Estimation of the Change Point of a Normal Process Mean with a Linear Trend Disturbance in SPC

Abstract

Knowing when a process changed would simplify the search and identification of the special cause. In this paper, we compare the maximum likelihood estimator (MLE) of the process change point designed for linear trends to the MLE of the process change point designed for step changes when a linear trend disturbance is present. As expected, our conclusions show that the MLE of the process change point designed for linear trends outperforms the MLE designed for step changes when the change type is a linear trend. We also present an approach based on the likelihood function for estimating a confidence set for the process change point. We study the performance of this estimator when it is used with a Shewhart x control chart and make direct performance comparisons with the estimated confidence sets obtained from the MLE for step changes. As expected, results show that better confidence can be obtained using the MLE for linear trends when a linear trend disturbance is present.