Non-parametric change-point approach for monitoring shifts in process location and variability

Abstract

Abstract:In statistical process control, detecting if the process is in control and the position of shift in an out-of-control process are critical research problems. If the normality assumption is satisfied, work has advanced in detecting shifts in mean and/or variance. However, the normality assumption is often not satisfied in many real life situations. We suggest a non-parametric Lepage-type change-point (LCP) control chart for jointly detecting process shifts in mean and variance, under non-normality. A comparison between our proposed method and a generalised likelihood ratio (GLR)-based method was made. Process data were simulated following normal and Laplace distributions. The performances of LCP and GLR were assessed and presented, using evaluated average run lengths, under the distributions considered. The LCP competed favourably with the GLR in a normal distribution. However, LCP outperformed GLR under the heavy-tailed distribution considered. We recommend the new approach for short-run situations where the underlying distributions are usually unknown.