An approach to the probability distribution of cusum run length

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ID: 301815
1972
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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.
Reference Key
openalex_W2056821499 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors D. Brook, D. A. Evans
Journal jurnal biometrika dan kependudukan
Year 1972
DOI
10.1093/biomet/59.3.539
URL
https://doi.org/10.1093/biomet/59.3.539
Keywords Keywords not found

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