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Fault Diversity in Software Reliability

Published online by Cambridge University Press:  27 July 2009

Philip J. boland
Affiliation:
Department of Statistics University College, Dublin Belfield, Dublin 4, Ireland
Frank proschan
Affiliation:
Department of StatisticsThe Florida State University Tallahassee, Florida 32306
Y. L. Tong
Affiliation:
School of Mathematics Georgia Institute of Technology Atlanta, Georgia 30332

Abstract

Diversity of bugs or faults in a software system is a factor contributing to software unreliability which has not yet been appropriately emphasized. This paper is written with the intention of demonstrating the impact of fault diversity on the time to detection of software bugs. A new discrete software reliability model based on the multinomial distribution is introduced. It is shown that for models of this type, the more diverse the fault probabilities are, the longer (stochastically) it takes to detect or eliminate any n faults, while the smaller (stochastically) will be the number of faults detected or eliminated during a given amount of time (or during a given number of inputs to the system). The impact of fault diversity is also demonstrated for the Jelinski–Moranda model.

Type
Articles
Copyright
Copyright © Cambridge University Press 1987

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References

Forman, E. H. and Singpurwalla, N. D. (1977). An empirical stopping rule for debugging and testing computer software. Journal of the American Statistical Association 72: 750757.Google Scholar
Goel, A. and Okumoto, K. (1979). Time-dependent error detection rate model for software reliability and other performance measures. IEEE Trans. Rel., R-28: 206211.CrossRefGoogle Scholar
Goudie, I. B. J. and Goldie, C. M. (1981). Initial size estimation for the linear pure death process. Biometrika 68: 543550.CrossRefGoogle Scholar
Jelinski, Z. and Moranda, P. B. (1972). Software reliability research. In Statistical Computer Performance Evaluation, ed. Freiberger, W., Academic Press, p. 465484.CrossRefGoogle Scholar
Joe, H. and Reid, N. (1985). Estimating the number of faults in a system. Journal of the American Statistical Association 80: 222226.CrossRefGoogle Scholar
Langberg, N. and Singpurwalla, N. (1985). A unification of some software reliability models. SIAM Journal of Scientific and Statistical Computing 6: 781790.CrossRefGoogle Scholar
Lehmann, E. L. (1959). Testing Statistical Hypothesis, J. Wiley and Sons, New York.Google Scholar
Littlewood, B. and Verrall, J. L. (1973). A Bayesian reliability growth model for computer software. Journal of the Royal Statistical Society Series C, 22; 332346.Google Scholar
Marshall, A. W. and Olkn, I. (1979). Inequalities: Theory of Majorization and its Applications, Academic Press, New York.Google Scholar
Musa, J. D. and Okumoto, K. (1984). A logarithmic Poisson execution time model for software reliability measurement. IEEE, Computer Society Press, p. 230238.Google Scholar
Nevius, S. E., Proschan, F., and Sethuraman, J. (1977). Schur functions in statistics II: Stochastic majorization. Annals of Statistics 5: 263273.CrossRefGoogle Scholar
Proschan, F. and Sethuraman, J. (1976), Stochastic comparisons of order statistics from heterogeneous populations, with applications in reliability. Journal of Multivari ate Analysis 6: 608616.CrossRefGoogle Scholar
Ross, S. M. (1985a). Statistical estimation of software reliability. IEEE Trans. Soft ware Eng., SE-11 479483.CrossRefGoogle Scholar
Ross, S. M. (1985b). Software reliability: The stopping rule problem. IEEE Trans. Software Eng., SE-11 14721476.CrossRefGoogle Scholar