Abstract

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.

摘要

抽样计划在监控生产系统和降低质量和维护相关成本方面发挥着重要作用。现有的抽样计划通常侧重于一个可分配的原因。但是，可能会出现多种可归因的原因，尤其是对于多级生产系统，并且由此产生的过程转移可能会向下游传播。本文解决了为不可靠的多级生产系统寻找最佳抽样计划的问题，该系统受到竞争和传播随机质量变化的影响。特别是，研究了一个带有两台不可靠机器的连续生产系统，这些机器以固定的生产率生产产品。假设两台机器都受到随机质量变化的影响，不合格率增加，并且可能会随着故障率的增加而突然失效。在生产线末端实施抽样计划，以确定系统是否发生了偏移。如果检测到过程偏移，将启动必要的维护操作。最佳样本量、采样间隔和接受阈值是通过在发出真实警报信号、有效生产率和系统可用性的平均时间约束条件下最小化长期成本率来确定的。提供了一个自动抛丸和喷漆系统的数值例子来说明所提出的采样计划的应用以及关键参数和系统约束对最佳采样计划的影响。此外，与忽略移位传播的替代模型相比，所提出的模型在各种情况下表现出更好的性能。