The Annals of Applied Statistics

Distribution-free cumulative sum control charts using bootstrap-based control limits

Snigdhansu Chatterjee and Peihua Qiu

Full-text: Open access

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.

Article information

Source
Ann. Appl. Stat., Volume 3, Number 1 (2009), 349-369.

Dates
First available in Project Euclid: 16 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1239888374

Digital Object Identifier
doi:10.1214/08-AOAS197

Mathematical Reviews number (MathSciNet)
MR2668711

Zentralblatt MATH identifier
1160.62095

Keywords
Cumulative sum control charts distribution-free procedures nonparametric model statistical process control resampling robustness

Citation

Chatterjee, Snigdhansu; Qiu, Peihua. Distribution-free cumulative sum control charts using bootstrap-based control limits. Ann. Appl. Stat. 3 (2009), no. 1, 349--369. doi:10.1214/08-AOAS197. https://projecteuclid.org/euclid.aoas/1239888374


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