Transient behavior of serial production lines with Bernoulli machines

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 ...