Performance comparison of TEWMA-Max and GWMA-Max control chart under Weibull distribution

Abstract

This study aims to compare the performance of the TEWMA-Max and GWMA-Max control charts in detecting changes in the process mean and variability under data following a Weibull distribution, which reflects real-world manufacturing processes that often deviate from the normality assumption. Both control charts are developed based on the concept of the Max control chart, where the TEWMA-Max chart employs a triple-layer exponential weighting scheme, while the GWMA-Max chart adopts a more flexible generalized weighting structure. To satisfy the normality assumption underlying these control charts, data generated from the Weibull distribution  were transformed to approximate a standard normal distribution using the inverse transform method. A Monte Carlo simulation was then conducted under the in-control condition  and under various out-of-control conditions resulting from changes in  and . Three types of process shifts were considered: mean shift (MS), variance shift (VS), and simultaneous mean and variance shift (MVS). The results indicate that the GWMA-Max chart yields lower values than the TEWMA-Max chart in most scenarios, particularly in the MS and MVS cases, indicating a faster detection of process changes. However, the performance of both charts decreases when only variance shifts occur (VS case), which is consistent with the inherent characteristic of Max-Type control charts that are generally more sensitive to mean shifts than to variance shifts.