Some simultaneous progressive monitoring schemes for the two parameters of a zero-inflated Poisson process under unknown shifts

Abstract

The zero-inflated Poisson (ZIP) distribution has been extensively studied in the literature during recent years. It is one of the most appropriate models for overdispersed data with an excessive number of zeros. Data of this type frequently arise in manufacturing processes with a low fraction of defective items. A ZIP model has two parameters; one presents the probability of extra zeros and the other stands for the expected Poisson count. In this article, we propose and study three new single control charts for detecting changes in either of the two parameters of a ZIP process. The performance of the schemes is studied via numerical simulation based on Monte-Carlo. We outline that all the existing control charts for monitoring ZIP processes are based on individual observations and assume that the shift sizes in either or both parameters are known. Our proposed schemes do not need any prior information related to shift size and can be used both for individual observations and subgroup samples. The results reveal that they are very effective in the detection of small and moderate shifts in process parameters. Practical implementation of the proposed schemes is also illustrated through an interesting real industrial data set on light emitting diodes (LED).

Keywords:

• average run length (ARL)
• maximum likelihood estimation
• simulation
• statistical process control
• Wald statistic

Acknowledgments

The authors are grateful to the two reviewers for their insightful comments that lead to a significant improvement of the manuscript and to the Editor in Chief Prof. Fugee Tsung for his encouragement to revise the article.