Nonparametric Analysis of the Order-Statistic Model in Software Reliability

In the literature on statistical inference in software reliability, the assumptions of parametric models and random sampling of bugs have been pervasive. We argue that both assumptions are problematic, the first because of robustness concerns and the second due to logical and practical difficulties. These considerations motivate the approach taken in this paper. We propose a nonparametric software reliability model based on the order-statistic paradigm. The objective of the work is to estimate, from data on discovery times observed within a type I censoring framework, both the underlying distribution F from which discovery times are generated and N, the unknown number of bugs in the software. The estimates are used to predict the next time to failure. The approach makes use of Bayesian nonparametric inference methods, in particular, the beta-Stacy process. The proposed methodology is illustrated on both real and simulated data

[1]  A. Raftery.  Inference and Prediction for a General Order Statistic Model with Unknown Population Size. , 1987 .

[2]  Thomas A. Mazzuchi,et al.  A Bayes empirical-Bayes model for software reliability , 1988 .

[3]  Bev Littlewood,et al.  A Non-Parametric Order Statistics Software Reliability Model , 1998, Softw. Test. Verification Reliab..

[4]  Jerald F. Lawless,et al.  Some Simple Robust Methods for the Analysis of Recurrent Events , 1995 .

[5]  Z. Jelinski,et al.  Software reliability Research , 1972, Statistical Computer Performance Evaluation.

[6]  Michael P. Wiper,et al.  Bayesian inference for a software reliability model using metrics information , 2001, ADIS.

[7]  Nozer D. Singpurwalla,et al.  Inference and Predictions from Poisson Point Processes Incorporating Expert Knowledge , 1995 .

[8]  S. Walker,et al.  Beta-Stacy processes and a generalization of the Polya urn scheme , 1997 .

[9]  T. Ferguson.  A Bayesian Analysis of Some Nonparametric Problems , 1973 .

[10]  M.-A. El-Aroui,et al.  A Bayes nonparametric framework for software-reliability analysis , 1996, IEEE Trans. Reliab..

[11]  Bev Littlewood,et al.  Likelihood Function of a Debugging Model for Computer Software Reliability , 1981, IEEE Transactions on Reliability.

[12]  Douglas R. Miller.  Exponential order statistic models of software reliability growth , 1986, IEEE Transactions on Software Engineering.

[13]  Ariela Sofer,et al.  A nonparametric software-reliability growth model , 1991 .

[14]  Purushottam W. Laud,et al.  Bayesian Nonparametric Inference for Random Distributions and Related Functions , 1999 .

[15]  Paul Damien,et al.  A Full Bayesian Non‐parametric Analysis Involving a Neutral to the Right Process , 1998 .

[16]  K. O. Ott,et al.  Statistical Evaluation of Major Human Errors During the Development of New Technological Systems , 1979 .

[17]  P. M. Nagel,et al.  Software reliability: Additional investigations into modeling with replicated experiments , 1984 .

[18]  Bev Littlewood,et al.  A Bayesian Reliability Growth Model for Computer Software , 1973 .

[19]  J. Bunge,et al.  Estimating the Number of Species: A Review , 1993 .

[20]  Harry Joe,et al.  Statistical Inference for General-Order-Statistics and Nonhomogeneous-Poisson-Process Software Reliability Models , 1989, IEEE Trans. Software Eng..