Some Reliability Fault-Testing Models

This paper presents several fault-testing models. Our system is composed of n components that either work or fail. The systems treated are the k-out-of-n type (k/n). This system works if and only if k or more of its components work, making the series (n/n) and parallel (1/n) systems special cases. Components can be individually tested and tests give perfect information. Each test has a time to complete it and testing procedures are judged by the expected cumulative testing time they require. In the first model, the components are assumed to function or fail independently of each other. A feasible test procedure must determine (as) if the system is working or has failed. This is solved for the series and parallel systems and, under a possibly restrictive hypothesis, for the general k/n system. In another model, the components are assumed to be nominally independent conditioned on the system being failed. Here a feasible test procedure must locate all failed components. This problem is solved for the general k/n system.