A Comparative Analysis of Mean Charts for Skewed Distributions

Abstract

This study employs extensive simulation approaches to evaluate how well Shewhart control charts monitor mean of non-normally distributed data. The main goals is to assess the accuracy of the average run length (ARL) under normal approximation and validate it as a theoretical measure of control chart efficacy. We conducted a systematic analysis of three different non-normal distributions: the Weibull, exponential, and generalised exponential. Different settings of parameters are considered to evaluate the effectiveness of the Shewhart chart. To determine how sensitive control chart behaviour is, a variety of scenarios are included in the study, including varying numbers of simulations and observations. The outcomes showed significant differences between the generalised exponential and Weibull distributions’ performances. In particular, the generalised exponential distribution demonstrated its stability and made control chart design easier by consistently achieving the desired ARL of 370 with a set threshold value across a wide range of parameter combinations. On the other hand, the Weibull distribution required different threshold values depending on shape parameters, which might make control tactics more difficult. These findings highlight the significance of comprehending distribution characteristics and their impact on control chart performance, and they offer useful insights into optimising control chart configurations for efficiently monitoring non-normally distributed processes