Joint inspection and product quality optimization for a system with delayed failure

Abstract

This paper proposes the integrated production, inspection, and quality planning of a machine with a two-stage delay time failure process (DTM). In a DTM, a failure proceeds with a potential defect. We assume a defective machine as one of the assignable causes of non-conforming products. The delay time is used as an opportunity to perform periodic quality control inspections of the products and detect higher than the acceptable level of non-conformity, which is an indicator of a defect in the machine. Before the arrival of a defect on the machine, the non-conforming products are produced with a contact rate. After a defect arrival, the proportion of non-conforming products increases with time until the machine failure or the detection of the defect at inspection. The reproduction of non-conforming products incurs extra penalty cost to the production. Moreover, in the case of higher than acceptable level of nonconformity, the defective machine is preventively replaced. If the machine fails, corrective replacement is carried out. We use a combination of stochastic mathematical formulation, simulation, and optimization to determine the optimal periodic inspection interval, which minimizes the total expected cost of the production. Several examples are provided to highlight some interesting aspects in the interactions between the production, quality, and maintenance.