Optimal sampling plan for an unreliable multistage production system subject to competing and propagating random shifts

Sampling plans play an important role in monitoring production systems and reducing quality- and maintenance-related costs. Existing sampling plans usually focus on one assignable cause. However, multiple assignable causes may occur, especially for a multistage production system, and the resulting process shift may propagate downstream. This article addresses the problem of finding the optimal sampling plan for an unreliable multistage production system subject to competing and propagating random quality shifts. In particular, a serial production system with two unreliable machines that produce a product at a fixed production rate is studied. It is assumed that both machines are subject to random quality shifts with increased nonconforming rates and can suddenly fail with increasing failure rates. A sampling plan is implemented at the end of the production line to determine whether the system has shifted or not. If a process shift is detected, a necessary maintenance action will be initiated. The optimal sample size, sampling interval, and acceptance threshold are determined by minimizing the long-run cost rate subject to the constraints on average time to signal a true alarm, effective production rate, and system availability. A numerical example on an automatic shot blasting and painting system is provided to illustrate the application of the proposed sampling plan and the effects of key parameters and system constraints on the optimal sampling plan. Moreover, the proposed model shows better performance for various cases than an alternative model that ignores shift propagation.