On the asymptotic behavior of adaptive testing strategy for software reliability assessment

In software reliability assessment, one problem of interest is how to minimize the variance of reliability estimator, which is often considered as an optimization goal. The basic idea is that an estimator with lower variance makes the estimates more predictable and accurate. Adaptive Testing (AT) is an online testing strategy, which can be adopted to minimize the variance of software reliability estimator. In order to reduce the computational overhead of decision-making, the implemented AT strategy in practice deviates from its theoretical design that guarantees AT's local optimality. This work aims to investigate the asymptotic behavior of AT to improve its global performance without losing the local optimality. To this end, a new AT strategy named Adaptive Testing with Gradient Descent method (AT-GD) is proposed. Theoretical analysis indicates that AT-GD, a locally optimal testing strategy, converges to the globally optimal solution as the assessment process proceeds. Simulation and experiments are set up to validate AT-GD's effectiveness and efficiency. Besides, sensitivity analysis of AT-GD is also conducted in this study.