LEAST-COST FAILURE DIAGNOSIS IN UNCERTAIN RELIABILITY SYSTEMS

In many textbook solutions, for systems failure diagnosis problems stu died using reliability theory and artificial intelligence, the prior p robabilities of different failure states can be estimated and used to guide the sequential search for failed components after the whole syst em fails. In practice, however, both the component failure probabiliti es and the structure function of the system being examined-i.e., the m apping between the states of its components and the state of the syste m-may not be known with certainty. At best, the probabilities of diffe rent hypothesized system descriptions, each specifying the component f ailure probabilities and the system's structure function, may be known to a useful approximation, perhaps based on sample data and previous experience. Cost-effective diagnosis of the system's failure state is then a challenging problem. Although the probabilities of component fa ilures are aleatory, uncertainties about these probabilities and about the system structure function are epistemic. This paper examines how to make best use of both epistemic prior probabilities for system desc riptions and the information gleaned from costly inspections of compon ent states after the system fails, to minimize the average cost of ide ntifying the failure state. Two approaches are introduced for systems dominated by aleatory uncertainties, one motivated by information theo ry and the other based on the idea of trying to prove a hypothesis abo ut the identity of the failure state as efficiently as possible. While the general problem of cost-effective failure diagnosis is computatio nally intractable (NP-hard), both heuristics provide useful approximat ions on small to moderate sized problems and optimal results for certa in common types of reliability systems, including series, parallel, pa rallel-series, and k-out-of-n systems. A hybrid heuristic that adaptiv ely chooses which heuristic to apply next after any sequence of observ ations (component test results) appears to give excellent results. Sev eral computational experiments are summarized in support of these conc lusions, and extensions to reliability systems with repair are briefly considered. Next, it is shown that diagnosis can proceed when aleator y and epistemic uncertainties are both present using the same techniqu es developed for aleatory probabilities alone. If only the epistemic p robability distribution of system descriptions is known, then the same heuristics that are used to diagnose a system's failure state for sys tems with known descriptions can also be used to identify the system a nd diagnose its failure state when there is epistemic uncertainty abou t the identity of the system. This result suggests a unified approach to least-cost failure diagnosis in reliability systems with both aleat ory probabilities of component failures and epistemic probabilities fo r system descriptions. (C) 1996 Elsevier Science Limited.