Evaluating capability of a bivariate zero-inflated poisson process

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.