Uncertainty analysis in software reliability modeling by Bayesian approach with maximum-entropy principle

In software reliability modeling, the parameters of the model are typically estimated from the test data of the corresponding component. However, the widely used point estimators are subject to random variations in the data, resulting in uncertainties in these estimated parameters. For large complex systems made up of many components, the uncertainty of each individual parameter amplifies the uncertainty of the total system reliability. Ignoring the parameter uncertainty can result in grossly underestimating the uncertainty in the total system reliability. This paper attempts to study and quantify the uncertainties in the software reliability modeling of a single component with correlated parameters and in a large system with numerous components. Previous works on quantifying uncertainties have assumed a sufficient amount of available data. However, a characteristic challenge in software testing and reliability is the lack of available failure data from a single test which often makes modeling difficult. This lack of data poses a bigger challenge in the uncertainty analysis of the software reliability modeling. To overcome this challenge, this paper proposes to utilize experts' opinions and historical data from previous projects to complement the small number of observations to quantify the uncertainties. This is done by combining the Maximum-Entropy Principle (MEP) into the Bayesian approach. This paper further considers the uncertainty analysis at the system level which contains multiple components, each with its respective model/parameter/uncertainty using a Monte Carlo approach. Some examples with different modeling approaches (NHPP, Markov, Graph theory) are illustrated to show the generality and effectiveness of the proposed approach. Furthermore, we illustrate how the proposed approach for considering the uncertainties in various components improves a large-scale system reliability model.