标题： 用于监测事件间时间的估计第二阶段威布尔控制图 显示英文标题

标题： Estimated Phase II Weibull control chart for monitoring times between events

摘要： 在统计过程控制中，威布尔分布可用于对具有递增、递减或恒定故障率的过程中的事件或故障（TBE）之间的时间进行建模。 具体而言，它有助于监控感兴趣的缺陷发生之间的时间，提供关于过程可靠性和性能的见解。 在本文中，我们考虑了监控威布尔分布尺度参数的增加或减少的双侧问题，假设形状参数为固定值。 较大的尺度参数表示事件随时间更分散，表明缺陷较少，而较小的值可能表明过程退化，导致缺陷数量增加。 当尺度参数未知时，它从第一阶段的观测值中估计得出，并通过用第一阶段观测值的估计值替换参数来获得插入式控制限。 鉴于估计控制限通常不如预期的这一广为接受的事实，使用两个条件指标——条件平均运行长度和条件ARL的标准差，对威布尔图的控制限进行了调整，以实现期望的受控（IC）性能。 为了评估所提出图表的受控和失控性能，进行了一项性能研究。 显示英文摘要

摘要： In statistical process control Weibull distribution can be used to model the time between events or failures (TBE) in a process with increasing decreasing or constant failure rates. Specifically it helps in monitoring processes where the time between defect occurrences is of interest providing insight into the process reliability and performance. In this paper we consider the two sided problem of monitoring either an increase or a decrease in the scale parameter of the Weibull distribution with control charts assuming the shape parameter to be fixed. A larger scale parameter indicates that events are more spread out over time suggesting fewer defects while a smaller value may suggest deterioration in the process resulting in a higher number of defects. When the scale parameter is unknown it is estimated from Phase I observations and the plug in control limits are obtained by replacing the parameter by its estimated value from the Phase I observations. Given the well accepted fact that estimated control limits often do not perform as expected, the control limits of the Weibull chart are adjusted to achieve the desired in control (IC) performance using two criteria that are conditional average run length and standard deviation of conditional ARL. A performance study is carried out in order to assess in control and out of control performances of the proposed charts.