A Statistical Theory for PERT Critical Path Analysis

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."