The impact of a free-repair warranty policy on EMQ model for imperfect production systems

In this study, the economic production quantity problem in the presence of imperfect processes for products sold under a free-repair warranty policy is considered. In the literature, that a production facility may deteriorate with time is assumed, and the time to shift from an in-control state to an out-of-control state is assumed to be exponentially distributed, i.e., the process failure rate is a constant. However, in many practical situations, the process possesses an increasing failure rate due to cumulative wear in producing items. This study is extended to consider a process subjected to random deterioration from an in-control state to an out-of-control state with a general shift distribution. A mathematical model representing the expected total cost per item is developed to determine the optimal production policy. The objective here is to obtain the optimal production run-length (lot size) so that the expected total cost per item is minimized. Different conditions for optimality, properties, and bounds on the optimal production run-length are provided. A numerical example is used to see the adequacy of using the exponential distribution when the actual distribution is Weibull with an increasing failure rate.