Sequential Designs with Application in Software Engineering

Abstract

Presented here is a Bayesian approach to test case allocation in the software reliability estimation. Bayesian analysis allows us to update our beliefs about the reliability of a particular partition as we test, and thus, dynamically re refine our allocation of test cases during the reliability testing process. We started with a fully sequential sampling scheme to estimate the reliability of a software system using partition testing. We have shown both theoretically and through simulation that the proposed scheme always performs at least as well as fixed sampling approaches where test case allocation is predetermined, and in all but the most unlikely circumstances, outperform them. Based on the sequential allocation, a multistage sampling scheme is established, which is less time consuming and more e efficient. Meanwhile, an e efficient sampling scheme is also developed to accommodate more situations. In the last chapter, we extend our study from parallel systems to series systems. We again use a Bayesian approach to allocate test cases to estimate the reliability of a series system with two components. A second-order lower bound for the incurred Bayes risk is established theoretically and Monte Carlo simulations with several proposed sequential designs are implemented to achieve this second-order lower bound for the incurred Bayes risk is established theoretically and Monte Carlo simulations with several proposed sequential designs are implemented to achieve this second-order lower bound.