An empirical bayes process monitoring technique for polytomous data

Jyh Jen H. Shiau, Chih-Rung Chen, Carol J. Feltz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish
Pages (from-to)13-28
Number of pages16
JournalQuality and Reliability Engineering International
Issue number1
StatePublished - 1 Feb 2005


  • Attribute data
  • Control charts
  • Dirichlet
  • Empirical Bayes
  • Multinomial
  • Polytomous
  • Quality control


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