ABSTRACT

In this article, we first propose an exponentially weighted moving average (EWMA) chart for monitoring both the shape and scale parameters of the Weibull distribution. The proposed chart was developed by incorporating two individual EWMA charts, one for monitoring the shape parameter and the other for monitoring both the shape and scale parameters. Particularly, it is shown that these two individual EWMA charts are mutually independent. Simulation studies are presented to compare the performance of the proposed EWMA chart and the existing Shewhart schemes with the EWMA setup. Further, to reduce the time for detecting an out-of-control (OC) process, an EWMA chart with variable sampling intervals (VSIs) and an adaptive EWMA chart with VSI for monitoring both the shape and scale parameters were also developed based on the proposed EWMA chart. The EWMA chart with VSI and the adaptive EWMA chart with VSI were studied and their performances were evaluated. An example to illustrate the applicability and implementation of the proposed charts is also provided.

摘要

在本文中，我们首先提出了一个指数加权移动平均 (EWMA) 图，用于监测威布尔分布的形状和尺度参数。提议的图表是通过合并两个单独的 EWMA 图表开发的，一个用于监测形状参数，另一个用于监测形状和尺度参数。特别地，这表明这两个单独的 EWMA 图表是相互独立的。模拟研究用于比较提议的 EWMA 图和现有的休哈特方案与 EWMA 设置的性能。此外，为了减少检测失控 (OC) 过程的时间，还开发了具有可变采样间隔 (VSI) 的 EWMA 图和具有 VSI 的自适应 EWMA 图，用于监测形状和尺度参数建议的 EWMA 图表。研究了带有 VSI 的 EWMA 图和带有 VSI 的自适应 EWMA 图并评估了它们的性能。还提供了一个示例来说明拟议图表的适用性和实施​​。