Quality-related measures of unreliable machines with preventive maintenance

In this paper, we study a production system in which some of the products made are defective. The distribution of such defective products is assumed to depend on the total number of products made since the last maintenance. Quality-related measures of interest are the average out-going quality (AOQ) and the variance of the out-going quality (VOQ) which we define as the mean and the variance of the long-run fraction of non-defective products respectively. The system is periodically maintained. Two maintenance policies are considered: one is to perform maintenance after a fixed number of products have been made; and the other is to perform maintenance when the machine becomes idle or a fixed number of products have been made. The system is modelled as an M/G/1 queue with vacations. The queue length of orders for products, the AOQ and VOQ are analysed for these two policies. Numerical examples are provided to compare the efficiency of the two models.