Optimal Allocations in the Construction of k-Out-of-n Reliability Systems.
STANFORD UNIV CALIF DEPT OF OPERATIONS RESEARCH
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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 Px, where Px is an increasing function such that PO 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 2 considers the case k 1. Conditions are presented on Px 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 4 the special case PX 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 Px x in Section 5. In the final section a related problem is considered. Modified author abstract
- Manufacturing and Industrial Engineering and Control of Production Systems