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We present a new inspection policy useful when testing is needed to detect failures of a single-unit system. It is supposed that tests may fail and give an erroneous result. The inspection policy minimizing cost per unit of time for an infinite time span is also discussed. In addition, we study the behaviour of the optimum policy for some time to failure distributions often assumed in reliability: exponential and Pareto.

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This paper deals with the maintenance policy of a system subject to periodical inspections aimed at detecting the occurrence of failures. After the first N − 1 failure, the system undergoes an imperfect repair that brings the system back to the operating condition while the Nth failure is followed by a perfect repair restoring the unit to an as-good-as-new condition. The limiting average availability as well as the minimum cost policy are discussed.