Effect of estimation under non-normality on the phase II performance of linear profile monitoring approaches

Recently, there have been several studies about control charts to monitor profiles, where the quality of a process/product is expressed as function of response and explanatory variable(s). Mostly, it is assumed that the in-control parameter values are known and the error terms are normally distributed. However, these assumptions are rarely satisfied in practice. In this study, we focused on three popular methods (EWMA-R, EWMA-3, and EWMA3(d2)) for monitoring simple linear profiles and the performance of them is examined via simulation where the in-control parameters are estimated and error terms have a Student’s t distribution or gamma distribution. In order to capture the sampling variation among different practitioners, average and standard deviation of the average run length (ARL) are used as performance measures. In conclusion, it is seen that the estimation effect becomes more severe as the error term distribution deviates from normality to a greater extent. In addition, although the average ARL values get closer to the desired values as the amount of Phase I data increases, their standard deviations remain far away from the acceptable level indicating a high practitioner-to-practitioner variability.