Abstract
In software reliability theory many different models have been proposed and investigated. some of these models intuitively match reality better than others. The properties of certain statistical estimation procedures in connection with these models are also model-dependent. In this paper we investigate how well the maximum likelihood estimation procedure and the parametric bootstrap behave in the case of the very well-known software reliability model suggested by Jelinski and Moranda (1972). For this study we will make use of simulated data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aalen, O. O. (1978) Non-parametric inference for a family of counting processes.Annals of Statistics,6, 701–726.
Andersen, P. K., Borgan, Ø., Gill, R. D. and Keiding, N. (1992)Statistical Methods Based on Counting Processes, Springer-Verlag, New York.
Bickel, P. J. and Freedman, D. (1981) Some asymptotic theory for the bootstrap.Annals of Statistics,9, 1196–1217.
Borgan, Ø. (1984) Maximum likelihood estimation in parametric counting process models, with applications to censored failure time data.Scandinavian Journal of Statistics,1, 1–16.
Gill, R. D. (1989) Non- and semi-parametric maximum likelihood estimators and the von Mises method 1622 (Part 1).Scandinavian Journal of Statistics,16, 97–128.
Hall, P. (1988) Theoretical comparison of bootstrap confidence intervals.Annals of Statistics,16, 927–953.
Helmers, R. (1991) On the edgeworth expansion and the bootstrap approximation for a studentizedU-statistic.Annals of Statistics,19, 470–484.
Jelinski, Z. and Moranda, P. (1972) Software Reliability Research.Statistical Computer Performance Evaluation, Academic Press, New York, pp. 465–484.
Kurtz, T. G. (1983) Gaussian approximations for Markov chains and counting processes.Bulletin of the International Statistical Institute,50, 361–375.
Moek, G. (1983) Software reliability models on trial: selection, improved estimation, and practical results. Report MP 83059 U, National Aerospace Laboratory NLR, Amsterdam.
Moek, G. (1984) Comparison of some software reliability models for simulated and real failure data.International Journal of Modelling & Simulation,4, 29–41.
Musa, J. D. (1975) A theory of software reliability and its application.IEEE Transactions on Software Engineering,3, 312–327.
Musa, J. D., Iannino, A. and Okumoto, K. (1987)Software Reliability: Measurement, Prediction, Application, McGraw-Hill, New York.
Pollard, D. (1989)Convergence of Stochastic Processes, Springer-Verlag, New York.
van Pul, M. C. (1990) Asymptotic properties of statistical models in software reliability. Report BS-R9011, Centre for Mathematics and Computer Science, Amsterdam.
Rao, C. R. (1973)Linear Statistical Interference and its Applications, Wiley, New York.
Singh, K. (1981) On asymptotic accuracy of Efron's bootstrap.Annals of Statistics,9, 1187–1195.
van der Vaart, A. W. (1987)Statistical Estimation in Large Parameter Spaces, CWI tract 44, Amsterdam.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Van Pul, M. Simulations on the Jelinski-Moranda model of software reliability; application of some parametric bootstrap methods. Stat Comput 2, 121–136 (1992). https://doi.org/10.1007/BF01891204
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01891204