Premium
Estimating the Change Point of a Poisson Rate Parameter with a Linear Trend Disturbance
Author(s) -
Perry Marcus B.,
Pignatiello Joseph J.,
Simpson James R.
Publication year - 2006
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.715
Subject(s) - cusum , estimator , statistics , mathematics , linear model , poisson distribution , confidence interval , disturbance (geology) , econometrics , computer science , paleontology , biology
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. We conclude that the MLE of the process change point designed for linear trends outperforms the MLE designed for step changes when a linear trend disturbance is present. 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 cumulative sum (CUSUM) control chart and make direct performance comparisons with the estimated confidence sets obtained from the MLE for step changes. The results show that better confidence can be obtained using the MLE for linear trends when a linear trend disturbance is present. Copyright © 2005 John Wiley & Sons, Ltd.