Detecting changes in probabilities of a multi—component process
- 1 January 1995
- journal article
- research article
- Published by Taylor & Francis in Sequential Analysis
- Vol. 14 (4) , 375-388
- https://doi.org/10.1080/07474949508836344
Abstract
Let ξ1,ξ2,… be iid random variables such that P(ξ1 = 1) = p, [ILM001] and set S0 = 0, Sn, = ξ1+…+ξn, n ≥ 1. Define the cusum (cumulative sum) stopping time , where h is a positive integer. We find asymptotic (as h → ∞) distributions of suitably normalized functions of N1(h) when (a)q > p (exponential) and (b) p = q. As an application we define a cusum procedure for detecting changes in probabilities of a multi—component process, and using (a) we obtain an asymptotic approximation for the average run length (ARL) of the given procedure. Moreover, under some suitable conditions we generalize the preceding asymptotic results for any sequence of iid random variables X1, X2,… with mean μ≤0.Keywords
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