Abstract

EWMA and Max-EWMA charts are considered efficient for individual as well as joint monitoring of mean and variance shifts in the production process. However, measurement error is affecting the efficiency of these charts. In this study we propose a maximum exponentially weighted moving average with measurement error using auxiliary information control chart and name it Max-EWMAMEAI control chart. The efficiency of this chart is highlighted and the effect of measurement error is shown by the values of $\mathit{ARLs}$ and $\mathit{SDRLs}$ calculated through simulations using linear covariate model. The case of linearly increasing variance is examined and multiple measurements technique has been applied to reduce the error effect. A real life example is also included to support the simulation results.

摘要

EWMA 和 Max-EWMA 图表被认为对于生产过程中的均值和方差变化的个体和联合监测是有效的。然而，测量误差正在影响这些图表的效率。在这项研究中，我们使用辅助信息控制图提出了具有测量误差的最大指数加权移动平均值，并将其命名为 Max-EWMAMEAI 控制图。该图表的效率被突出显示，测量误差的影响由$\mathit{ARL}$和$\mathit{SDRL}$通过使用线性协变量模型的模拟计算。检验了方差线性增加的情况，并应用了多次测量技术来减少误差影响。还包括一个真实的例子来支持模拟结果。