Joint economic design of production, continuous sampling inspection and preventive maintenance of a deteriorating production system

Standard continuous sampling procedures and tables are conventionally applicable only to continuous production processes that are statistically 'in-control'. Consequently, these standards cannot be used to control quality in deteriorating production processes. Moreover, existing continuous sampling models do not consider interactions with production, inventory and maintenance aspects. In this paper, we attempt to fill these gaps in the literature. We investigate the joint design and optimization of a type-1 continuous sampling plan (CSP-1), make-to-stock production and preventive maintenance of a stochastic production system subject to both quality and reliability deteriorations. Two models of CSP-1 are considered and compared: the classical CSP-1 as in the standard procedures, and a CSP-1 plan with a stopping rule that is combined with condition-based maintenance. For both models, the optimization problem is to minimize the total incurred cost under a constraint on the outgoing quality. A combination of mathematical formulation, simulation and optimization techniques is used to solve such stochastic and constrained problems. Numerical examples are given to illustrate the resolution approach and to highlight some interesting aspects in the interactions between production, inventory, quality, maintenance and reliability. The results obtained demonstrate that sampling inspection plans realize significant cost savings compared to the 100% inspection which is commonly used in the literature of integrated models, and that using the CSP-1 with an inspection stopping rule for deteriorating processes is more cost-effective than the classical CSP-1.