Effect of contaminated phase I data on the phase II – EWMA control chart performance under non-normality

Abstract

Estimation of unknown process parameters is critical in statistical process control/monitoring (SPC/M). Retrospective data is usually used to identify the process in-control state behavior in terms of estimating the process parameters. Practitioners analyze the retrospective data in order to handle out-of-control observations before estimating the parameters. However, chances to overlook some out-of-control observations do exist; in which case, the Phase I data is said to be contaminated. In this study, we aim to assess the impact of having contaminated retrospective data on the performance of the EWMA chart; assuming non-normal processes. Two distributions are considered; the t-distribution to represent a symmetric heavy-tailed distribution with two contamination scenarios, and the Gamma distribution to represent a skewed one. A weighted variance EWMA chart is used with the Gamma distribution to account for the skewness. Our results revealed that under the t-distribution a contamination with respect to the mean is more serious than a contamination with respect to the degrees of freedom. Under the gamma distribution, the estimation effect generally and contamination effect specifically are more serious on smaller shape parameter values (heavily skewed).