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A probablistic analysis for an optimal screening problem
Authors:M. G. Iovino  F. Spizzichino
Affiliation:(1) Department of Statistics, University of Perugia, Perugia, Italy;(2) Department of Mathematics, University of Rome, Rome, Italy
Abstract:Summary We consider a lotL formed byN apparently similar unitsW 1,…,W N, where each of theW i may come from one of two different populationsP 1 andP 2;T 1,…,T N denote the corresponding lifetimes. The units fromP i undergo a failure of kindi and their survival function isS i (t). We assume that the failure rate function 
$$lambda _i (t) =  - frac{d}{{dt}}log S_i (t) (i = 1,2)$$
are known and that the units fromP 1 are ?substandard?: λ 1 (t)≥λ 2 (t), ∀t≥0. We want to putW 1,…,W N under a pre-operational test (burn-in test) in order to eliminate at least a great part of the substandard units and we face the problem of obtaining a rule for stopping the test under the assumption that, with the failure of a unit, it is possible to recognize the population from which the unit comes. Such a problem will be formalized as an optimal stopping problem for a suitably defined Markov process. Our study shall evidentiate some fundamental aspects of the problem and the role of the prior distribution of the (random) numberM 0 of those units inL coming fromP 1 (substandard). The latter distribution has a great influence on the form of the solution. This research was supported by the C.N.R. Project ?Statistica Bayesiana e Simulazione in Affidalità e Modellistica Biologica?.
Keywords:60G40  60K10  62L15  62N05
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