Optimal diagnostic procedure for failures in a series system

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Abstract
A mathematical model is developed for diagnosing a faulty component module in a series system when discernible symptoms are not observable. The modules have arbitrary life-time distributions. An optimal testing sequence for searching a faulty module yielding minimum expected testing cost is developed, based on the causative failure probabilities of the modules conditioned on their ages at system failure, and their associated testing costs. The necessary and sufficient conditions satisfied by such a sequence are derived.

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