On the true detection probability of the uniformly optimal search plan

The gold standard for designing a search plan is to select a target distribution and then find the uniformly optimal search plan based on it. This approach has been successfully applied in several high-profile civil and military search missions. Since the target distribution is subjective and chosen at an analyst's discretion, it is natural to ask whether this approach can generate a search plan that maximizes the true detection probability at each moment. This article gives a negative answer by establishing that, under mild conditions, for a given target distribution and the optimal search plan based on it, there is another target distribution whose induced uniformly optimal search plan leads to an increased true detection probability at every moment. In particular, it implies that the problem of finding a search plan that maximizes the true detection probability at each moment remains unsolved.