Jaiio2010presentation

1. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Non homogeneous and Compound Poisson Software Reliability Models ASSE 2010 - 11th Argentine Symposium on Software Engineering Néstor R. Barraza School of Engineering, University of Buenos Aires

2. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Software Development Phases Quality: Standards and Methods ISO-IEC 9126 (1991) ISO-IEC 14598 (1995) ISO-IEC 15504 (1998) CMMI (1991) Software Analysis Reliability Metrics

3. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Software Development Phases. Reliability SR Models Growth Models Markov Chains [7] Clusters [21] ...

4. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography

5. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography

6. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Software Reliability Growth Models Probability of failures is a stochastic process P(N(t) = n). Number of failures are predicted as the expected value µ(t) = E[N(t)].

7. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Software Reliability Growth Models Model µ(t) Delayed S-shaped a(1 − (1 + b t)e−b t ) Log Power α lnβ (1 + t) t Gompertz a(bc ) (−d t) ) Yamada Exponential a(1 − e−b c (1−e )

8. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Non-homogeneous Poisson process models λ(t)n P(N(t) = n) = exp(−λ(t)) n! λ(t) = a(1 − exp(−bt)) Goel − Okumoto 1 λ(t) = ln(λ0 θt + 1) Musa − Okumoto θ E[N(t)] = λ(t)

9. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Compound Poisson process models m (λ t)k P(N(t) = n) = exp(−λt) f ∗k (X1 + X2 + · · · + Xk = n) k! k =1 E[N(t)] = λ t E[X ]

10. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Compound Poisson. Compounding Distribution P(X ) = (1 − r )r x−1 Geometric. Sahinoglu’s ﬁrst proposal. aX exp(−a) P(X ) = X ! 1+exp(a) Poisson Truncated at Zero. This proposal.

11. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Compound Poisson. Parameters Estimation Mean value unbiased estimator ˆ m ˆ n λ= E[X ] = ∆t m ˆ ˆ  E[N(t)] = λ t E[X ] n Simple failure rate = t  ∆t

12. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Poisson Truncated at Zero. Parameter Estimation m ˆ 1 a= m xi Plackett i=1 xi >1 n{n−1} ˆ a= m n Tate and Goen (Unbiased Minimum Varianze) {m} n where m is the Stirling number of the second kind

13. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Poisson Truncated at Zero. Mode Estimator Diminution in the cluster size as the testing phase progresses is better taken into account by the mode estimator. Also it has faster adaptation.

14. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Software Reliability models prediction

15. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Software Reliability models prediction

16. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Software Reliability Growth Models Comparison Compound Non-Homogeneous Linear m(t) Non linear m(t) Available for several ML convergence problem Estimation methods Input: Mean time Input: Arrival rate and between failures failures clusters size m(t) adjusted by m(t) adjusted by the inhomogenity cluster size expectation Parameters are Parameters are estimated simultaneously estimated independently

26. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Compound Non Homogeneous Poisson? m (λ(t))k P(N(t) = n) = exp(−λ(t)) f ∗k (X1 +X2 +· · ·+Xk = n) k! k =1 ˆ ˆ E[N(t)] = λ(t) E[X ]

27. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Software Reliability and Quality Models SEI CMM Level Multiplier Level 1 1.5 Level 2 1 Level 3 0.4 Level 4 0.1 Level 5 0.05 Parameter adjustement as proposed in [11].

28. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Software Reliability Actual Practice Predicted by experts (too conservative or too optimistic) Lack of failures reports Failures history ignored Released time badly estimated Released when major bugs have been ﬁxed

33. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Conclusions A comparison between two Poisson based models has been shown The behavior of the mode estimator has been studied Results for real data were analyzed Advantages and Disadvantages has been pointed out

34. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Bibliography Almering V., von Genuchten M., Cloudt G., Sonnemans P. J. M.: Using Software Reliability Growth Models in Practice, IEEE Software, 24, 82-88 (2007) Barraza N. R., Applications and Analysis of Cooperative Phenomena using Statistical Mechanics, Contagion and Chains of Rare Events, Ph.D. Thesis, School of Engineering, University of Buenos Aires (1999) Barraza N. R., Pfefferman J. D., Cernuschi-Frï£¡as B., Cernuschi F.: An application of the chains-of-rare-events model to software development failure prediction, in Proc. 5th Int. Conf. Reliable Software Technologies. ser. Lecture

35. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Notes in Computer Science, H. B. Keller and E. Plï£¡dereder, Eds: Springer-Verlag, 1845, 185-195 (2000). Blocklehurst S., Chan P. Y., Littlewood B., Snell J.: Recalibrating Software Reliability Models, IEEE Trans. on Soft. Eng., 16, 458-470 (1990) Goel N. L., Okumoto K., Time-dependent error detection rate model for software reliability and other performances measures, IEEE Trans. on Reliability 28, 206-211 (1979) Gokhale, Swapna S. and Trivedi, Kishor S.: Log-Logistic Software Reliability Growth Model, The 3rd IEEE International Symposium on High-Assurance Systems

36. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Engineering, pp. 34-41, IEEE Computer Society, Washington, DC, USA (1998) Goseva-Popstojanova K., Trivedi K.: Failure Correlation in Software Reliability Models, IEEE Trans. on Reliability, 49, 37-48 (2000) Hossain S. A., Dahiya R. C.: Estimating the Parameters of a Non-homogeneus Poisson-Process Model for Software Reliability, IEEE Transactions on Reliability, 42, 604-612 (1993) Jelinski Z, Moranda P.: Software Reliability Research, in Statistical Computer Performance Evaluation, ed. W. Freiberger, New York, Academic Press, 465-484 (1972)

37. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Jeske D. R. and Pham H.: On the Maximum Likelihood Estimates for the Goel-Okumoto Software Reliability Model, The American Statistician, 55, 219-222 (2001) Cole G. F. and Keene S. N., Reliability and Growth of Fielded Software, Reliability Review, 5-26, (1994) Littlewood B., Verral J., A Bayesian Reliability Growth Model for Computer software Reliability, Proc. IEEE Symposium on Computer Software Reliability, New York, 70-76 (1973) Musa, J. D., Iannino A., and Okumoto K.: Software Reliability, Measurement, Prediction, Application, McGraw-Hill, (1989)

38. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Musa, J. D., Okumoto K.: Logarithmic Poisson Execution Time Model for Software Reliability Measurement, Proc. 7th. Int. Conf. Software Eng., 230-238 (1984) Plackett R. L.: The Truncated Poisson Distribution, Biometrics, 9, 485-488 (1953) Ray, B. K., Liu Z., Ravishanker N.: Dynamic Reliability Models for Software Using Time-Dependent Covariates, ASA Technometrics, 48, 1-10 (2006) Sahnioglu M.: Compound Poisson Software Reliability model, IEEE Trans. Soft. Eng. 18, 624-630 (1992) Sahnioglu M. and Can U.: , Alternative Parameter Estimation Methods for the Compound Poisson Software

39. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Reliability Model with Clustered Failure Data, Software Testing, Veriﬁcation and Reliability. 7, 35-37 (1997) Stringfellow C. and Andrews A. A.: An Empirical Method for Selecting Software Reliability Growth Models, Empirical Software Engineering, 7, 319-343, (2002). Tate R. F. and Goen R. L.: Minimum Variance Unbiased Estimation for the Truncated Poisson Distribution, Annals of Mathematical Statistics, 29, 755-765 (1958) Tian J.: Better reliability assessment and prediction through data clustering, IEEE Trans. Soft. Eng. 28, 997-1007 (2002) The Data & Analysis Center for Software, http://www.thedacs.com

40. Title Software Reliability Software Reliability Growth Models Non-homogeneous Poisson process models SRGM Comparison Software Reliability Actual Practice Conclusions Bibliography Xie M., Hong G. Y., Wohlin C.: A Practical Method for the Estimation of Software Reliability Growth in the Early Stage of Testing, Proc. of 7th Intl. Symposium on Software Reliability Engineering, Albuquerque, USA, 116-123 (1997) Yamada S., Ohba M., Osaki S.: S-Shaped Software Reliability Growth Models and Their Applications, IEEE Trans. Reliability, 33, 289-292, (1984) Zhao M., Xie M.: On the Log-Power NHPP Software Reliability Model, Proc. of 3rd Intl. Symposium on Software Reliability Engineering, Research Triangle Park, North Carolina, 14-22. (1992)

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