面向小批量生产过程的贝叶斯控制图经济设计

在已有静态控制图的基础上,通过贝叶斯方法利用样本信息对过程信息进行更新.借助贝叶斯理论和马尔科夫链构造了生产过程的贝叶斯状态转移矩阵及检测概率模型,考虑了扰动发生的时间对成本函数的影响,将过程信息的更新与检测概率模型相结合,构造了抽样间隔、样本量和控制限随过程信息时变的动态控制图.运用直接搜索算法搜索最优解,结果表明过程信息的更新对决策效果有着显著的影响,使用动态控制图的单件产品期望成本要小于静态控制图的单件成本.

Economic design of a Bayesian chart for short-run production

The paper presents a Bayesian cost minimization model based on pure economic performance criteria. Based on the static chart,it employed the Bayesian method which used sample information to update the information of the process.Process transition matrix and inspection probabilistic model were formulated according to the Bayesian theory and the Markov chain method.Thus,the influence of the time of the disturbance occurrence on process cost was taken into consideration.The updated process information was then combined with the inspection probabilistic model to design the Bayesian chart.The Bayesian chart allows all the three parameters,namely,the sample interval,sample size and control limit location,to change during production. Computational study indicates that the Bayesian chart decreases the total process cost remarkably,especially when the initial out-of-control probability is relatively large.