Tail behaviour of a general family of control charts
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Wolfgang Schmid
Abstract
In this paper we consider a general control scheme. The control statistic Zt is equal to an arbitrary weighted sum of the past observations Xt,...,X1. This approach covers most of the applied control schemes like for instance moving average, EWMA and ARMA(1,1) charts. The process {Xt} is assumed to be a stationary Gaussian process. The aim of the work is to analyze the behaviour of the tail probability of the run length N=inf{t∈ℕ:Zt−E(Zt)>c√{Var(Zt)}} with respect to the autocorrelation of {Xt}. It is shown under which conditions on the weights and on the autocorrelations of {Xt} the correlation between Zt and Zt−i is a nondecreasing function in the autocorrelations of the observed process. Using this result it can be proved that the probability of a false alarm is a nondecreasing function of the autocorrelations of {Xt}, too. The weight conditions are verified for several well-known charts.
© 2003 Oldenbourg Wissenschaftsverlag GmbH
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Articles in the same Issue
- Editorial Note
- A note on Bayesian detection of change-points with an expected miss criterion
- The estimation problem of minimum mean squared error
- Parameter estimation for some non-recurrent solutions of SDE
- Variational sums and power variation: a unifying approach to model selection and estimation in semimartingale models
- A robust generalized Bayes estimator improving on the James-Stein estimator for spherically symmetric distributions
- Tail behaviour of a general family of control charts
