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An approach to the probability distribution of cusum run length

BROOK, D., EVANS, D. A.·1972·Biometrika
DOI 10.1093/biomet/59.3.539
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Abstract

The classical method of studying a cumulative sum control scheme of the decision interval type has been to regard the scheme as a sequence of sequential tests, to determine the average sample number for these component tests and hence to study the average run length for the scheme. A different approach in which the operation of the scheme is regarded as forming a Markov chain is set out. The transition probability matrix for this chain is obtained and then the properties of this matrix used to determine not only the average run lengths for the scheme, but also moments and percentage points of the run-length distribution and exact probabilities of run length. The method may be used with any discrete distribution and also, as an accurate approximation, with any continuous distribution for the random variable which is to be controlled. Examples are given for the cases of a Poisson random variable and a normal random variable.

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Metadata

Authors
BROOK, D., & EVANS, D. A.
Venue
Biometrika
Publisher
Oxford University Press (OUP)
Published
1972
Volume
59
Issue
3
Pages
539-549
ISSN
  • 0006-3444 (ISSN-L)
  • 1464-3510
DOI
10.1093/biomet/59.3.539
OpenAlex
W2056821499
Cited by
885
References
0
FWCI
1.61
Type
journal article
Language
en
Open access
closed

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CoChat. (2026). Citation check: An approach to the probability distribution of cusum run length. https://app.cochat.ai/papers/10.1093/biomet/59.3.539
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BROOK, D., & EVANS, D. A. (1972). An approach to the probability distribution of cusum run length. Biometrika. https://doi.org/10.1093/biomet/59.3.539

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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.