Bayesian inspection model for the production process subject to a random failure

Consider a sequence of items produced on a high-speed mass production line which is subject to a random failure. When an item in the sequence is inspected it is possible to obtain directional information about the exact timing of a process failure – before or after producing the inspected item. Using this directional information this paper proposes Bayesian inspection procedures that deal with three related problems: (i) how often to inspect items on the production line; (ii) how to conduct the search for more defective items; and (iii) when to stop the search process and salvage the remaining items. Based on various cost factors, the problem of optimal inspection interval, optimal search process and an optimal stopping rule is formulated as a profit-maximization model via a dynamic programming approach. For the production process with an unknown failure rate, Bayesian methods of estimating the process failure rate are proposed. The proposed Bayesian inspection procedures can be applied to a wide variety of high-speed mass production processes such as printing labels, filling containers or mixing ingredients.