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Determining the Reference Sample Size Needed to Control the Accuracy of the Conditional in‐control ARL of a Normal‐theory CUSUM
Author(s) -
Jeske Daniel R.
Publication year - 2016
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1952
Subject(s) - cusum , sample size determination , statistics , statistic , computer science , sample (material) , control (management) , probabilistic logic , mathematics , artificial intelligence , chemistry , chromatography
The question considered in this paper is how large does an in‐control reference sample need to be in order to control the effects of using estimated parameters when using a normal‐theory cumulative sum (CUSUM) tracking statistic? Previous research has demonstrated the effect of estimation errors on the conditional in‐control average run length of the CUSUM. The contributions of this paper are simple analytical tools that determine the required reference sample size needed to ensure probabilistic control of the relative error of the conditional in‐control average run length. The availability of these tools rounds out the design phase of the CUSUM by enabling a practical procedure for determining the needed size of the reference sample. Copyright © 2016 John Wiley & Sons, Ltd.