Transient behavior of serial production lines with Bernoulli machines

Abstract

The steady-state performance of production systems with unreliable machines has been analyzed extensively during the last 50 years. In contrast, the transient behavior of these systems remains practically unexplored. Transient characteristics, however, may have significant manufacturing implications. Indeed, if, for example, transients are sluggish and the steady state is reached only after a relatively long settling time, the production system may lose some of its throughput, thus leading to a lower efficiency. This paper is devoted to analytical and numerical investigation of the transient behavior of serial production lines with machines having the Bernoulli reliability model. The transients of the states (i.e., the probabilities of buffer occupancy) are described by the Second Largest Eigenvalue (SLE) of the transition matrix of the associated Markov chain. The transients of the outputs (i.e., production rate, PR, and work-in-process, WIP) are characterized by both the SLE and Pre-Exponential Factors (PEF). We study SLE and PEF as functions of machine efficiency, buffer capacity and the number of machines in the system. In addition, we analyze the settling times of PR and WIP and show that the former is often much shorter than the latter. Finally, we investigate production losses due to transients and show that they may be significant in serial lines with relatively large buffers and many machines. To avoid these losses, it is suggested that all buffers initially be half full. For two- and three-machine lines these analyzes are carried out analytically; longer lines are investigated by simulations.