## The Annals of Applied Probability

#### Abstract

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.

#### Article information

Source
Ann. Appl. Probab., Volume 2, Number 3 (1992), 752-765.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aoap/1177005658

Digital Object Identifier
doi:10.1214/aoap/1177005658

Mathematical Reviews number (MathSciNet)
MR1177908

Zentralblatt MATH identifier
0753.62051

JSTOR