小批量生产过程VSI控制图经济设计

Economic design of VSI control chart for short-run production

本文设计了一种面向小批量生产过程的变抽样区间(variable sample interval,VSI)控制图.根据参数的变化情况,变参数(variable parameter,VP)控制图被分为包括VSI控制图在内的几种不同类型的控制图.在带来成本节省的同时,VP控制图也增加了操作的复杂性;综合考虑成本节省和操作复杂性,VSI控制图被证明是最有效的一种控制图.经济设计控制图的核心是成本的最优化,传统经济图在设计时,没有考虑扰动发生的时刻对成本的影响.本文对过程状态进行重新划分,考虑了扰动发生的不同时刻对过程成本的影响;利用马尔科夫链和贝叶斯理论,构造了抽样区间随过程信息更新而变化的动态控制图.仿真结果表明:相比于已有的VSI控制图,本文设计的控制图更具有成本优势,因此具有更大的实用价值.

This paper presents an economically designed VSI control chart for short-run production. According to the different parameter/parameters that changes/change over time, VP （variable parameter） control charts can be classified into several different types, including VSI control chart. While bringing cost savings, VP control chart adds up to the complexity of the operation. VSI chart has been reckoned one of the most effective and efficient sort of control chart considering both cost savings and operational complexity. The crux of the economic design of control chart is the optimization of cost, but the impact of the occurrence time of the disturbance on cost has not been taken into account in the traditional economic design of control charts. In this paper, process state is re-divided and the influence of the time of the disturbance occurrence on process cost is taken into consideration. Employing the Markov chain method and the Bayesian theory, we construct a dynamic control chart of which the sampling interval changes with the update of the process information. Simulation results show that compared to prior VSI control chart, control chart designed in this paper is more cost-advantageous and thus of more practical value.