可变抽样区间图经济设计分析

Economic Design of X-bar Chart with Variable Sampling Intervals

传统控制图是静态的,其抽样区间为固定常数,往往不能及时发现生产过程异常。针对这种情况,本文在综合抽样成本、生产次品损失、误报警和漏报警损失、发现并纠正过程异常成本等基础上,提出可变抽样区间X图的经济设计方法。根据过程实际状态和由抽样结果采取的决策构建了一个二维时间离散的马尔可夫链,提出优化模型,并利用遗传算法寻找控制图参数的最优解。数值计算给出本文模型的具体求解过程。灵敏度分析研究了各参数对最优样本容量、控制限、警戒限、抽样区间及单位时间平均成本的影响。

The conventional control charts are static, i.e., the sampling intervals are fixed in the duration of operation. In this paper, we develop the economic design of the variable sampling intervals X-bar chart. To describe the actual state of the process and the decision that is made at each sampling instance, a two-dimensional discrete-time Markov chain is presented. The genetic algorithm is employed to search for the optimal values of the parameters. An example is provided to illustrate the solution procedure. A sensitivity analysis is carried out to investigate the effects of cost and model parameters on the solution of the economic design.