Two MEWMA Charts for Gumbel's Bivariate Exponential Distribution

Abstract

Data described by the exponential distribution are commonly encountered in manufacturing processes, reliability analysis, and human-service management. Time between events (TBE) charts have been suggested to monitor exponential data. However, existing studies on TBE charts are limited to univariate cases assuming there is only one process characteristic of interest. In this paper, two multivariate exponential weighted moving average (MEWMA) charts are proposed for the simultaneous monitoring of the mean vector of Gumbel's bivariate exponential (GBE) TBE model: One based on the raw observations and the other based on the transformed data. A numerical example is given to illustrate the implementation of the two MEWMA charts. We compare the average run-length performances of the two proposed charts with the following individual TBE charts pairs: the paired individual t charts, the paired individual exponentially weighted moving-average (EWMA) charts on raw data, and the paired individual EWMA charts on transformed data. The results of the comparative studies show that our MEWMA charts outperform all the other charts. The proposed MEWMA charts can be easily extended to higher dimensions. Some brief discussions concerning monitoring Gumbel's multivariate exponential model with more than two variables are also included.