A synthetic multivariate exponentially weighted moving average scheme for monitoring of bivariate Gamma distributed processes

Abstract

AbstractSeveral scholarly works intrinsically assume that the frequency and magnitude of events are two independent variables . However, in many practical situations, it is necessary to consider the dependence between these two characteristics of events. In this paper, two Smith–Adelfang–Tubbs (SAT) models, namely, the four‐ and the five‐parameter bivariate Gamma distributions (BGD) with a particular dependency parameter, are first reviewed. Then, a synthetic multivariate exponentially weighted moving average (synthetic MEWMA, or SMEWMA) type scheme is proposed to monitor the individual BGD observations (subgroups of size one) generated from those two specific SAT models. The Monte‐Carlo simulation method is developed to evaluate the run length () properties of the recommended SMEWMA BGD scheme in both the zero‐state and the steady‐state cases. Furthermore, we discuss the average run length (ARL) of the proposed SMEWMA BGD scheme with different design parameters, and then compare both the zero‐state and the steady‐state out‐of‐control ARL performances of the recommended SMEWMA BGD scheme with those of the classic MEWMA chart, the paired individual Gamma chart, and the MCUSUM chart. Simulation results suggest that the overall performance of the recommended SMEWMA BGD scheme is superior to the other comparative schemes. Finally, the implementation of the proposed SMEWMA BGD scheme is illustrated with a natural flood event dataset .