First passage analysis of a two-stage production system with rework

This paper incorporates the concept of rework in the probabilistic analysis of two-stage transfer-line production systems and derives explicit analytical expressions for some of the system characteristics using the state-space method and regeneration point technique. All the random variables involved in the analysis are assumed to be arbitrarily distributed except the arrival time which is assumed to follow an exponential distribution. Numerical illustrations have also been presented for some particular cases.