Stochastic analysis of a two-stage production system with two parallel machines in the first stage and subject to inspection

The paper deals with the stochastic analysis of a two-stage production system with two production machines in parallel in the first stage and subject to inspection. The time taken to process a job on a machine and the time taken for inspection of the finished job are random governed by probability distributions which are quite general. Semi-finished jobs processed by the machines in the first-stage are transferred to the machine in the second stage for further processing. Machine in the second stage processes two type of products based on the semi-finished products transferred from the machines in the first stage. Inspection is carried out of the items processed by machine in the second stage and only good items are accepted, while others are scrapped. The analysis is carried out by employing the state-space method and the regeneration-point technique. Several measures of system performance, transient in nature, are evaluated. A cost analysis is also carried out by using some of the measures of system performance obtained.