Constraints for safe partition testing strategies

Although previous studies have shown that partition testing strategies are not always very effective, with appropriate restrictions on the test allocation they can be guaranteed to be safe, in the sense that they will never be less reliable in detecting at least one failure than random testing, Several sufficient conditions for this have already been established in the literature. In particular, the proportional sampling strategy, which allocates test cases in proportion to the size of the subdomains from which they are selected, has been proved to be safe for all programs. In practice, since the number of test cases must be positive integers, often the proportional sampling strategy can only be approximated. This paper examines the necessary conditions for safe partition testing strategies. We also prove that, when the input domain is large enough with respect to the numbers of failure-causing inputs and test cases, a safe partition testing strategy cannot deviate from the proportional sampling strategy other than rounding due to integral constraints.