An Outlier Detection Approach to Recognize the Sources of a Process Failure within a Multivariate Poisson Process

Among attribute processes, the number of nonconformities conforming to a Poisson distribution is among the most crucial quality attributes. Furthermore, owing to the variety of quality attributes, the significance of the multivariate Poisson process in industry cannot be overstated. An out-of-control multivariate Poisson process can be detected using an alarm on a multivariate control chart. Nevertheless, pinpointing the specific quality attributes that led to the process shifts is complex. The study focuses on the causes that lead to process shifts in multivariate Poisson processes, unlike the majority of studies examining shifts in multivariate normal processes. This paper initially presents a statistical method for detecting outliers in a multivariate Poisson distribution. Furthermore, a progressive testing algorithm is then developed to identify the variables responsible for a failure within a multivariate Poisson process. According to simulation results, the proposed approach can effectively determine the sources of a process fault within a multivariate Poisson process.