Abstract

The Adaptive Exponentially Weighted Moving Average (AEWMA) control chart is known to be effective in detecting range of shifts simultaneously. Moreover, the AEWMA chart is known to diminish the inertia effect. The AEWMA chart is usually investigated while assuming that the monitored process follows a continuous distribution; commonly the normal distribution. In practice, however, monitored data could be of a discrete-type. We aim in this study to propose a discrete-version from the AEWMA chart; namely the Poisson AEWMA chart. The chart is compared with its counterparts; the Poisson EWMA chart and Poisson CUSUM chart using the ARL and RMI metrics. Our results show that the Poisson AEWMA chart performs more efficiently in detecting shifts of various sizes with an RMI value approaching zero. The Poisson CUSUM chart has the worst performance. Moreover, the proposed Poisson AEWMA chart is capable of detecting shifts faster than an approach based on normal approximation even for large values of the mean defects. In addition, the superiority of the Poisson AEWMA chart in diminishing the inertia effect is illustrated through a numerical example. The example shows that the Poisson AEWMA chart is capable of detecting out of control situations very fast even if the chart statistic is in a disadvantageous position before a shift occurs.

摘要

众所周知，自适应指数加权移动平均 (AEWMA) 控制图可有效地同时检测偏移范围。此外，已知 AEWMA 图表可以减少惯性效应。AEWMA 图通常在假设受监控过程遵循连续分布的情况下进行调查；一般为正态分布。然而，在实践中，监控数据可能是离散类型的。我们在这项研究中的目标是从 AEWMA 图表中提出一个离散版本；即泊松 AEWMA 图。该图表与其对应物进行了比较；使用 ARL 和 RMI 指标的 Poisson EWMA 图和 Poisson CUSUM 图。我们的结果表明，泊松 AEWMA 控制图在检测 RMI 值接近零的各种大小的偏移时更有效。Poisson CUSUM 图的性能最差。而且，建议的 Poisson AEWMA 图能够比基于正态近似的方法更快地检测偏移，即使对于大的平均缺陷值也是如此。另外，通过数值例子说明了泊松AEWMA图在减小惯性效应方面的优越性。该示例显示 Poisson AEWMA 图能够非常快速地检测失控情况，即使图统计量在发生偏移之前处于不利位置。