Measuring capabilities of zero-inflated processes

Abstract

The high-quality processes usually have more count of zeros than are expected under chance variation of its underlying Poisson or other count distribution. Therefore, these processes are usually referred to as zero-inflated processes. The zeroinflated processes are commonly modelled by zero-inflated Poisson (ZIP) or zero-inflated negative binomial (ZINB) distribution. In a manufacturing set up, the evaluation of process capability index of a zero-inflated process can be useful in many ways, e.g. i) predicting how well the process will hold the specifications, ii) selecting between competing vendors, and iii) assisting product developers/designers in modifying the process, etc. However, researchers have given very little attentions on this aspect of zero-inflated processes. Only one such attempt is reported in literature. But, it does not always represent the true capabilities of zero-inflated processes, and sometimes it may give very misleading impression about the capability of the concerned process. In this article, the concept of Borges and Ho (2001) is applied to zero-inflated processes and a new approach for computation of process capability index of zero-inflated processes is developed. The proposed method reveals the true capabilities of zero-inflated processes consistently. Application of the proposed approach and its effectiveness are illustrated using two datasets published by past researchers.