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Technometrics Volume 26, 1984 - Issue 1
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Original Articles

On the Markov Chain Approach to the Two-Sided CUSUM Procedure

William H. Woodall Department of Mathematics and Statistics, University of Southwestern Louisiana, Lafayette, LA, 70504
Pages 41-46 | Published online: 23 Mar 2012
 
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Abstract

A Markov chain representation is given for the two-sided, possibly asymmetric, cumulative sum (CUSUM) procedure of Ewan and Kemp (1960) for integer-valued random variables. The approach taken by Brook and Evans (1972) for the one-sided CUSUM procedure to determine exact and approximate expressions for the run length distribution, its moments, and its percentage points is extended to the two-sided CUSUM procedure. The number of states included in the Markov chain is minimized in order to make the methods as efftcient as possible.

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Related Research Data

Robust cusum: a robustness study for cusum quality control schemes
Source: Informa UK Limited
The Distribution of the Run Length of One-Sided CUSUM Procedures for Continuous Random Variables
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Sampling inspection of continuous processes with no autocorrelation between successive results
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Fast Initial Response for CUSUM Quality-Control Schemes: Give Your CUSUM A Head Start
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The probability distribution and the expected value of a stopping variable associated with one-sided cusum procedures for non-negative integer valued random variables
Source: Informa UK Limited
An approach to the probability distribution of cusum run length
Source: Oxford University Press (OUP)
Sampling inspection of continuous processes with no autocorrelation between successive results
Source: JSTOR
The computation of average run length and average time to signal: an overview
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Some Characteristics of Page's Two-sided Procedure for Detecting a Change in a Location Parameter
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