On the phase i Shewhart control chart limits for minimizing mean squared error When the Data are contaminated

A Shewhart-type control statistic lacks memory of previous observations on a monitored quality characteristic. Therefore, Shewhart-type control charts are known to be relatively insensitive to moderate-to-small sized shifts in the process parameters.Yet, these charts are recommended in the literature for the design stage of a control chart, namely Phase I, where unknown process parameters are estimated and the control limits are set for online process monitoring in Phase II. There are several studies that considered time-weighted control charts for the Phase I application, as well as alternative estimators, to improve the design for monitoring in Phase II. Some studies also considered the design of Shewhart control charts based on false alarm rates or overall false alarm probabilities, where it is concluded that the control limits may be widened. In this study, we simulate assignable causes of variation by contaminating sets of Phase I observations and investigate the use of traditional Shewhart control chart for parameter estimation when the observations are normally distributed. By varying the distance of the control limits from the center-line, Phase I Shewhart control charts are evaluated in terms of the true and false alarm percentages, number of iterations performed to finalize the Phase I analysis, and the mean squared error of the parameter estimates. Some practical recommendations are provided.