Optimal selection and release problem in software testing process: A continuous time stochastic control approach

Abstract

This paper studies a joint selection of test cases and release problem for a software under test with predetermined classes of test cases and release time deadline. The software test manager can make three alternative choices dynamically during software testing progress before the deadline: continue testing and select a class of test cases, release the software, or scrap the software, with the objective of minimizing the cumulative testing cost plus penalty cost after releasing or scrapping the software. We formulate the problem as a continuous time stochastic control model and provide a mathematically rigorous method to establish the concavity of the optimal cost function. Based on this property, we are able to characterize that the optimal release policy has a threshold structure. Moreover, the thresholds are founded to be monotone in the residual time length in the case of homogeneous release cost. Besides, we put forward a method based on low convex envelope and discover that the optimal selection policy also has a threshold or other simple structure, if the running cost or the removal cost is the same for all classes. Finally, we present an approximation algorithm of computing the optimal cost function, by which some numerical examples are studied to justify our theoretical results and the robustness of our policy. We also conduct a case study to compare our dynamic selection and release testing policy with two other commonly used testing policies and find that our policy is the best in most instances.