Statistical process control of multi-attribute count data has received much attention with modern data-acquisition equipment and online computers. The multivariate Poisson distribution is often used to monitor multivariate attributes count data. However, little work has been done so far on under- or over-dispersed multivariate count data, which is common in many industrial processes, with positive or negative correlation. In this study, a Shewhart-type multivariate control chart is constructed to monitor such kind of data, namely the multivariate COM-Poisson (MCP) chart, based on the MCP distribution. The performance of the MCP chart is evaluated by the average run length in simulation. The proposed chart generalizes some existing multivariate attribute charts as its special cases. A real-life bivariate process and a simulated trivariate Poisson process are used to illustrate the application of the MCP chart.

The concept of length-biased distribution can be employed in the development of proper models for the lifetime data. Length-biased distribution is a special case of the more general form known as the weighted distribution. This article introduces a new class of Maxwell length-biased distribution. The statistical properties of the proposed distribution are determined, including shape, kth moment, reliability function, hazard function, reverse hazard function, and so on. The maximum likelihood estimate (MLE), method of moments (MM) estimate, and Bayesian estimate of the unknown parameter are derived. An illustrative example demonstrates the application of the proposed distribution in real life.