Development of Modified MaxAEWMA Control Chart based on Auxiliary Information

Abstract

Usually, two different EWMA charts are used to screen the mechanism average and dispersion. Chen and Xie 2001 was the first to introduce the idea to screen both mean and variance simultaneously, with a single statistic known as MxEWMA but a deficiency of MxEWMA is that when the jump size is known, it provides its optimal run length performance which is rarely known in usual practice. This point demands to use an adaptive chart known as MxAEWMA control chart. As it can be observed from (Abbas, Riaz, & Does, 2014; Haq, 2017; Riaz, 2008a, 2008b) that utilizing auxiliary information in the control charting technique at the estimation stage, can enhance the capability of their performance over existing charts. Similarly, introducing auxiliary information to the existing MxAEWMA chart can amplify its potentiality to invigilate the mean and dispersion of the procedure simultaneously of a normally distributed mechanism. This step of involving an auxiliary information to the existing efficient MxAEWMA would increase its sensitivity out-of-control signals. That would bring an ease to the industrial level by less consumption of time that was wasted before in supervising two different control charts for average and variance of the manufacturing mechanism. For this purpose, some transformation by (Quesenberry, 1995) are made on these EWMA statistics to follow the same distribution that will be standard normal distribution which will help to plot them on the same chart