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

By Snigdhansu Chatterjee, Peihua Qiu. 2009

139 citations recorded by the source corpus.

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.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/00788599610cd85f37246206adf03704d50bbe03

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Citations in the corpus

Design and implementation of CUSUM exceedance control charts for unknown location (2014, methodology): “Chatterjee and Qiu (2009) proposed NPCUSUM charts using bootstrap control limits.”
A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification (2021, background): “…are other lines of work in statistics with equal claim to the term “distribution-free” especially when it is interpreted asymptotically, such as permutation tests [20], quantile regression [8], rank tests [21–23], and even the bootstrap [24, 25]— the following is not a history of those topics .”
Another Look at the EWMA Control Chart with Estimated Parameters (2015, methodology): “Recently, Chatterjee and Qiu (2009) prop- osed estimating the control limits of the CUSUM chart using the bootstrap.”
Phase I Distribution-Free Analysis of Univariate Data (2013, background): “…available nonpara- Vol. 45, No. 3, July 2013 273 www.asq.org metric charts are for Phase II applications (see e.g., Chakraborti et al. (2008), Chatterjee and Qiu (2009), Zou and Tsung (2010), Qiu and Li (2011), Capizzi and Masarotto (2012)), whereas at the present only a few Phase I…”