Abstract
We describe a model for a random failure set in a fixed interval of the real line. (Failure sets are considered in input-domain-based theories of software reliability.) The model is based on an extended binary splitting process. Within the described model, we investigate the problem of how to select k test points such that the probability of finding at least one point of the failure set is maximized. It turns out that for values k > 2, the objective functions to be maximized are closely related to solutions of the Poisson-Euler-Darboux partial differential equation. Optimal test points are determined for arbitrary k in an asymptotic case where the failure set is, in a certain sense, “small” and “intricate,” which is the relevant case for practical applications.
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