Evaluating capability of a bivariate zero-inflated poisson process

Abstract

A zero-inflated Poisson (ZIP) distribution is commonly used for modelling zero-inflated process data with single type of defect, and for developing appropriate tools for instituting statistical process control of manufacturing processes. However, in reality, such manufacturing scenarios are very common where more than one type of defect can occur. For example, occurrences of defects like solder short circuits (shorts) and absence of solder (skips) are very common on printed circuit boards. In literature, different forms of bivariate zero-inflated Poisson (BZIP) distributions are proposed, which can be used for modelling the manufacturing scenarios where two types of defects can occur. Control charts are designed for monitoring for such processes using BZIP models. Although evaluation of capability is an integral part of statistical process control of a manufacturing process, researchers have given very little effort on this aspect of zero-inflated processes. Only a few articles attempted to evaluate the capability of a univariate zero-inflated process and no work is reported on evbaluating capability of a bivariate zero-inflated process. In this paper, a methodology for measuring capability of a bivariate zero-inflated process is presented. The proposed methodology is illustrated using two case studies.

A process capability index for zero-inflated processes

“…Table 2 shows the values of the parameters of the chosen four ZI Poisson distributions and the expected proportions of ZD, AC and NC units in these ZI Poisson processes. Now process capability indices for these ZI Poisson processes are evaluated using Patil and Shirke (2012), Pal and Gauri (2021) and the proposed approaches. The results of these analysis are presented in Table 3.…”

“…There are many research articles on developing appropriate control charts for monitoring of ZI processes (Chang and Gan, 1999;Sim and Lim, 2008;Zamzuri, 2015;Rakitzis et al, 2017;Tian et al, 2019;Alevizakos and Koukouvinos, 2021). However, only Patil and Shirke (2012) and Pal and Gauri (2021) have attempted to measure the capability of a ZI process. Patil and Shirke (2012) have modified the Perakis and Xekalaki (2005) proposed index by incorporating the inflation of zero parameter into index.…”

“…However, only Patil and Shirke (2012) and Pal and Gauri (2021) have attempted to measure the capability of a ZI process. Patil and Shirke (2012) have modified the Perakis and Xekalaki (2005) proposed index by incorporating the inflation of zero parameter into index. But it fails to represent the true capabilities of ZI processes consistently.…”

“…To the best of our knowledge, only Patil and Shirke (2012) and Pal and Gauri (2021) have attempted to measure capability of a ZI process. Number of defects is mainly smaller-the-better (STB) type of quality characteristic and the specified requirement for number of defects is usually defined in terms of upper specification limit (USL) of number of defects in a unit product.…”

“…Number of defects is mainly smaller-the-better (STB) type of quality characteristic and the specified requirement for number of defects is usually defined in terms of upper specification limit (USL) of number of defects in a unit product. Patil and Shirke (2012) have modified the Perakis and Xekalaki (2005) proposed index by incorporating the inflation of zero parameter into index, and applied it for measuring the capability of a ZI Poisson (ZIP) process. But it fails to represent the true capabilities of ZI processes consistently.…”