The performance of multivariate CUSUM control charts with estimated parameters

Mahmoud A. Mahmoud · Petros E. Maravelakis

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Advanced Statistical Process Monitoring Fault Detection and Control Systems Management Systems and Quality Improvement

Abstract

In this paper, we study the effect of estimating the vector of means and the variance–covariance matrix on the performance of two of the most widely used multivariate cumulative sum (CUSUM) control charts, the MCUSUM chart proposed by Crosier [Multivariate generalizations of cumulative sum quality-control schemes, Technometrics 30 (1988), pp. 291–303] and the MC1 chart proposed by Pignatiello and Runger [Comparisons of multivariate CUSUM charts, J. Qual. Technol. 22 (1990), pp. 173–186]. Using simulation, we investigate and compare the in-control and out-of-control performances of the competing charts in terms of the average run length measure. The in-control and out-of-control performances of the competing charts deteriorate significantly if the estimated parameters are used with control limits intended for known parameters, especially when only a few Phase I samples are used to estimate the parameters. We recommend the use of the MC1 chart over that of the MCUSUM chart if the parameters are estimated from a small number of Phase I samples.

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References

1992A Multivariate Exponentially Weighted Moving Average Control Chart 1988Multivariate Generalizations of Cumulative Sum Quality-Control Schemes 2006Effects of Parameter Estimation on Control Chart Properties: A Literature Review 1990Comparisons of MultivariateCUSUMCharts 1985Multivariate CUSUM Quality-Control Procedures 1987A Note on Multivariate CUSUM Procedures 2005The Inertial Properties of Quality Control Charts 1996A Markov Chain Model for the Multivariate Exponentially Weighted Moving Averages Control Chart

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