Reliability-Base Performance Measure for Stochastic Networks

Abstract

An important performance measure for stochastic manufacturing networks is the system reliability, defined as the probability that the production output meets or exceeds a specified demand. This paper reviews and highlights the drawbacks of the previous works, including twenty one archival publications and the most recent published analytical Song rule. The major error in the twenty one archival publications error assumes that entities in the network are discrete and indivisible, while the analysis is based upon continuous flow through the network. That is, they assume that the number of defective items is a real number, instead of a random variable following a binomial distribution. We claim that the analytical approach in Song rule is valid for non-rework case, but is incorrect for general system reliability with reworking when the rework and non-rework path share the same capacity. This note corrects the mistakes in Song rule when the rework and non-rework path share the same capacity. The proposed analytical approach can be easily generalized to general system reliability with multiple reworks. The Song rule and the proposed corrected version of Song rule in this note are computationally inefficient and are only recommended as a validator instead of a problem solver. For big-scale system reliability, the simulation approach are recommended as the problem solver.