Indirect parameter elicitation procedures for some distributions with bounded support – with applications in Program Evaluation and Review Technique (PERT)

The introduction of the Program Evaluation and Review Technique (PERT) dates back to the 1960s and has found wide application since then in the planning of construction projects. Difficulties with the interpretation of the parameters of the beta distribution let Malcolm et al. (Malcolm, D.G., et al., 1959. Application of a technique for research and development program evaluation. Operations Research, 7, 646–649) to elicit them indirectly via the classical expressions for the PERT mean and variance for an activity's completion time. These expressions are specified, given a lower and upper bound estimates a and b and a most likely estimate θ for the activity's duration. Despite a by now 50 -year controversy exemplified by current articles still questioning the PERT mean and variance elicitation approach, their use is still prevalent in current operations research and industrial engineering college text books. In this article an overview is presented of some alternative approaches that have been suggested, ...

[1]  S. Kotz,et al.  A link between two-sided power and asymmetric Laplace distributions: with applications to mean and variance approximations , 2005 .

[2]  J. René van Dorp,et al.  An Elicitation Procedure for the Generalized Trapezoidal Distribution with a Uniform Central Stage , 2007, Decis. Anal..

[3]  D. Vose.  Risk Analysis: A Quantitative Guide , 2000 .

[4]  Eugene David Hahn,et al.  Mixture densities for project management activity times: A robust approach to PERT , 2008, Eur. J. Oper. Res..

[5]  Jerzy Kamburowski,et al.  New validations of PERT times , 1997 .

[6]  PleguezueloRafael HerrerıAs,et al.  A note on the reasonableness of PERT hypotheses , 2003 .

[7]  Frederick S. Hillier,et al.  Introduction to Management Science; A Modeling and Case Studies Approach with Spreadsheets , 1999 .

[8]  Samuel Kotz,et al.  A novel method for fitting unimodal continuous distributions on a bounded domain utilizing expert judgment estimates , 2006 .

[9]  Rafael Herrerías Pleguezuelo,et al.  Revisiting the PERT mean and variance , 2011, Eur. J. Oper. Res..

[10]  Louis Y. Pouliquen,et al.  Risk analysis in project appraisal , 1970 .

[11]  J. René van Dorp,et al.  Statistical dependence through common risk factors: With applications in uncertainty analysis , 2005, European Journal of Operational Research.

[12]  D. Keefer,et al.  Better estimation of PERT activity time parameters , 1993 .

[13]  D. Malcolm,et al.  Application of a Technique for Research and Development Program Evaluation , 1959 .

[14]  D Golenko-Ginzburg,et al.  PERT assumptions revisited , 1989 .

[15]  Samuel Kotz,et al.  A novel extension of the triangular distribution and its parameter estimation , 2002 .

[16]  Robert T. Clemen,et al.  The use of probability elicitation in the high-level nuclear waste regulation program , 1995 .

[17]  Samuel Kotz,et al.  Beyond Beta: Other Continuous Families Of Distributions With Bounded Support And Applications , 2004 .

[18]  Seyyed M. T. Fatemi Ghomi,et al.  Path critical index and activity critical index in PERT networks , 2002, Eur. J. Oper. Res..

[19]  Daniel Gómez,et al.  A rule for slack allocation proportional to the duration in a PERT network , 2008, Eur. J. Oper. Res..

[20]  M W Sasieni,et al.  A note on PERT times , 1986 .

[21]  K. MacCrimmon,et al.  An Analytical Study of the PERT Assumptions , 1964 .

[22]  T. Kotiah,et al.  Another Look at the PERT Assumptions , 1973 .

[23]  William H. Press,et al.  Numerical Recipes in Pascal , 2007 .

[24]  A. O'Hagan,et al.  Statistical Methods for Eliciting Probability Distributions , 2005 .

[25]  T. K. Littlefield,et al.  Reply-An Answer to Sasieni's Question on PERT Times , 1987 .

[26]  Eric R. Zieyel.  Operations research : applications and algorithms , 1988 .

[27]  José García Pérez,et al.  A note on the reasonableness of PERT hypotheses , 2003, Oper. Res. Lett..

[28]  Robert Taggart.  Ship design and construction , 1980 .

[29]  Anand Paul,et al.  On path correlation and PERT bias , 2008, Eur. J. Oper. Res..

[30]  J. E. Selvidge,et al.  ASSESSING THE EXTREMES OF PROBABILITY DISTRIBUTIONS BY THE FRACTILE METHOD , 1980 .

[31]  J. M. Herrerías-Velasco,et al.  The generalized two-sided power distribution , 2009 .

[32]  Frank E. Grubbs.  Letter to the Editor---Attempts to Validate Certain PERT Statistics or “Picking on PERT” , 1962 .