Fault Diagnosis with Imperfect Tests

This paper derives a minimum s-expected cost sequence of built-in-tests (BITs) which will partition modular equipment into mutually exclusive groups of modules. After a fault in the equipment, one of these groups will be identified by a BIT diagnostic subsystem as the group which contains a faulty module. The BITs are imperfect in the sense only that they might not detect all of the possible faults in the equipment; they are perfect in the sense that fault indications are never false. The proportion of faults detectable by each BIT is known. Both the cost of a BIT and the probability that a BIT will pass or fail are functions of which modules are tested. A recursive algorithm is developed which determines a sequence of BITs with a minimum s-expected life-cycle cost. The recursive algorithm is applied to a 4-element numerical example. The algorithm has neither been proved nor implemented for a computer.