Probability of first passage analysis of a two-stage transfer-line production system with rework

This paper provides an integrated framework to consider manufacturing, inspection and rework activities simultaneously in two-stage transfer-line production systems. The purpose of this paper is to analyse some of the transient state characteristics, pertaining to the probability of first passage of the system to some specific states of interest, of a two-stage transfer-line production system subject to an initial buffer of infinite capacity and rework. The first stage of the production system is never starved and the second stage is never blocked. A stochastic model is developed to analyse the system and analytical expressions for some of the system characteristics have been obtained using the state space method and regeneration point technique under the assumption that the distributions of the various random variables involved in the analysis are arbitrary. Numerical illustrations have also been presented for some particular cases.