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Paper, PWASET Volume 26, 2007, ISSN 1307-6884, 720-725 c.
The Moranda’s Geometric de-Eutrophication model alleviates some of the objections to the Jelinski Moranda model for software failures. In Moranda Geometric de-Eutrophication model, N(t) is defined as the number of faults detected in the time interval (0, t]. In this paper, N(t) is studied as a pure birth stochastic process, where failure rates decrease geometrically with a detection and fixing of a fault. This paper demonstrates the use of a recursive scheme to study the probability of detecting ' n' number of bugs in time (0, t]. The method uses a constructed table which makes this method more easier compared to all the other existing methods to compute the Probability of removal of n number of faults in time (0,t] i.e. Pn (t), intensity function λ(t), and Probability that the software does not fail in the interval (t, t +t ] i.e. (t). In the proposed procedure Pn (t) involves (n +1) terms and each term is multiplied by a constant, obtained from the constructed table. The developed system performs with 90% accuracy as compared to earlier system and approximately 10% reduction in time for projects with size (delivered object code instructions) in the range of 5000-21000 and the tabular and the recursive technique has made the system simple to understand.
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PROCEEDINGS OF WORLD ACADEMY OF SCIENCE, ENGINEERING AND TECHNOLOGY VOLUME 26 DECEMBER 2007 ISSN 1307-6884
A Recursive Method for Reliability Computation of Moranda’s Geometric Software Reliability Model Parvinder Singh Sandhu, Amit Kamra, and Hari Singh
Pn (t) Probability of removal of n number of faults in time (0,t] m, k Parameters in the Geometric de- Eutrophication model T (T0, T1, T2...) fTi p.d.f of T μ(t) Mean number of faults discovered by time λ(t) Intensity function of the process N(t) τ Mission time of the software Rt (t) Probability that the software does not fail in the interval (t,t +t ]
Abstract—The Moranda’s Geometric de-Eutrophication model alleviates some of the objections to the Jelinski Moranda model for software failures. In Moranda Geometric de-Eutrophication model, N(t) is defined as the number of faults detected in the time interval (0, t]. In this paper, N(t) is studied as a pure birth stochastic process, where failure rates decrease geometrically with a detection and fixing of a fault. This paper demonstrates the use of a recursive scheme to study the probability of detecting ' n' number of bugs in time (0, t]. The method uses a constructed table which makes this method more easier compared to all the other existing methods to compute the Probability of removal of n number of faults in time (0,t] i.e. Pn (t), intensity function λ(t), and Probability that the software does not fail in the interval (t, t +t ] i.e. (t). In the proposed procedure Pn (t) involves (n +1) terms and each term is multiplied by a constant, obtained from the constructed table. The developed system
I. INTRODUCTION
T
HE times between failures are statistically independent exponential random variables with given failure rates and the failure rates decrease geometrically with the detection of a fault as in [18]. Reference [7] tells about the statistical methods of reliability handling. References [1],[2],[8]-[14] propose some basic concepts of software reliability, software reliability estimation and modeling and analysis of software reliability. Using an intuitive approach, Musa, Lannino, Okumoto [13] derived expression for mean and the intensity functions of the process N (t), which counts the number of faults, detected in the time interval [0,t] for the Moranda’s geometric de-Eutrophication model. In software reliability models times between failures category include models that provide estimates of the times between fail