基于定数截尾样本监控Weibull分布形状参数的控制图设计

Control charts for monitoring the shape parameter of Weibull distribution based on typeⅡ censored sample

基于定数截尾样本提出了单侧和双侧ARL无偏控制图监控Weibull分布形状参数的变化.提出的控制图仅依赖于样本容量n,失效数r和指定的受控平均链长ARL_O.利用模拟方法研究了常见(r,n)组合下提出的控制图在失控状态下的平均链长性质.模拟结果显示,对于形状参数小和中等的向下飘移,文中提出的控制图要优于现有文献的结果.特别是对形状参数中等程度的向下飘移,当失效数r较大时,提出的控制图的平均链长比现有结果小了近一半.由于单侧控制图比双侧控制图能更快地发出报警信号,故建议应尽可能地使用单侧控制图监控形状参数变化.最后用一个例子说明了所提控制图的应用.

This paper proposes one-sided and two-sided control charts for monitoring changes in the Weibull shape parameter based on Type II censored sample. The control limits depend only on sample size, the numbers of failure and the specified in-control average run length. By Monte-Carlo simulations, performance of the proposed control charts for some combinations of （n,r） is studied. The simulation results show that the proposed charts perform better than the charts developed by Pascual et al. （2012）. In particular, when downward shift size is moderate, the out-of-control ARLs of the proposed charts have only half ones of Pascual et al. （2012）. One-sided charts for detecting the changes in shape parameter are used because they can signM an out-of-control status sooner than the two-sided charts. Finally, an example is given to illustrate proposed charts.