On the quantitative definition of risk
Abstract
A quantitative definition of risk is suggested in terms of the idea of a “set of triplets”. The definition is extended to include uncertainty and completeness, and the use of Bayes' theorem is described in this connection. The definition is used to discuss the notions of “relative risk”, “relativity of risk”, and “acceptability of risk”.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Cites
Social Benefit versus Technological Risk
Starr, C. (1969) · Science · doi:10.1126/science.165.3899.1232 · Cited by 1,752 · see citing works
Social Benefit Versus Technological Risk: What is Our Society Willing to Pay for Safety?
Starr, C. (2018) · Renewable Energy · doi:10.4324/9781315793245-125 · Cited by 1,006 · see citing works
Rowe, W. D. (1977) · Medical Entomology and Zoology · Cited by 446 · see citing works
Risk Assessment Review Group Report to the U. S. Nuclear Regulatory Commission
Lewis, H. W., Budnitz, R. J., Rowe, W. D., et al. (1979) · IEEE Transactions on Nuclear Science · doi:10.1109/tns.1979.4330198 · Cited by 114 · see citing works
Okrent, D. (1980) · Science · doi:10.1126/science.208.4442.372 · Cited by 96 · see citing works
Nußbaum, M. (1975) · Biometrische Zeitschrift · doi:10.1002/bimj.19750170211 · Cited by 73 · see citing works
Data specialization for plant specific risk studies
Apostolakis, G., Kaplan, S., Garrick, B. J., et al. (1980) · Nuclear Engineering and Design · doi:10.1016/0029-5493(80)90133-8 · Cited by 61 · see citing works
Self-citationIntroduction to Probability and Statistics from a Bayesian Viewpoint.
Barton, D. E., & Lindley, D. V. (1966) · Biometrika · doi:10.2307/2334092 · Cited by 47 · see citing works
On the use of Bayes' Theorem in assessing the frequency of anticipated transients
Kaplan, S., Garrick, B. J., & Bieniarz, P. (1981) · Nuclear Engineering and Design · doi:10.1016/0029-5493(81)90116-3 · Cited by 17 · see citing works
Self-citationOn the Use of a Bayesian Reasoning in Safety and Reliability Decisions—Three Examples
Kaplan, S., & Garrick, B. J. (1979) · Nuclear Technology · doi:10.13182/nt79-a32258 · Cited by 15 · see citing works
Self-citationAssessment of the frequency of failure to scram in light-water reactors
Apostolakis, G., Kaplan, S., Garrick, B. J., et al. (1979) · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · Cited by 8 · see citing works
Self-citationDefense-in-depth approach to safety in light of TMI-2
Breen, R. J. (1980) · Transactions of the American Nuclear Society · Cited by 5 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
A review of definitions and measures of system resilience
Hosseini, S., Barker, K., & Ramirez-Marquez, J. E. (2016) · Reliability Engineering & System Safety · doi:10.1016/j.ress.2015.08.006 · Cited by 1,892 · see citing works
Risk assessment and risk management: Review of recent advances on their foundation
Aven, T. (2016) · European Journal of Operational Research · doi:10.1016/j.ejor.2015.12.023 · Cited by 1,713 · see citing works
“Some areas seem to have found the answer a long time ago, for instance the nuclear industry, which has been founded on the Kaplan and Garrick (1981) definition (the triplet scenarios, consequences and probabilities) for more than three decades; others acknowledge the need for further developments,…”
BackgroundA review of cyber security risk assessment methods for SCADA systems
Cherdantseva, Y., Burnap, P., Blyth, A., Eden, P., Jones, K., Soulsby, H., & Stoddart, K. (2016) · Computers & Security · doi:10.1016/j.cose.2015.09.009 · Cited by 606 · see citing works
“Risk assessment answers the following three questions (Kaplan and Garrick, 1981): • What can go wrong?”
BackgroundInfluentialArtificial intelligence, systemic risks, and sustainability
Galaz, V., Centeno, M. A., Callahan, P. W., Causevic, A., Patterson, T., Brass, I., Baum, S., Farber, D., Fischer, J., Garcia, D., et al. (2021) · Technology in Society · doi:10.1016/j.techsoc.2021.101741 · Cited by 497 · see citing works
On the definition of cyber-physical resilience in power systems
Arghandeh, R., von Meier, A., Mehrmanesh, L., & Mili, L. (2016) · Renewable and Sustainable Energy Reviews · doi:10.1016/j.rser.2015.12.193 · Cited by 404 · see citing works
Secure Control Systems: A Quantitative Risk Management Approach
(2015) · IEEE Control Systems · doi:10.1109/mcs.2014.2364709 · Cited by 316 · see citing works
Cyber security risk assessment for SCADA and DCS networks
Ralston, P. A. S., Graham, J. H., & Hieb, J. L. (2007) · ISA Transactions · doi:10.1016/j.isatra.2007.04.003 · Cited by 267 · see citing works
Wangen, G., Hallstensen, C., & Snekkenes, E. (2018) · International Journal of Information Security · doi:10.1007/s10207-017-0382-0 · Cited by 109 · see citing works
Williams, C. J., Pierson, F. B., Robichaud, P. R., & Boll, J. (2014) · International Journal of Wildland Fire · doi:10.1071/wf12161 · Cited by 66 · see citing works
Fragmenting global business processes: A protection for proprietary information
Gooris, J., & Peeters, C. (2016) · Journal of International Business Studies · doi:10.1057/jibs.2015.44 · Cited by 66 · see citing works
Mokhtari, A., & Frey, H. C. (2005) · Risk Analysis · doi:10.1111/j.1539-6924.2005.00679.x · Cited by 66 · see citing works
“Leaving it to chance”—Passive risk taking in everyday life
Keinan, R., & Bereby-Meyer, Y. (2012) · Judgment and Decision Making · doi:10.1017/s1930297500003259 · Cited by 55 · see citing works
Cost-benefit analysis of airport security: Are airports too safe?
Stewart, M. G., & Mueller, J. (2014) · Journal of Air Transport Management · doi:10.1016/j.jairtraman.2013.11.003 · Cited by 55 · see citing works
TollsOnly Please—Homomorphic Encryption for Toll Transponder Privacy in Internet of Vehicles
Karim, H., & Rawat, D. B. (2022) · IEEE Internet of Things Journal · doi:10.1109/jiot.2021.3056240 · Cited by 43 · see citing works
Cybersecurity Threats, Vulnerability and Analysis in Safety Critical Industrial Control System (ICS)
Lou, X., & Tellabi, A. (2020) · Studies in Systems, Decision and Control · doi:10.1007/978-3-030-31328-9_4 · Cited by 13 · see citing works
- Authors
- Kaplan, S., & Garrick, B. J.
- Affiliations
- Kaplan (United States) (US)
- Venue
- Risk Analysis
- Publisher
- Wiley
- Published
- 1981-03
- Volume
- 1
- Issue
- 1
- Pages
- 11-27
- ISSN
- 0272-4332 (ISSN-L)
- 1539-6924
- OpenAlex
- W2147704565
- Cited by
- 3,103
- References
- 12
- Citations by year
- 2026: 127 · 2025: 117 · 2024: 125 · 2023: 121 · 2022: 122 · 2021: 163 · 2020: 160 · 2019: 136 · 2018: 149 · 2017: 163 · 2016: 135 · 2015: 173 · 2014: 137 · 2013: 125 · 2012: 154
- FWCI
- 23.98
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Risk Analysis (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Risk and Safety Analysis
- Social Sciences › Sociology and Political Science › Risk Perception and Management
- Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
- Keywords
- uncertainty, completeness, Bayes' theorem, relative risk
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review