参数未知下基于定数截尾样本监控指数分布的控制图设计

Control charts for the monitoring of exponentially distributed characteristics based on type-Ⅱ censored samples adjusted for parameter estimation

实际应用中,过程的目标参数常常未知,需由第Ⅰ阶段数据集估计得到.不同的第Ⅰ阶段数据集会导致目标参数的不同估计值和不同的控制图控制限,因此也意味着不同的控制图表现.对于某个实际工作者而言,最可能的情况是他手中仅有一个第Ⅰ阶段数据集,因此研究基于一个给定的第Ⅰ阶段数据集所构建的控制图表现,即条件表现更具现实意义.该文研究了参数未知时针对定数截尾样本数据指数分布控制图的条件表现,推导出了参数估计下控制图条件平均链长的精确分布,并利用条件平均链长分布及其数字特征评价了参数估计对控制图表现的影响,结果显示参数估计严重影响着控制图的表现.于是,又提出了精确分析方法设计了具有理想条件表现的控制图.最后用一个例子说明如何执行本文所提控制图.

In most practical applications,the in-control parameters of the process are often unknown and have to be estimated from an in-control Phase I data set.Different Phase I data sets can lead to different estimates and thus different control chart limits and different control chart performance.The most likely situation is that one practitioner only has one Phase I data set.In this case,it is more meaningful to study the performance of the control chart based on a given Phase I data set,i.e.,conditional performance.This paper considers the conditional performance of the control charts for monitoring changes in the exponential distribution based on Type II censored sample.First,for the control charts with estimated parameter,the exact probability distributions of the conditional average run length(ARL),is derived.Then the control chart performance is studied in regard to the percentiles,mean and standard deviation of the conditional ARL distribution.Since parameter estimation seriously affects control charts performance,an exact method is developed to design the adjusted control charts with desired conditional in-control performance.Finally,an example is used to illustrate the implementation of the proposed control charts.