Multivariate Zero-Inflated Poisson Models and Their Applications

TLDR

The zero‑inflated Poisson distribution is useful for modeling manufacturing processes that produce many defect‑free items, and the multivariate ZIP model can detect specific equipment problems and reduce multiple defect types simultaneously. This article proposes types of multivariate ZIP models and investigates their distributional properties. The study develops and analyzes multivariate zero‑inflated Poisson models for manufacturing defect data. Simulation shows maximum‑likelihood estimation outperforms the method of moments in bias, variance, and coverage, and real‑world examples demonstrate the procedures’ utility for fault detection and covariate effect analysis.

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.