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Linear Poisson checking schedules. (English) Zbl 0847.90061
Summary: The problem of minimizing expected cost until detection of failure is addressed here, using random checking schedules. Homogeneous Poisson checking processes are investigated first, leading to the explicit determination of the optimal solution in a simple nonlinear programming problem. Then the case of non-homogeneous Poisson processes, with linear intensity, is considered. In this case, an approximation of the original problem is discussed. A unique optimal solution is proved to exist and it is then characterized, using the Kuhn-Tucker conditions.
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