Graduate Thesis Or Dissertation

 

A practical way to include merge bias in calculating total project duration of a PERT network Public Deposited

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  • Uncertainty of the magnitude of merge bias in PERT networks has long been of concern to the users of this technique. A simple rule to determine the magnitude has since posed a problem. The purpose of this thesis was to develop empirical rules to correct the time estimates of cumulative durations as found by the conventional PERT calculation procedure. Merge bias is insignificant when a large number of activities in a network are left skewed. The bias is also considered insignificant when the near critical path length is less than 70 percent of the critical path length. However, merge bias is a definite factor in other networks. The bias is significant and cannot be ignored in a network whose nodes on the critical path have a large number of near critical paths with lengths close to the critical path length. Monte Carlo simulations of series and parallel networks were used to compare experienced durations with PERT calculated times to realize the same node of the networks. Since the average simulated time is accurate, the difference was the bias in the PERT calculated time. The difference is made up of two distinct parts, activity bias and merge bias. Simulation of series networks was used to study activity bias. The activity bias in the PERT time estimates was then eliminated to determine the magnitude of merge bias. Simulation of the networks required a computer program to perform the large number of iterations of the networks whose activities three time estimates are specified and follow a beta distribution. A FORTRAN IV based PERT simulation model was developed. The model was tested for its accuracy and capability of generating the beta distributions of the activities. The results of the model were compared with the ordinates of a beta distribution generated by a computer program. The magnitude of bias for typical small parallel networks was used to form the merge bias correction table. The table gives the magnitude of bias due to two activities merging at a node. One of these activities is the critical activity. The table is entered corresponding to the mean and standard deviation values of the critical and near critical activities of the network. It is based on the symmetrical distributions of the two activities. The activity on the critical path is always assumed to have symmetrical distribution. A rule was developed to normalize the near critical path activity when it has an unsymmetrical distribution. In such cases, the mode of the activity is treated as the mean of an equivalent symmetrical distributed activity. To determine the magnitude of bias for merge nodes on the critical path of a network, the process of segregating the network at the merge nodes into small networks is described. The decomposition of limited networks into typical small networks is shown. A rule for the reduction of activities in series to an equivalent single activity is given. When more than two activities merge at a node, the rule of addition of the bias due to each path is developed and substantiated.
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