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Two-Sample Bayesian Predictive Analyses for an Exponential non-Homogeneous Poisson Process in Software Reliability

Open Journal of Statistics 2014年第9期4卷 742-750页

作者： Albert Orwa Akuno Luke Akong’o Orawo Ali Salim Islam Department of Mathematics Egerton University Egerton Kenya

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.

关键词： nonhomogeneous Poisson Process Software Reliability Models non-informative Priors Bayesian Approach

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One-Sample Bayesian Predictive Analyses for an Exponential non-Homogeneous Poisson Process in Software Reliability

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Open Journal of Statistics 2014年第5期4卷 402-411页

作者： Albert Orwa Akuno Luke Akong’o Orawo Ali Salim Islam Department of Mathematics Egerton University Egerton Kenya

The Goel-Okumoto software reliability model, also known as the Exponential nonhomogeneous Poisson Process,is one of the earliest software reliability models to be proposed. From literature, it is evident that most of the study that has been done on the Goel-Okumoto software reliability model is parameter estimation using the MLE method and model fit. It is widely known that predictive analysis is very useful for modifying, debugging and determining when to terminate software development testing process. However, there is a conspicuous absence of literature on both the classical and Bayesian predictive analyses on the model. This paper presents some results about predictive analyses for the Goel-Okumoto software reliability model. Driven by the requirement of highly reliable software used in computers embedded in automotive, mechanical and safety control systems, industrial and quality process control, real-time sensor networks, aircrafts, nuclear reactors among others, we address four issues in single-sample prediction associated closely with software development process. We have adopted Bayesian methods based on non-informative priors to develop explicit solutions to these problems. An example with real data in the form of time between software failures will be used to illustrate the developed methodologies.

关键词： nonhomogeneous Poisson Process non-informative Priors Software Reliability Models Bayesian Approach

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