Comparison of change-points in multivariate statistical process control using the performance of Lapage-type (nonparametric)

Abstract

The inability of the Shewhart‟s, the EWMA, and the CUSUM, Hotelling‟s T2 and many other control charts to indicate the time of shift poses great problems in production, Medicine, etc. To overcome the problems the need to identify the period of change (shift) in the process becomes inevitable. The study used Lapage-type Change-point (LCP) to detect the simultaneous shift in both mean and variance. In the study we compare the performance of generalized likelihood ratio change-point (GLRCP) a parametric-base with our proposed method (LCP) at different varying start-ups using real life data. We run the data on Normal, Laplace and Lognormal distributions and also Average Run Length (ARL₀) to assess the performance of the methods. Evaluating in-control ARLs (IC-ARLs) for each of the methods at change-point 250 and ARL₀ 500 indicates the same performance irrespective of the start-up value; LCP and GLR methods have rather a similar performance IC-ARLs at change-point 50 and change-point 100 under the normality assumptions, but under non-normal distributions, LCP has substantially higher IC-ARLs compared to GLRCP at 20. The LCP outperformed the GLRCP when applied to children bronchial pneumonia status. We therefore recommend that new method be used in short-run situations and also when underlying distributions are usually unknown.