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March 2009 Distribution-free cumulative sum control charts using bootstrap-based control limits
Snigdhansu Chatterjee, Peihua Qiu
Ann. Appl. Stat. 3(1): 349-369 (March 2009). DOI: 10.1214/08-AOAS197

Abstract

This paper deals with phase II, univariate, statistical process control when a set of in-control data is available, and when both the in-control and out-of-control distributions of the process are unknown. Existing process control techniques typically require substantial knowledge about the in-control and out-of-control distributions of the process, which is often difficult to obtain in practice. We propose (a) using a sequence of control limits for the cumulative sum (CUSUM) control charts, where the control limits are determined by the conditional distribution of the CUSUM statistic given the last time it was zero, and (b) estimating the control limits by bootstrap. Traditionally, the CUSUM control chart uses a single control limit, which is obtained under the assumption that the in-control and out-of-control distributions of the process are Normal. When the normality assumption is not valid, which is often true in applications, the actual in-control average run length, defined to be the expected time duration before the control chart signals a process change, is quite different from the nominal in-control average run length. This limitation is mostly eliminated in the proposed procedure, which is distribution-free and robust against different choices of the in-control and out-of-control distributions.

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Snigdhansu Chatterjee. Peihua Qiu. "Distribution-free cumulative sum control charts using bootstrap-based control limits." Ann. Appl. Stat. 3 (1) 349 - 369, March 2009. https://doi.org/10.1214/08-AOAS197

Information

Published: March 2009
First available in Project Euclid: 16 April 2009

zbMATH: 1160.62095
MathSciNet: MR2668711
Digital Object Identifier: 10.1214/08-AOAS197

Keywords: Cumulative sum control charts , distribution-free procedures , nonparametric model , Resampling , robustness , statistical process control

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.3 • No. 1 • March 2009
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