Open Access
August, 1992 Buying with Exact Confidence
S. R. Dalal, C. L. Mallows
Ann. Appl. Probab. 2(3): 752-765 (August, 1992). DOI: 10.1214/aoap/1177005658


We derive some results which may be helpful to buyers of software testing for faults, or to buyers of large lots screening for defectives. Suppose that a fixed but unknown number $n$ of faults or defectives remain before testing. In the testing phase they are observed at random times, $X_1, X_2, \cdots, X_n$, which are order statistics corresponding to $n$ i.i.d. random variables. Since testing is usually an ongoing activity, this distribution is typically known. Under this assumption we derive a stopping criterion that guarantees, for any specified level $\alpha$ and integer $m$, that for all $n > m$, with probability exactly $1 - \alpha$, when stopping occurs, the software has no more than $m$ faults remaining. We study various properties of this stopping rule, both finite and asymptotic, and show that it is optimal in a certain sense. We modify a conservative stopping rule proposed by Marcus and Blumenthal to make it exact, and we give some numerical comparisons.


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S. R. Dalal. C. L. Mallows. "Buying with Exact Confidence." Ann. Appl. Probab. 2 (3) 752 - 765, August, 1992.


Published: August, 1992
First available in Project Euclid: 19 April 2007

zbMATH: 0753.62051
MathSciNet: MR1177908
Digital Object Identifier: 10.1214/aoap/1177005658

Primary: 60G40
Secondary: 62G30 , 62L15 , 62N99

Keywords: Optimal stopping , sampling inspection , Software testing

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.2 • No. 3 • August, 1992
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