Abstract:
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In the context of reliability, testing the homogeneity of a Poisson process often sparks interest and previous studies, notably by Laplace and Bain et al. and Engelhardt et al. offer implementable methodologies. Interestingly, some of these tests do not preserve symmetry under changing alternatives. In this work, staying under the overarching assumption of Poissonness, we offer an alternative, based on a careful reversal of event times, which will lead to an enhanced power in certain cases. Such situations will be characterized under both time and failure truncated sampling schemes and using alternatives that are both smooth (i.e. power law or Weibull intensity) and rough (i.e. step intensities). In addition to exploring real world examples, we shall formulate a scheme to generalize the approach to testing any given rate, liberating the analyses from the strict confines of homogeneity.
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