability of success of a single concept trial, as before. The value of k must be estimated, but we can indicate a range in which the result can be expected. As central values, we take t 0  = 15 years, τ exp  = 5y, R 1,s  = 2.K.C 0,s (i.e. the payback time is one third of the lifetime) and τ disc  = 15y (corresponding to an annual discount percentage of ~7%). The latter effectively places the economic horizon at about 30 years from now (factor 10 reduction of value), i.e. around 2050, the crucial time for climate action. For energy technologies, this would seem to be a sensible horizon for the evaluation of future value, both from an economical and a societal perspective.

For the number of plants in Gen1 we consider the range 30–500, bearing in mind that one needs to build a minimum number to warrant the cost of development; that for innovation and the avoidance of technology lock-in the scale jump between generations should not be too large; and that in view of the 10 4 power plants target, the exponential growth should transition to linear growth at N = 500–1000. (For comparison: fission Gen2 comprises ~400 plants).

Inserting these numbers in ( 8 ), k comes out in the range [7–50].

Figure 8a shows the optimization curve for the numerical factor k  = 30 and the probability of success of a single trial p  = 0.3. A broad optimum is found for N in the range 5 to 8, for which the investment in the R&D amounts to about 30% of expectation value of the revenues. Figure 8b plots N opt and the corresponding revenues as function of k, showing that for a broad range of the latter, the number of parallel tries warranted by the revenues is in the range 5–15, the higher values being indicated for the cases with lower probability of success. For k  > 20 the value of N opt becomes quite insensitive to k . Finally, we must bear in mind that in practice the total number of independent concepts may be limited to only a handful.

(a) Model optimization of the number of parallel trials of different concepts. The cost of the trial process is proportional to the number of concepts tried, whereas the probability of (at least one) successful trial levels off. Taking the latter as a multiplier of the expected revenues, an optimum is found which depends on the probability of success of a single concept ( P  = 0.3 in this example) and the lifetime revenue of a single power plant, which is discounted, because it is in the future. Discount percentage, rate of deployment and the profitability of a single plant determine the absolute value of the revenue curve, represented by the factor k; (b) the optimum N (full lines) and corresponding net revenue (dashed lines) for P  = 0.15, 0.2, and 0.3 respectively.

The bottom line of this analysis then is that in any scenario in which fusion power is to become a serious contributor to the energy landscape the best strategy today is to try as many different concepts in parallel as possible.

The key to increasing the value of fusion energy, i.e. increasing the multiplier k, lies in acceleration. By reducing the time until deployment starts, the discount due to the factor exp(−t 0 /τ disc ) can be reduced, whereas a faster exponential growth reduces the impact of discounting during deployment.

From this attempt at quantifying the economics of learning in the development phase, we see that:

There is an economic incentive to shorten the time to demonstration, even if that means significant extra spending on an annual basis.

There is a clear economic advantage in trying multiple concepts in parallel. It depends a bit on the probability of success assigned to each concept, but typically more than five parallel tracks are warranted, which means in practice that it is economically sound strategy to try all reasonable options on the table.

The optimization depends, but not critically, on the estimation of the future revenues. Here it is important where we put the financial horizon. In the analysis above we have adopted the logic that the revenues of Gen1 are taken into consideration, where the number of Gen1 plants M is a variable to be chosen. This fits in the logic of deployment in a sequence of generations: during the deployment of Gen1 new investments must be made to develop a better and cheaper Gen2. In that second round a similar analysis could be done.

To recoup the investment made in the development phase, the number of plants that contribute to the generation of revenues must be significantly larger than 10. Here we see the danger of technology lock-in: If Gen1 consists of a large number of power plants of the same design, it will be difficult for a radically different design to enter the arena for Gen2. It would, therefore, be advantageous to pursue multiple different options in Gen1 and postpone down-selection to Gen2. In the analysis in Sec.3 we saw that it is advantageous to limit the scale jump between generations, hence the intergeneration time, to allow innovation during exponential growth. But the intergeneration time should also allow time to learn, which means it must exceed the build time by at least a few years in which reactors of the new generation are operational. Ergo, the build time emerges as the crucial determinant in the development and reducing it as much as possible should be driving the design of fusion power plants.

In summary, we have discussed building blocks leading up to an analysis of the innovation strategy for nuclear fusion. To start, we have shown that the pace at which the energy transition can be realized is limited by the lifetime of the supplementing technologies, not the incumbents. Breaking this relationship to achieve a ‘forced transition’ leads inevitably to an overshoot in industrial capacity. We illustrated this logic with the examples of the introduction of LED lighting and smartphones, and showed that the lifetime of wind and PV power is just short enough to be compatible with the goals in the IEA NetZeroEmission scenario. For infrastructure with a significantly longer lifetime, such as nuclear fission or fusion, a significant contribution by 2050 is unlikely to be realisable—which isn’t to say that it cannot play an important role the second half of the century.

We then analysed how the build time, learning time and generation time are related. In relation to innovation, or the possibility to achieve efficient learning, we identified the learning rate-limited and generation time-limited regimes. Here, too, technologies that are characterized by large unit size and correspondingly long build time stand apart. These are apt to suffer from slow learning due to the limited time between start of operation of a new generation and the launch of the next generation. This intrinsic conflict of time scales is exacerbated when fast exponential growth is required. In that case, there is either very limited learning from one generation to the next, or there is a very large jump in volume between generations. The latter entails a large technological risk, even apart from the fact that it is difficult to make an industry—at that scale—grow in quantum jumps. The history of nuclear fission bears witness of these issues, having stayed with Gen2 reactor design for several decades while showing limited learning. For nuclear fusion, the same unfavourable characteristics are seen.

Two strategies can be followed in order to alleviate these principal drawbacks. First, in order to accelerate learning, fusion should adopt a strategy of testing out as many potential technical solutions at the same time as possible. In the present phase of development, this applies to fundamentally different reactor concepts. By extension, once one or more viable reactor concepts have been identified and demonstrated, this strategy should be applied at the subsystem level. In this way the amount of learning in a given time can be increased, i.e. the learning rate is enhanced. To lift the generation time limitation, the build time must be reduced as much as possible. This means that concepts or designs that are modular or linear are favoured over those that have an intrinsically complex build-up, and that an accelerated assembly process is worth an extra cost.

Both strategies require increased funding levels compared to a linear ‘pick the winner’ approach. But as we argued in ‘Estimation of the optimal parallelisation: Case study of nuclear fusion’ section on the basis of a Net Present Value analysis, both steps follow a sound economic logic. Parallelisation of trials, in a given amount of time, de-risks through accelerated learning. This results in a higher evaluation of the future revenues. Acceleration of the sequence of generations made possible by a reduction of the build time has many advantages, but simply the fact that it brings the revenues forward and therefore reduces the discounting warrants significant spending on shortening the build time. In addition, a shortened build time, for a given generation time, leaves more time for learning per generation.

Returning to the observation that in the past few years the number of fusion start-ups has grown quickly to more than 40 worldwide in 2023, we note that together they appear to constitute the strategy outlined above. They are all committed to drastically shortening build times, several of them are already actively organizing the supply chains and aim for designs and manufacturing processes that allow modularization and parallelization of production and assembly. Whereas each works on acceleration and de-risking of their own project, on the macro-level, too, these companies together de-risk and accelerate the development of a fusion reactor. Effectively they move fusion in the direction of the lower left corner in Fig. 7 . Investors recognize this portfolio aspect and several of them back multiple private fusion companies.

In the analysis in ‘Estimation of the optimal parallelisation: Case study of nuclear fusion’ section 4, it was assumed that all concepts have equal probability of success, and that these probabilities are uncorrelated. Neither of these conditions will be fulfilled in practice, but the effects of loosening them are not fundamental. If the probabilities are unequal, we could sort the concepts by probability of success and limit the parallel trials to the topmost successful ones—imagining for the minute that we possess the prescience to do that. With reference to Fig. 8a , this would result in a probability curve that shows a steeper rise to saturation, where the level of saturation will not quite reach unity. This does not affect the estimation of N opt in a fundamental way, it just gives a shift to the lower values, whereas the absolute value of <R 1  > will come out lower, too. In terms of spending the available budget wisely, one could argue that the less likely concepts may require (much) less money for a proof of principle. This is reflected in the distribution of private funding for the fusion start-ups, of which only a handful receive by far the largest share of the total funding [ 10 ]. The assumptions that the probabilities of success are uncorrelated is certainly not fully realistic. After all, the concepts aim at overcoming the same obstacles that make nuclear fusion such a hard problem. However, despite common factors, it is also true that the different approaches make different choices. Magnetic confinement systems have fundamentally different issues than inertial confinement approaches, in some systems the neutron activation of the ‘first wall’ material is a crucial problem that is avoided altogether in alternative concepts that feature a reactor design that does not have a first wall, other concepts are based on an aneutronic fusion reaction avoiding the issues with neutron damage and activation at the cost of a smaller reaction rate, etc. Therefore, while there is certainly some degree of correlation between the probabilities of success, there is also ample variability that decorrelates them.

These considerations leave the main conclusion unaltered: the best strategy is to try all reasonable options. And notably, trying to ‘pick the winner’ does not appear to be a good strategy in any scenario. A portfolio approach in which the risk is spread over 5–15 different concepts is the rational approach, where ideally a few concepts are kept for further development in Gen1.

Based on considerations of the speed of the required energy transition, the characteristic times of learning and innovation during such a transition, and the concept of growth through generations, we argue that the parallel development of as many fusion concepts as are available, even those that have a modest probability of success, is an economically sound strategy. It reduces the risk of the development of fusion power and brings its deployment forward, factors that increase its value, both in terms of monetary return on investment as in terms of contribution to a sustainable energy system. In addition, we gave arguments why a reduction of the build time of fusion reactor is key to successful deployment and generation-on-generation learning.

The authors should like to acknowledge the discussions with Guido Lange, and with undergraduate students who did projects in the TU/e techno-economics-of-fusion-energy team over the past few years: Polle van Berlo, Ruben Wierda, Dilys Mertens, Pavan Teki, Noel Weerensteyn, Alexander Lugtenberg, Mustahsan Majeed, Sophie Broekers, Thimo Gubbels, and Shaughn Prickarts.

This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No. 101052200 — EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

The authors do not have any conflicts of interest.

The paper is the result of a close collaboration between both authors. The writing was mostly done by NLC.

Niek Lopes Cardozo (Conceptualization [lead], Data curation [lead], Formal analysis [lead], Funding acquisition [lead], Investigation [lead], Methodology [lead], Project administration [lead], Resources [lead], Software [lead], Supervision [equal], Validation [lead], Visualization [lead], Writing—original draft [lead]) and Samuel Ward (formal analysis [supporting], Investigation [supporting], Methodology [supporting], Validation [supporting], Writing—original draft [supporting]).

All data used is from publicly available sources, as referenced. The SSG model and the analysis in Section 4 are analytical.

The impact of climate change is in the news every day. To give one official quote: In his closing speech at the COP27 conference (Nov 2022, Sharm el Sheikh) UN secretary-General stated: “But let’s be clear. Our planet is still in the emergency room. We need to drastically reduce emissions now—and this is an issue this COP did not address. A fund for loss and damage is essential—but it’s not an answer if the climate crisis washes a small island state off the map—or turns an entire African country to desert. The world still needs a giant leap on climate ambition. The red line we must not cross is the line that takes our planet over the 1.5° temperature limit. To have any hope of keeping to 1.5, we need to massively invest in renewables and end our addiction to fossil fuels.

See e.g. the unprecedented hike of the gas price following the start of the Russian invasion of Ukraine.

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