The Two-Moment Approximations for Manufacturing Performance With Non-Renewal Processes

The complexity of manufacturing systems characterized by multi-product processing, preventive and corrective maintenance, and setup, presents a notable challenge for predicting the system performance. These characteristics involve significant interference in product flows while generating non-renewable flows with very high variability.

Decomposition of queuing networks is a common method of approximation, by which the first two moments of the arrival processes are approximated and then used to yield approximations of the system performance. Yet, decomposition methods cannot cope with the complexity of non-renewable flow with high variability. Thus, the accuracy of the two-moment approximations, as part of decomposition method, decreases significantly. Variability function \is a method for coping with this challenge, by approximating equivalent variabilities of non-renewal arrival processes depending on one of the characteristics of the downstream queue, instead of simple variability parameters.

We present the traffic intensity-dependent variability function, which considers high external variability, as well as the waiting time-dependent variability function, which considers high variability generated within the network. The first function is calculated analytically while the second one, suggested here, relies on simulation as well, due to the complexity of the problem. Applying queuing theory for the departure process from single queue to determine the waiting time-dependent variability function reduces significantly the simulation effort. Currently, the waiting time-dependent variability function has been developed for systems with downtimes. It is described by a dual-class system where the first class represents the customer class and the second class represents downtime events, but it can be extended to general multi-class networks as well. Numerical experiments show that both traffic intensity- and waiting time-dependent variability functions are required for predicting the performance of manufacturing systems. When using both functions, the results demonstrate a relative error four times smaller than the best relevant existing procedures in literature.