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A Statistical Theory for PERT Critical Path Analysis

Author

Listed:
  • H. O. Hartley

    (Institute of Statistics, Texas A & M University)

  • A. W. Wortham

    (Institute of Statistics, Texas A & M University)

Abstract

PERT and Critical Path techniques are enjoying exceptionally broad application in industrial and military activities. These techniques and their application have without doubt contributed significantly to better planning, control, and general organization of many programs. Although some currently used PERT computations take account of the variation in the completion times of individual operations, the methods used are approximate and are known to lead to (a) optimistic project completion times and (b) misidentifications of "critical paths." In this paper the effect of these approximations is assessed and an unbiassed statistical distribution theory for PERT developed. Both analytic theory and numerical analysis are used to achieve this but in certain situations approximate evaluations by Monte Carlo have to be made. Moreover, a new classification of PERT networks is presented along with two methods of analysis which do not have the deficiencies noted above. The classification system delineates clearly between "uncrosaed," "crossed," and "mixed networks."

Suggested Citation

  • H. O. Hartley & A. W. Wortham, 1966. "A Statistical Theory for PERT Critical Path Analysis," Management Science, INFORMS, vol. 12(10), pages 469-481, June.
    • Handle: RePEc:inm:ormnsc:v:12:y:1966:i:10:p:b469-b481
    DOI: 10.1287/mnsc.12.10.B469
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    Cited by:

    1. Stephen P. Boyd & Seung-Jean Kim & Dinesh D. Patil & Mark A. Horowitz, 2005. "Digital Circuit Optimization via Geometric Programming," Operations Research, INFORMS, vol. 53(6), pages 899-932, December.
    2. Yousry Abdelkader, 2010. "Adjustment of the moments of the project completion times when activity times are exponentially distributed," Annals of Operations Research, Springer, vol. 181(1), pages 503-514, December.
    3. Fatemi Ghomi, S. M. T. & Hashemin, S. S., 1999. "A new analytical algorithm and generation of Gaussian quadrature formula for stochastic network," European Journal of Operational Research, Elsevier, vol. 114(3), pages 610-625, May.
    4. Lee, Heejung & Suh, Hyo-Won, 2008. "Estimating the duration of stochastic workflow for product development process," International Journal of Production Economics, Elsevier, vol. 111(1), pages 105-117, January.
    5. Sigal, C.E. & Pritsker, A.A.B. & Solberg, J.J., 1979. "The use of cutsets in Monte Carlo analysis of stochastic networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(4), pages 376-384.
    6. Tetsuo Iida, 2000. "Computing bounds on project duration distributions for stochastic PERT networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(7), pages 559-580, October.
    7. Fatemi Ghomi, S. M. T. & Rabbani, M., 2003. "A new structural mechanism for reducibility of stochastic PERT networks," European Journal of Operational Research, Elsevier, vol. 145(2), pages 394-402, March.
    8. Catalina García & José Pérez & Salvador Rambaud, 2010. "Proposal of a new distribution in PERT methodology," Annals of Operations Research, Springer, vol. 181(1), pages 515-538, December.
    9. Schmidt, Craig W. & Grossmann, Ignacio E., 2000. "The exact overall time distribution of a project with uncertain task durations," European Journal of Operational Research, Elsevier, vol. 126(3), pages 614-636, November.

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