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The use of the compound Poisson local formulation of Stein's method to obtain reliability bounds is discussed. In the context of the consecutive-k-out-of-n model, the approximations obtained are comparable with the best known for the system, which rely heavily on its special structure. In contrast, Stein's method for the compound Poisson approach can be applied equally effectively in many more-complicated models.>
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Barbour et al. (1995) studied this question.
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