X-bar图和预防性维修周期的优化设计

Optimization Design of X-bar Chart and Preventive Maintenance Policies

假定生产设备在运行正常时加工产品的关键质量特性服从正态分布,设备异常将引起质量特性的均值发生漂移,设备是否异常需通过检测才能判定。用X图对设备的状态进行监控,根据抽检时设备状态的变化情况构建一个马尔可夫链,在综合抽样成本、误判损失、失控运行损失及维修成本的基础上,提出同时优化控制图参数和预防性维修间隔的数学模型,讨论了均值漂移对决策变量的影响。

It is assumed that the key quality characteristic is a normal random variable when the process is operating properly. The process mean is subject to shift, and this type of shift can be attributed to an equipment failure. The equipment failure is not easy to detect.An X-bar chart is used to monitor the condition of the process. The discrete-time Markov decision process which is to obtain the optimal combined SPC and PM policy is presented. We develop a general mathematical model for the joint optimization of the control chartparameters and the time of PM. The effect of shift parameter on the decision variables is studied.