The Run Length Distribution of the CUSUM Chart with Estimated Parameters

L. Allison Jones; Charles W. Champ; Steven E. Rigdon

doi:10.1080/00224065.2004.11980254

The Run Length Distribution of the CUSUM Chart with Estimated Parameters

L. Allison Jones, Charles W. Champ, Steven E. Rigdon

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

128 Scopus citations

Abstract

The CUSUM control chart is a popular method used to monitor the performance of production processes. The performance of the CUSUM is generally evaluated with the assumption that the process parameters are known. In practice, the parameters are rarely known and are frequently replaced with estimates from an in-control reference sample. We discuss the run length distribution of the CUSUM with estimated parameters and provide a method for approximating this distribution and moments. We evaluate the performance of the CUSUM with estimated parameters in a variety of practical situations.

Original language	American English
Journal	Journal of Quality Technology
Volume	36
DOIs	https://doi.org/10.1080/00224065.2004.11980254
State	Published - Jan 1 2004

Disciplines

Education
Mathematics

Keywords

CUSUM
Estimated Parameters
Run Length Distribution

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10.1080/00224065.2004.11980254License: Unspecified

https://www.researchgate.net/publication/283820081_The_Run_Length_Distribution_of_the_CUSUM_with_Estimated_Parameters

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title = "The Run Length Distribution of the CUSUM Chart with Estimated Parameters",

abstract = "The CUSUM control chart is a popular method used to monitor the performance of production processes. The performance of the CUSUM is generally evaluated with the assumption that the process parameters are known. In practice, the parameters are rarely known and are frequently replaced with estimates from an in-control reference sample. We discuss the run length distribution of the CUSUM with estimated parameters and provide a method for approximating this distribution and moments. We evaluate the performance of the CUSUM with estimated parameters in a variety of practical situations.",

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AU - Champ, Charles W.

AU - Rigdon, Steven E.

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N2 - The CUSUM control chart is a popular method used to monitor the performance of production processes. The performance of the CUSUM is generally evaluated with the assumption that the process parameters are known. In practice, the parameters are rarely known and are frequently replaced with estimates from an in-control reference sample. We discuss the run length distribution of the CUSUM with estimated parameters and provide a method for approximating this distribution and moments. We evaluate the performance of the CUSUM with estimated parameters in a variety of practical situations.

AB - The CUSUM control chart is a popular method used to monitor the performance of production processes. The performance of the CUSUM is generally evaluated with the assumption that the process parameters are known. In practice, the parameters are rarely known and are frequently replaced with estimates from an in-control reference sample. We discuss the run length distribution of the CUSUM with estimated parameters and provide a method for approximating this distribution and moments. We evaluate the performance of the CUSUM with estimated parameters in a variety of practical situations.

KW - CUSUM

KW - Estimated Parameters

KW - Run Length Distribution

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/498

UR - https://www.researchgate.net/publication/283820081_The_Run_Length_Distribution_of_the_CUSUM_with_Estimated_Parameters

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M3 - Article

SN - 0022-4065

VL - 36

JO - Journal of Quality Technology

JF - Journal of Quality Technology

ER -

The Run Length Distribution of the CUSUM Chart with Estimated Parameters

Abstract

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