Abstract
This paper develops a model to determine the optimal reliability and production rate that achieves the biggest total integrated profit for an imperfect production process under allowable shortage. In this system, production facility may shift ‘in-control’ state to an ‘out-control state’ at any random time. The basic assumption of the classical EPL model is that 100% of product is of perfect quality. Here we consider two type of production process in a cycle time. One is ‘in-control’ state at the starting of the production which provides conforming quality items and second one is ‘out-control’ state after certain time due to higher production rate and production run time. The proposed model is formulated assuming that a certain percent of total product which described by a function is defective. The imperfect quality items are reworked at a cost to restore its quality to the original one. The total cost function is illustrated by numerical examples and also its sensitivity analysis is carried out.