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December, 1990 Improved Bounds for the Average Run Length of Control Charts Based on Finite Weighted Sums
Walter Bohm, Peter Hackl
Ann. Statist. 18(4): 1895-1899 (December, 1990). DOI: 10.1214/aos/1176347887


The average run length (ARL) is a key variable for assessing the properties of process control procedures. For continuous sampling procedures that are based on finite weighted sums (such as the moving sum technique) closed form expressions of the ARL are not available in the literature. For normally distributed random variables, Lai gives bounds for the ARL. In this paper we derive a lower bound of the ARL that (1) does not depend on normality and (2) in many situations is much sharper than the one obtained by Lai. Our results also imply that Lai's upper bound deviates from the true value less than the number of terms in the sum. Furthermore, we show that the applicability of Lai's bounds is not restricted to normally distributed control variables.


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Walter Bohm. Peter Hackl. "Improved Bounds for the Average Run Length of Control Charts Based on Finite Weighted Sums." Ann. Statist. 18 (4) 1895 - 1899, December, 1990.


Published: December, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0731.62152
MathSciNet: MR1074444
Digital Object Identifier: 10.1214/aos/1176347887

Primary: 62N10
Secondary: 60G40 , 60G50

Keywords: average run length , nonnormal control variable , quality control , weighted sums

Rights: Copyright © 1990 Institute of Mathematical Statistics


Vol.18 • No. 4 • December, 1990
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