Exact and Approximate Solutions to Two-Stage Transfer Lines with General Uptime and Downtime Distributions

Abstract

We consider a transfer line with two unreliable stages and an intermediate buffer storage of a finite capacity. It is assumed that the distribution of uptimes and downtimes of each stage are of phase type. It is also assumed that a part may be scrapped with a certain probability when the stage processing it breaks down. Using the phase structure of the underlying distributions, the system is modelled as a Markov chain. This model is used to study the behavior of the system. It is also used to find out whether a two moment approximation to the uptime and downtime distributions is adequate. A simple approximation to the production rate that involves only the first two moments of the uptime and downtime distributions is also developed. It is shown that this approximation is quite reasonable.