ABSTRACT

This paper explores the effect of measurement errors on a joint monitoring control chart by using three different techniques (i) covariate method (ii) multiple measurements (iii) linear increasing variance. The joint monitoring control chart in the presence of measurement errors are discussed by using an exponentially weighted moving average statistic in the generalized likelihood ratio (GLR) test statistic under ranked set sampling and pair ranked set sampling (PRSS) procedures. For this purpose, different out-of-control scenarios including mean shifts, variance shifts, and simultaneous shifts are discussed under the considered sampling schemes. The performance of the joint monitoring control chart is evaluated in terms of average run length (ARL) and the standard deviation of run length (SDRL) by conducting an extensive simulation study. The results show that PRSS procedure can reduce the adverse effect of measurement errors on the detection ability of joint monitoring control chart. An example is provided with real data set for the implementation of the joint monitoring control chart in the presence of measurement errors.

摘要

本文通过使用三种不同的技术（i）协变量方法（ii）多次测量（iii）线性增加方差，探讨了测量误差对联合监控控制图的影响。在排序集抽样和成对排序集抽样（PRSS）程序下，使用广义似然比（GLR）测试统计中的指数加权移动平均统计，讨论了存在测量误差的联合监控控制图。为此，在考虑的采样方案下讨论了不同的失控场景，包括均值漂移，方差漂移和同时漂移。通过进行广泛的模拟研究，根据平均行程（ARL）和行程标准差（SDRL）评估联合监控控制图的性能。结果表明，PRSS程序可以减少测量误差对联合监测控制图检测能力的不利影响。提供了一个带有实际数据集的示例，用于在存在测量误差的情况下实施联合监控控制图。