Optimal Allocations in the Construction of k-Out-of-n Reliability Systems.

摘要

The authors want to build n components so as to form an n component system which will function if at least k of the components function. If x dollars is invested in building a component then this component will function with probability P(x),where P(x) is an increasing function such that P(O) = O. The problem of interest is to determine how much money should be invested in each component so as to maximize the probability of attaining a functioning system. The authors are interested in this problem both in the sequential and in the nonsequential case. Section 2considers the case k = 1. Conditions are presented on P(x) under which (a) it is optimal to put an equal investment in all n components and (b) it is optimal to put the total fortune A into a single component. In Section 3,it is shown that the equal investment condition carries over to the case of general k. In Section 4the special case P(X) = x in the sequential situation is considered and the optimal policy is determined when k = 2. A conjecture as to the optimal policy in the general case is also made. Several remarks are made concerning the non-sequential case with P(x) = x in Section 5. In the final section a related problem is considered. (Modified author abstract)