Article2011

Two MEWMA Charts for Gumbel's Bivariate Exponential Distribution

48 citations0/0 files storedJournal of Quality Technology

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Advanced Statistical Process Monitoring Statistical Distribution Estimation and Applications Fault Detection and Control Systems

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.

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References

1992A Multivariate Exponentially Weighted Moving Average Control Chart 1988Multivariate Generalizations of Cumulative Sum Quality-Control Schemes 1990Comparisons of MultivariateCUSUMCharts 1985Counted Data CUSUM's 2001A Rank-Based Multivariate CUSUM Procedure 2002Robustness to Non-Normality of the Multivariate EWMA Control Chart 1983Quality Control Techniques for "Zero Defects"2008Distribution-free multivariate process control based on log-linear modeling

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2020Multivariate time-between-events monitoring: An overview and some overlooked underlying complexities 2016High quality process monitoring using a class of inter-arrival time distributions of the renewal process 2017Simultaneously monitoring frequency and magnitude of events based on bivariate gamma distribution 2020A multivariate CUSUM control chart for monitoring Gumbel's bivariate exponential data 2015Monitoring of Time‐Between‐Events with a Generalized Group Runs Control Chart

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