Two-Sample Bayesian Predictive Analyses for an Exponential Non-Homogeneous Poisson Process in Software Reliability
ABSTRACT
The Goel-Okumoto software reliability model is one of the earliest attempts to use a non-homogeneous Poisson process to model failure times observed during software test interval. The model is known as exponential NHPP model as it describes exponential software failure curve. Parameter estimation, model fit and predictive analyses based on one sample have been conducted on the Goel-Okumoto software reliability model. However, predictive analyses based on two samples have not been conducted on the model. In two-sample prediction, the parameters and characteristics of the first sample are used to analyze and to make predictions for the second sample. This helps in saving time and resources during the software development process. This paper presents some results about predictive analyses for the Goel-Okumoto software reliability model based on two samples. We have addressed three issues in two-sample prediction associated closely with software development testing process. Bayesian methods based on non-informative priors have been adopted to develop solutions to these issues. The developed methodologies have been illustrated by two sets of software failure data simulated from the Goel-Okumoto software reliability model.
The Goel-Okumoto software reliability model is one of the earliest attempts to use a non-homogeneous Poisson process to model failure times observed during software test interval. The model is known as exponential NHPP model as it describes exponential software failure curve. Parameter estimation, model fit and predictive analyses based on one sample have been conducted on the Goel-Okumoto software reliability model. However, predictive analyses based on two samples have not been conducted on the model. In two-sample prediction, the parameters and characteristics of the first sample are used to analyze and to make predictions for the second sample. This helps in saving time and resources during the software development process. This paper presents some results about predictive analyses for the Goel-Okumoto software reliability model based on two samples. We have addressed three issues in two-sample prediction associated closely with software development testing process. Bayesian methods based on non-informative priors have been adopted to develop solutions to these issues. The developed methodologies have been illustrated by two sets of software failure data simulated from the Goel-Okumoto software reliability model.
KEYWORDS
Nonhomogeneous Poisson Process, Software Reliability Models, Non-Informative Priors, Bayesian Approach
Nonhomogeneous Poisson Process, Software Reliability Models, Non-Informative Priors, Bayesian Approach
Cite this paper
Akuno, A. , Orawo, L. and Islam, A. (2014) Two-Sample Bayesian Predictive Analyses for an Exponential Non-Homogeneous Poisson Process in Software Reliability. Open Journal of Statistics, 4, 742-750. doi: 10.4236/ojs.2014.49069.
Akuno, A. , Orawo, L. and Islam, A. (2014) Two-Sample Bayesian Predictive Analyses for an Exponential Non-Homogeneous Poisson Process in Software Reliability. Open Journal of Statistics, 4, 742-750. doi: 10.4236/ojs.2014.49069.
References
[1] Nuria, T.R. (2011) Stochastic Comparisons and Bayesian Inference in Software Reliability. Ph.D. Thesis, Universidad Carlos III de Madrid, Madrid. [2] Satya, P., Bandla, S.R. and Kantham, R.R.L. (2011) Assessing Software Reliability Using Inter Failures Time Data. International Journal of Computer Applications, 18, 975-978. [3] Daniel, R.J. and Hoang, P. (2001) On the Maximum Likelihood Estimates for the Goel-Okumoto Software Reliability Model. The American Statistician, 55, 219-222.
http://dx.doi.org/10.1198/000313001317098211 [4] Meth, M. (1992) Reliability Growth Myths and Methodologies: A Critical View. Proceedings of the Annual Reliability and Maintainability Symposium, New York, 230-238. [5] Yu, J.-W., Tian, G.-L. and Tang, M.-L. (2007) Predictive Analyses for Nonhomogeneous Poisson Processes with Power Law Using Bayesian Approach. Computational Statistics & Data Analysis, 51, 4254-4268.
http://dx.doi.org/10.1016/j.csda.2006.05.010 [6] Razeef, M. and Mohsin, N. (2012) Software Reliability Growth Models: Overview and Applications. Journal of Emerging Trends in Computing and Information Sciences, 3, 1309-1320. [7] Akuno, A.O., Orawo, L.A. and Islam, A.S. (2014) One-Sample Bayesian Predictive Analyses for an Exponential Non-Homogeneous Poisson Process in Software Reliability. Open Journal of Statistics, 4, 402-411.
http://dx.doi.org/10.4236/ojs.2014.45039 [8] Musa, J. (1987) Software Reliability: Measurement, Prediction, Application. McGraw-Hill, New York. [9] Sheldon, R. (2002) Simulation. 3rd Edition, Academic Press, Waltham. [10] Hossain, S.A. and Dahiya, R.C. (1993) Estimating the Parameters of a Non-Homogenous Poisson-Process Model for Software Reliability. IEEE Transactions on Reliability, 42, 604-612.
[1] Nuria, T.R. (2011) Stochastic Comparisons and Bayesian Inference in Software Reliability. Ph.D. Thesis, Universidad Carlos III de Madrid, Madrid. [2] Satya, P., Bandla, S.R. and Kantham, R.R.L. (2011) Assessing Software Reliability Using Inter Failures Time Data. International Journal of Computer Applications, 18, 975-978. [3] Daniel, R.J. and Hoang, P. (2001) On the Maximum Likelihood Estimates for the Goel-Okumoto Software Reliability Model. The American Statistician, 55, 219-222.
http://dx.doi.org/10.1198/000313001317098211 [4] Meth, M. (1992) Reliability Growth Myths and Methodologies: A Critical View. Proceedings of the Annual Reliability and Maintainability Symposium, New York, 230-238. [5] Yu, J.-W., Tian, G.-L. and Tang, M.-L. (2007) Predictive Analyses for Nonhomogeneous Poisson Processes with Power Law Using Bayesian Approach. Computational Statistics & Data Analysis, 51, 4254-4268.
http://dx.doi.org/10.1016/j.csda.2006.05.010 [6] Razeef, M. and Mohsin, N. (2012) Software Reliability Growth Models: Overview and Applications. Journal of Emerging Trends in Computing and Information Sciences, 3, 1309-1320. [7] Akuno, A.O., Orawo, L.A. and Islam, A.S. (2014) One-Sample Bayesian Predictive Analyses for an Exponential Non-Homogeneous Poisson Process in Software Reliability. Open Journal of Statistics, 4, 402-411.
http://dx.doi.org/10.4236/ojs.2014.45039 [8] Musa, J. (1987) Software Reliability: Measurement, Prediction, Application. McGraw-Hill, New York. [9] Sheldon, R. (2002) Simulation. 3rd Edition, Academic Press, Waltham. [10] Hossain, S.A. and Dahiya, R.C. (1993) Estimating the Parameters of a Non-Homogenous Poisson-Process Model for Software Reliability. IEEE Transactions on Reliability, 42, 604-612.