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 journalArticle

79 Citations (Scopus)

Abstract

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
JournalTechnometrics
Volume41
Issue number1
StatePublished - Feb 1999
Externally publishedYes

Fingerprint

Poisson Model
Defects
Multivariate Models
Zero
Manufacturing
Zero Distribution
Poisson distribution
Free Product
Maximum Likelihood Method
Method of Moments
Coverage Probability
Fault Detection
Method of moments
Fault detection
Maximum likelihood
Covariates
Electronic equipment
Simulation Study
Electronics
Modeling

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Li, C-S., Lu, J. C., Park, J., Kim, K., Brinkley, P. A., & Peterson, J. P. (1999). Multivariate zero-inflated poisson models and their applications. Technometrics, 41(1), 29-38.

Multivariate zero-inflated poisson models and their applications. / Li, Chin-Shang; Lu, Jye Chyi; Park, Jinho; Kim, Kyungmoo; Brinkley, Paul A.; Peterson, John P.

In: Technometrics, Vol. 41, No. 1, 02.1999, p. 29-38.

Research output: Contribution to journalArticle

Li, C-S, Lu, JC, Park, J, Kim, K, Brinkley, PA & Peterson, JP 1999, 'Multivariate zero-inflated poisson models and their applications', Technometrics, vol. 41, no. 1, pp. 29-38.
Li C-S, Lu JC, Park J, Kim K, Brinkley PA, Peterson JP. Multivariate zero-inflated poisson models and their applications. Technometrics. 1999 Feb;41(1):29-38.
Li, Chin-Shang ; Lu, Jye Chyi ; Park, Jinho ; Kim, Kyungmoo ; Brinkley, Paul A. ; Peterson, John P. / Multivariate zero-inflated poisson models and their applications. In: Technometrics. 1999 ; Vol. 41, No. 1. pp. 29-38.
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