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Test Point Optimization in a Branching-Process-Based Reliability Model

Published online by Cambridge University Press:  27 July 2009

Gabriele Danninger  and
Walter J. Gutjahr
Gabriele Danninger
Affiliation:
Department of Statistics, Operations Research and Computer Science, University of Vienna, A-1010 Vienna, Austria
Walter J. Gutjahr
Affiliation:
Department of Statistics, Operations Research and Computer Science, University of Vienna, A-1010 Vienna, Austria
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Abstract

We describe a model for a random failure set in a fixed interval of the real line. (Failure sets are considered in input-domain-based theories of software reliability.) The model is based on an extended binary splitting process. Within the described model, we investigate the problem of how to select k test points such that the probability of finding at least one point of the failure set is maximized. It turns out that for values k > 2, the objective functions to be maximized are closely related to solutions of the Poisson-Euler-Darboux partial differential equation. Optimal test points are determined for arbitrary k in an asymptotic case where the failure set is, in a certain sense, “small” and “intricate,” which is the relevant case for practical applications.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 8 , Issue 4 , October 1994 , pp. 591 - 609
Copyright
Copyright © Cambridge University Press 1994

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