The purpose of this paper is to use Bayesian probability theory to analyze the software reliability model with multiple types of faults. The probability that all faults are detected and corrected after a series of independent software tests and correction cycles is presented. This in turn has a number of applications, such as how long to test a software, estimating the cost of testing, etc.
The use of Bayesian probabilistic models, when compared to traditional point forecast estimation models, provides tools for risk estimation and allows decision makers to combine historical data with subjective expert estimates. Probability evaluation is done both prior to and after observing the number of faults detected in each cycle. The conditions under which these two measures, the conditional and unconditional probabilities, are the same is also shown. Expressions are derived to evaluate the probability that, after a series of sequential independent reviews have been completed, no class of fault remains in the software system by assuming the prior distribution as Poisson and binomial.
From results in Sections 4 and 5 it can be observed that the conditional and unconditional probabilities are the same if the prior probability distribution is Poisson and binomial. In these cases the confidence that all faults are deleted is not a function of the number of faults observed during the successive reviews but it is a function of the number of reviews, the detection probabilities and the mean of the prior distribution. This is a remarkable result because it gives a circumstance in which the statistical confidence from a Bayesian analysis is actually independent of all observed data. From the result in Section 4 it can be seen that exponential formula could be used to evaluate the probability that no fault remains when a Poisson prior distribution is combined with a multinomial detection process in each review cycle.
The paper is part of research work for a PhD degree.
Vasanthi, T. and Arulmozhi, G. (2013), "Software reliability estimation using Bayesian approach", International Journal of Quality & Reliability Management, Vol. 30 No. 1, pp. 97-107. https://doi.org/10.1108/02656711311288441
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