An optimum testing algorithm for some symmetric coherent systems

Abstract A symmetric coherent system (or k-out-of-n system) is a system composed of n components CO1, CO2 …, COn, each component existing in either a working or failing state. Such a system is in a working state if and only if k or more of its components are working, where 1 ⩽ k ⩽ n. It is assumed that the components can only be tested individually, and every test gives perfect information as to whether the tested component is working or failing. Let Pi, be the a priori probability that the component COi is working and Ci, be the cost of testing component COi. An optimal (minimum total expected cost) testing algorithm is an algorithm to determine the condition of a given symmetric coherent system by testing some of its components individually. In general, such an algorithm is a sequential process, that is, the next component to be tested is a function of the outcomes of the tests already applied. Every (optimal) testing algorithm corresponds to a (optimal) feasible testing policy which is basically a binary rooted tree with some component assigned to each node. In this paper an algorithm is presented for constructing an optimal feasible testing policy for symmetric coherent systems, where C i P i ≠ C j P j and C i (1 − P i ) ≠ C j (1 − P j ) whenever i ≠ j. This algorithm can be implemented as an optimal testing algorithm with polynomial complexity. Moreover, it is proven that any optimal testing algorithm corresponds to some feasible testing policy which can be generated by this algorithm.