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Estimating the Mean and Variance of Subjective Distributions in PERT and Decision Analysis

Author

Listed:
  • C. Perry

    (The University of New England, New South Wales)

  • I. D. Greig

    (The University of New England, New South Wales)

Abstract

The original PERT formulae [5] employ the mode and endpoints to estimate the mean and standard deviation of subjective probability distributions. Though widely-used, they have met with criticism for their inaccuracy, and for their being limited to the beta distribution when there is no a priori reason why the distribution should be beta ([4], [6]). This note presents alternative, accurate and relatively distribution-free formulae for estimating the means and standard deviations of subjective probability distributions.

Suggested Citation

  • C. Perry & I. D. Greig, 1975. "Estimating the Mean and Variance of Subjective Distributions in PERT and Decision Analysis," Management Science, INFORMS, vol. 21(12), pages 1477-1480, August.
    • Handle: RePEc:inm:ormnsc:v:21:y:1975:i:12:p:1477-1480
    DOI: 10.1287/mnsc.21.12.1477
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    Cited by:

    1. Abazari, Seyed Reza & Aghsami, Amir & Rabbani, Masoud, 2021. "Prepositioning and distributing relief items in humanitarian logistics with uncertain parameters," Socio-Economic Planning Sciences, Elsevier, vol. 74(C).
    2. Azaron, Amir & Katagiri, Hideki & Sakawa, Masatoshi & Kato, Kosuke & Memariani, Azizollah, 2006. "A multi-objective resource allocation problem in PERT networks," European Journal of Operational Research, Elsevier, vol. 172(3), pages 838-854, August.
    3. Pérez, José García & Martín, María del Mar López & García, Catalina García & Sánchez Granero, Miguel Ángel, 2016. "Project management under uncertainty beyond beta: The generalized bicubic distribution," Operations Research Perspectives, Elsevier, vol. 3(C), pages 67-76.
    4. Amir Azaron & Hideki Katagiri & Masatoshi Sakawa, 2007. "Time-cost trade-off via optimal control theory in Markov PERT networks," Annals of Operations Research, Springer, vol. 150(1), pages 47-64, March.
    5. Kotz, Samuel & van Dorp, J. René, 2005. "A link between two-sided power and asymmetric Laplace distributions: with applications to mean and variance approximations," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 383-394, March.
    6. Joel Goh & Nicholas G. Hall, 2013. "Total Cost Control in Project Management via Satisficing," Management Science, INFORMS, vol. 59(6), pages 1354-1372, June.
    7. Lau, Hon-Shiang & Lau, Amy Hing-Ling & Kottas, John F., 2000. "A comparison of procedures for estimating the parent probability distribution from a given set of fractiles," European Journal of Operational Research, Elsevier, vol. 120(3), pages 657-670, February.
    8. Dillon, John L. & Perry, Chad, 1977. "Multiattribute Utility Theory, Multiple Objectives And Uncertainty In Ex Ante Project Evaluation," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 45(01-2), pages 1-25, March.
    9. Hon-Shiang Lau & Amy Hing-Ling Lau & Chrwan-Jyh Ho, 1998. "Improved Moment-Estimation Formulas Using More Than Three Subjective Fractiles," Management Science, INFORMS, vol. 44(3), pages 346-351, March.
    10. C. Y. Yiu & C. S. Tam, 2006. "Rational under-pricing in bidding strategy: a real options model," Construction Management and Economics, Taylor & Francis Journals, vol. 24(5), pages 475-484.
    11. A Jessop, 2011. "Using imprecise estimates for weights," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(6), pages 1048-1055, June.
    12. Hahn, Eugene David, 2008. "Mixture densities for project management activity times: A robust approach to PERT," European Journal of Operational Research, Elsevier, vol. 188(2), pages 450-459, July.
    13. Saurabh Bansal & Genaro J. Gutierrez & John R. Keiser, 2017. "Using Experts’ Noisy Quantile Judgments to Quantify Risks: Theory and Application to Agribusiness," Operations Research, INFORMS, vol. 65(5), pages 1115-1130, October.
    14. Wenhui Zhao & Nicholas G. Hall & Zhixin Liu, 2020. "Project Evaluation and Selection with Task Failures," Production and Operations Management, Production and Operations Management Society, vol. 29(2), pages 428-446, February.
    15. Azaron, Amir & Fatemi Ghomi, S.M.T., 2008. "Lower bound for the mean project completion time in dynamic PERT networks," European Journal of Operational Research, Elsevier, vol. 186(1), pages 120-127, April.
    16. Ali E. Abbas & David V. Budescu & Hsiu-Ting Yu & Ryan Haggerty, 2008. "A Comparison of Two Probability Encoding Methods: Fixed Probability vs. Fixed Variable Values," Decision Analysis, INFORMS, vol. 5(4), pages 190-202, December.
    17. M Revie & T Bedford & L Walls, 2010. "Evaluation of elicitation methods to quantify Bayes linear models," Journal of Risk and Reliability, , vol. 224(4), pages 322-332, December.
    18. Azaron, Amir & Fynes, Brian & Modarres, Mohammad, 2011. "Due date assignment in repetitive projects," International Journal of Production Economics, Elsevier, vol. 129(1), pages 79-85, January.
    19. Lau, Hon-Shiang & Somarajan, C., 1995. "A proposal on improved procedures for estimating task-time distributions in PERT," European Journal of Operational Research, Elsevier, vol. 85(1), pages 39-52, August.
    20. Watson, W.D. & Anderson, Jock R., 1977. "SPATIAL v. TIME-SERIES DATA FOR ASSESSING RESPONSE RISK," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 45(03), pages 1-5, September.

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