Multivariate zero-inflated poisson models and their applications

Chin-Shang Li, Jye Chyi Lu, Jinho Park, Kyungmoo Kim, Paul A. Brinkley, John P. Peterson

Research output: Contribution to journalArticlepeer-review

99 Scopus citations


The zero-inflated Poisson (ZIP) distribution has been shown to be useful for modeling outcomes of manufacturing processes producing numerous defect-free products. When there are several types of defects, the multivariate ZIP (MZIP) model can be useful to detect specific process equipment problems and to reduce multiple types of defects simultaneously. This article proposes types of MZIP models and investigates distributional properties of an MZIP model. Finite-sample simulation studies show that, compared to the method of moments, the maximum likelihood method has smaller bias and variance, as well as more accurate coverage probability in estimating model parameters and zero-defect probability. Real-life examples from a major electronic equipment manufacturer illustrate how the proposed procedures are useful in a manufacturing environment for equipment-fault detection and for covariate effect studies.

Original languageEnglish (US)
Pages (from-to)29-38
Number of pages10
Issue number1
StatePublished - Feb 1999
Externally publishedYes


  • Maximum likelihood
  • Mixture distribution
  • Multivariate Bernoulli
  • Multivariate Poisson
  • Quality control
  • Zero-defect probability

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability


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