Optimal Sequencing of Items In a Consecutive-2-out-of-n System

A consecutive-2-out-of-n system is an array of n items in a line such that the system fails if and only if two consecutive items both fail. Suppose that the items have different probabilities of failing and that the system can be arranged into any sequence of the n items. Which sequence minimizes the probability of a system failure? It has been conjectured that the best sequence is one which essentially interlaces the more reliable items with the less reliable items. This paper partially supports the conjecture by proving it for the case that: a) the n probabilities take on only two distinct values, and b) the n probabilities take on only three distinct values, including either a zero or a one.