Multivariate double sampling |S| charts for controlling process variability

Arsen Grigoryan · Donya He

44 citations0/0 files storedInternational Journal of Production Research

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Advanced Statistical Process Monitoring Management and Optimization Techniques Fault Detection and Control Systems

Abstract

A new multivariate statistical process variability control scheme, the multivariate double sampling (MDS) |S| control chart scheme for controlling shifts in a variance–covariance matrix, is proposed. An MDS |S| chart is a double-stage extension of a single-stage control chart based on the sample generalized variance. The statistical efficiency in terms of average run length of the MDS |S| charts is compared with that of traditional and adaptive sample size control charts based on the sample generalized variance for a bivariate case. The results of the comparison show that the MDS |S| charts provide a significant improvement in efficiency for detecting shifts of any range over these schemes. The performance of the MDS |S| charts in terms of detecting power is also compared with that of the modified likelihood ratio test, the sum of standardized variances for principal components charts and a decomposition procedure. The results of the comparison show that for certain out-of-control situations, the performance of the MDS |S| chart is among those of the best schemes.

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References

1999Research Issues and Ideas in Statistical Process Control 2013Multivariate Quality Control 2002Design of double- and triple-sampling X-bar control charts using genetic algorithms 2001GENERALIZED VARIANCE CHART DESIGN WITH ADAPTIVE SAMPLE SIZES. THE BIVARIATE CASE 1999Statistical properties of the lsi multivariate control chart 2002Construction of double sampling s‐control charts for agile manufacturing 1996DISPERSION CONTROL FOR MULTIVARIATE PROCESSES

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