Overview

A control chart is often used to detect a change in a process. Following a control chart signal, knowledge of the time and magnitude of the change would simplify the searchforand identification of the assignable cause. In this research, emphasis is placed on count processes where overdispersion has occurred. Overdispersion is common in practice and occurs when the observed variance is larger than the theoretical variance of the assumed model. Although the Poisson model is often used to model count data, the two parameter gamma-Poisson mixture parameterization of the negative binomial distribution is often a more adequate model for overdispersed count data. In this research effort, maximum likelihood estimators for the time of a step change in each of the parameters of the gamma-Poisson mixture model are derived. MonteCarlo simulation is used to evaluate the rootmean square error performance of these estimators to determine their utility in estimating the change point, following a control chart signal. Results show that the estimators provide process engineers with accurate and useful estimates for the time of step change. In addition, an approach for estimating a confidence set for the process change point will be presented. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

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