Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-12-01T09:04:43.077Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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