Buying with exact confidence
type: Item
instance of: scholarly article
title: Buying with exact confidence
zbMATH Open document ID: 0753.62051
author: Siddhartha R. Dalal
author: Colin L. Mallows
published in: The Annals of Applied Probability
publication date: 1993-01-17T00:00:00Z
review text: The following stopping time problem arises e.g. in software testing: let \((X_ k)\) be a sequence of independent times with known common (continuous) distribution \(F\). The \(X_ k\) represent the times at which events occur and a finite number of such times is observed. Let \(K(t)\) be the number of events observed before \(t\), \(K(t)=\) number of indices \(\{j\mid X_ j\leq t\}\). Then consider an increasing sequence \((b_ k)\) and stop at \(\tau=b_ J\) where \(J=\) smallest \(j\) with \(K(b_ j)<j\). Then for \(m\geq 0\), \(\alpha\in(0,1)\), \((b_ j)\) can be chosen such that for all \(n>m\), \(P(n-K(\tau)>m\mid n)=\alpha\). In other words, if the random variable \(N\) represents the number of events with distribution supported on \((m+1,\infty)\), then \(P(N- K(\tau)>m)=\alpha\). The properties of this stopping time are studied and compared to earlier results. Finally, numerical examples are given.
Mathematics Subject Classification ID: 62L15
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 62P30
Mathematics Subject Classification ID: 62G30
Mathematics Subject Classification ID: 62N99
zbMATH DE Number: 97558
zbMATH Keywords: screening for defectives
zbMATH Keywords: sampling inspection
zbMATH Keywords: software testing
reviewed by: Michael Kohlmann
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aoap/1177005658
OpenAlex ID: W2082348226
DOI: 10.1214/AOAP/1177005658
description: scientific article; zbMATH DE number 97558