Premium
An Empirical Bayes Process Monitoring Technique for Polytomous Data
Author(s) -
Shiau JyhJen H.,
Chen ChihRung,
Feltz Carol J.
Publication year - 2005
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.604
Subject(s) - polytomous rasch model , estimator , hyperparameter , computer science , bayes' theorem , dirichlet distribution , dirichlet process , mathematics , statistics , econometrics , bayesian probability , algorithm , item response theory , mathematical analysis , boundary value problem , psychometrics
When a product item is tested, usually one has more information than just pass or fail. Often there are categories of failure modes. The purpose of this paper is to develop a method to monitor the fractions of the tested items falling into different categories of pass/fail modes. Using the multinomial model with Dirichlet prior, we describe the theory underlying an empirical Bayes approach to monitoring polytomous data generated in manufacturing processes. A pseudo maximum likelihood estimator (PMLE) and the method‐of‐moments estimator (MME) of the hyperparameters of the prior distribution are considered and compared by a simulation study. It is found that the PMLE performs slightly better than the MME. A monitoring scheme based on the marginal distributions of the observed pass/fail fractions is proposed. The average run length behavior of the proposed monitoring scheme is investigated. Finally, an example to illustrate the use of the technique is given. Copyright © 2004 John Wiley & Sons, Ltd.