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Abstract
This article deals with the optimal inspection of a stochastically failing system with known lifetime distribution when a failure can be detected by inspection only. At a predetermined moment a plan stops with a special action which is not necessary an inspection. The objective function is the expected loss per cycle. As the duration of checking is non-negligible there are three different kinds of errors concerning the systems state at the end of and inspection epoch. We derive several conditions for the (N-) optimality of inspection plans, and in case of a uniformly distributed lifetime of the system we calculate (N-) optimal plans, which we compare with the numerical results of Luss/Kander and Hunter.