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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.

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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References

1.Ames, W.F. (1969). Numerical methods for partial differential equations. London: Nelson.Google Scholar
2.Athreya, K.B. & Ney, P.E. (1972). Branching processes. New York: Springer.CrossRefGoogle Scholar
3.Beizer, B. (1990). Software testing techniques. New York: Van Nostrand Reinhold.Google Scholar
4.Danninger, G. & Gutjahr, W.J. (in preparation). Efficient blackbox test data selection for programs with numerical inputs.Google Scholar
5.Gutjahr, W.J. (1991). Software-Testen mit Zufallsdaten: Eine Effizienzbewertung. Österreichische Zeitschrift für Statistik und Informatik 21: 57–70.Google Scholar
6.Gutjahr, W.J. (1994). Connection reliabilities in stochastic acyclic networks. Random Structures and Algorithms 5: 57–72.CrossRefGoogle Scholar
7.Harris, T.E. (1963). The theory of branching processes. Berlin: Springer.CrossRefGoogle Scholar
8.Kolmogorov, A. (1941). Über das logarithmische normale Verteilungsgesetz der Dimensionen der Teilchen bei Zerstückelung. Doklady Akademii Nauk SSSR 31: 99–101.Google Scholar
9.Myers, G.J. (1979). The art of software testing. New York: Wiley.Google Scholar
10.Ramamoorthy, G.V. & Bastani, F.B. (1982). Software reliability–Status and perspectives. IEEE Transactions on Software Engineering SE-8: 354–371.CrossRefGoogle Scholar
11.Sauer, R. & Szabo, L. (1969). Mathematische Hilfsmittel des Ingenieurs II. Berlin: Springer.CrossRefGoogle Scholar