Progressive mean as a special case of exponentially weighted moving average: Discussion

Abbas¹ showed mathematically that progressive mean statistic can be viewed as exponentially weighted moving average statistic with varying sensitivity parameter. A recently published study claims to invalidate the result using the justification that the variance of progressive mean (PM) statistic is different from the variance of exponentially weighted moving average statistic. This study reiterates and extends the initial result established by Abbas¹ and proves mathematically that not only the statistics but also the sampling variance of PM becomes a special case of exponentially weighted moving average with varying sensitivity parameter. Moreover, the study discusses that the performance of PM chart declines for steady state process and how it can be recovered by combining it with Shewhart chart.