Article2018

Optimal CUSUM and adaptive CUSUM charts with auxiliary information for process mean

35 citations0/0 files storedJournal of Statistical Computation and Simulation

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Advanced Statistical Process Monitoring Probability and Statistical Research Fault Detection and Control Systems

Abstract

The CUSUM chart is good enough to detect small-to-moderate shifts in the process parameter(s) as it can be optimally designed to detect a particular shift size. The adaptive CUSUM (ACUSUM) chart provides good detection over a range of shift sizes because of its ability to update the reference parameter using the estimated process shift. In this paper, we propose auxiliary-information-based (AIB) optimal CUSUM (OCUSUM) and ACUSUM charts, named AIB-OCUSUM and AIB-ACUSUM charts, using a difference estimator of the process mean. The performance comparisons between existing and proposed charts are made in terms of the average run length (ARL), extra quadratic loss and integral relative ARL measures. It is found that the AIB-OCUSUM and AIB-ACUSUM charts are more sensitive than the AIB-CUSUM and ACUSUM charts, respectively. Moreover, the AIB-ACUSUM chart surpasses the AIB-OCUSUM chart when detecting a range of mean shift sizes. Illustrative examples are given to support the theory.

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References

1992Introduction to Statistical Quality Control 1954CONTINUOUS INSPECTION SCHEMES 1959Control Chart Tests Based on Geometric Moving Averages 2000Control Chart Tests Based on Geometric Moving Averages 1988Multivariate Generalizations of Cumulative Sum Quality-Control Schemes 1982Combined Shewhart-CUSUM Quality Control Schemes 1985Multivariate CUSUM Quality-Control Procedures 1991Multivariate Quality Control Based on Regression-Adjusted Variables

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