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Research Article

Evaluating the Project Completion Time When Non-Identical Beta Distributions Govern the Activity Networks

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References

  • Abdelkader, Y. H. (2003). Erlang distributed activity times in stochastic activity networks. Kybernetika, 39(3), 347–358.
  • Abdelkader, Y. H. (2004a). Computing the moments of order statistic from nonidentically distributed Erlang variables. Statistical Papers, 45(4), 563–570. https://doi.org/10.1007/BF02760568
  • Abdelkader, Y. H. (2004b). Evaluating project completion times when activity times are weibull distributed. European Journal of Operational Research, 157(3), 704–715. https://doi.org/10.1016/S0377-2217(03)00269-8
  • Abdelkader, Y. H. (2006). Stochastic activity networks with truncated exponential activity times. Journal of Applied Mathematics and Computing, 20(1–2), 119–132. https://doi.org/10.1007/BF02831927
  • Abdelkader, Y. H., & Al-Ohali, M. (2013). Estimating the completion time of stochastic activity networks with uniform distributed activity times. Archives Des Sciences Journal, 66(4), 115–134.
  • Abdelkader, Y. H., Barakat, H. M., & Taher, T. S. (2020). Evaluating the project completion time when activity networks follow beta distribution. Asian-European Journal of Mathematics. https://doi.org/10.1142/S1793557121501102
  • Arnold, B. C., Balakrishnan, H. N., & Nagraja, H. N. (1992). A first course in order statistics. Wiley.
  • Balakrishnan, N. (1994a). Order statistics from non-identically exponential random variables and some applications. Computational Statistics & Data Analysis, 18(2), 203–238. https://doi.org/10.1016/0167-9473(94)90172-4
  • Balakrishnan, N. (1994b). Order statistics from non-identically right-truncated exponential random variables and some applications. Communications in Statistics - Theory and Methods, 23(12), 3373–3393. https://doi.org/10.1080/03610929408831453
  • Balakrishnan, N., & Balasubramanian, K. (1995). Order statistics from non-identically power function random variables. Communications in Statistics - Theory and Methods, 24(6), 1443–1454. https://doi.org/10.1080/03610929508831564
  • Barakat, H. M., & Abdelkader, Y. H. (2000). Computing the moments of order statistic from nonidentically distributed Weibull variables. Journal of Computational and Applied Mathematics, 117(1), 85–90. https://doi.org/10.1016/S0377-0427(99)00343-X
  • Barakat, H. M., & Abdelkader, Y. H. (2004). Computing the moments of order statistic from nonidentically random variables. Statistical Methods and Applications, 13, 15–26. https://doi.org/10.1007/s10260-003-0068-9
  • Barakat, H. M., & El-Shandidy, M. A. (2015). On the computing of the moments of bivariate order statistics. Journal of Statistical Planning and Inference, 134(1), 15–25. https://doi.org/10.1016/j.jspi.2004.02.011
  • Barakat, H. M., Nigm, E. M., & Khaled, O. M. (2019). Statistical techniques for modelling extreme value data and related applications (1st ed.). Cambridge Scholars Publishing.
  • Childs, A., & Balakrishnan, N. (1998). Generalized recurrence relations for the moments of order statistics from non-identically Pareto and truncated Pareto random variables with applications to robustness. In N. Balakrishnan & C. R. Rao (Eds.), Handbook of statistics (Vol. 16, pp 403–438). Elsevier.
  • Elmaghraby, S. E. (2000). On criticality and sensitivity in activity networks. European Journal of Operational Research, 127(2), 220–238. https://doi.org/10.1016/S0377-2217(99)00483-X
  • Giznburg, D. G. (1989). A new approach to activity time distribution in PERT. Journal of the Operational Research Society, 40(4), 389–393. https://doi.org/10.1057/jors.1989.57
  • Hahn, E. D., & López Martín, M. M. (2015). Robust project management with the tilted beta distribution. SORT, 39(2), 253–272.
  • Hartley, H. O., & Wortham, A. W. (1966). A statistical theory for PERT critical path analysis. Management Science, 12(10), B-469–481. https://doi.org/10.1287/mnsc.12.10.B469
  • Hernández-Bastida, A., & Fernández-Sánchez, M. P. (2019). How adding new information modifies the estimation of the mean and the variance in PERT: A maximum entropy distribution approach. Annals of Operations Research, 274(1–2), 291–308. https://doi.org/10.1007/s10479-018-2857-4
  • Kambarowski, J. (1985b). An upper bound on the expected completion time of PERT networks. European Journal of Operational Research, 21(2), 206–212. https://doi.org/10.1016/0377-2217(85)90032-3
  • Kamburowski, J. (1985a). Normally distributed activity durations in PERT networks. The Journal of the Operational Research Society, 36(11), 1051–1057. https://doi.org/10.2307/2582437
  • Magott, J., & Skudlarski, K. (1993). Estimating the mean completion time of PERT networks with exponentially distributed duration of activities. European Journal of Operational Research, 71(1), 70–79. https://doi.org/10.1016/0377-2217(93)90261-K
  • Malcolm, D. G., Rose Boom, J. H., Clark, C. E., & Fazar, W. (1959). Applications of a technique for research and development program evaluation. Operations Research, 7(5), 646–669. https://doi.org/10.1287/opre.7.5.646
  • Pritsker, A. B., & Kiviat, P. J. (1969). Simulation with GASP II. Prentice-Hall.
  • Robillard, P., & Trahan, M. (1977). The completion time of PERT networks. Operations Research, 25(1), 15–29. https://doi.org/10.1287/opre.25.1.15
  • Sculli, D., & Wong, K. L. (1985). The maximum and sum of two Beta variables and the analysis of PERT networks. Omega, 13(3), 233–240. https://doi.org/10.1016/0305-0483(85)90061-1
  • Skudlarski, K. (1991). Generalized stochastic Petri nets analyzer (in Polish). Informatyka (Computer Science), 5, 3–6.
  • Udoumoh, E. F., & Ebong, D. W. (2017). A review of activity time distributions in risk analysis. American Journal of Operations Research, 07(06), 356–371. https://doi.org/10.4236/ajor.2017.76027

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