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On the conditional in‐control ARL of a CUSUM statistic
Author(s) -
Jeske Daniel R.
Publication year - 2016
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2162
Subject(s) - cusum , statistics , statistic , sample size determination , context (archaeology) , control chart , mathematics , statistical process control , computer science , sample (material) , econometrics , process (computing) , paleontology , chemistry , chromatography , biology , operating system
Reference samples are frequently used to estimate in‐control parameters, which are then used as the true in‐control parameters during the monitoring phase of Statistical Process Control (SPC) applications. The SPC literature has recognized that even small errors in parameter estimates determined from reference samples can have a large impact on the conditional (given the values of the estimated parameters) in‐control average run length. However, there is little quantitative guidance on how large the reference sample should be to minimize this impact. In this paper, under the context of a recently developed Cumulative Sum (CUSUM) designed to detect translations in exponential distributions, a reference sample size formula for controlling relative error of the conditional in‐control average run length is derived. The result in this paper is a stepping stone for reference sample size formulas in more general settings. Copyright © 2016 John Wiley & Sons, Ltd.