Optimal Allocations in the Construction ofk-Out-of-nReliability Systems

Abstract

We 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 are invested in building a component, then this component will function with probability P ( x ). Given a total income of A dollars, the problem of interest is to determine how much money we should invest in each component so as to maximize the probability of attaining a functioning system. This problem is considered both in the sequential and in the nonsequential cases. Conditions under which it is optimal to allocate A / n units at each stage, when A is your initial fortune, are presented. The special case P ( x ) = min( x , 1) is also considered in detail.