An EMQ model with inspections and random machine failures

In the classical Economic Manufacturing Quantity (EMQ) model, it is assumed that all items produced are of perfect quality and the production facility never breaks down. However, in real production, the product quality is usually a function of the state of the production process which may deteriorate over time and the production facility may fail randomly. In this paper, we study the effect of machine failures on the optimal lot size and on the optimal number of inspections in a production cycle, The formula for the long-run expected average cost per unit time is obtained for a generally distributed time to failure. An optimal production/inspection policy is found by minimising the expected average cost.