Component Level Versus System Level -Out-of- Assembly Systems

A well-known principle in engineering is that redundancy at the component level is generally more reliability effective than that at the system level. Here, the redundancy simply means that components are connected in parallel. Motivated by this principle, in this paper, a more general problem of assembling [Formula Omitted]-out-of-[Formula Omitted] systems optimally is studied. We consider two assembled systems: one is by assembling a [Formula Omitted]-out-of-[Formula Omitted] system and a [Formula Omitted]-out-of-[Formula Omitted] system at the system level, and the other is by assembling them at a component level. With some appropriate assumptions on [Formula Omitted] and [Formula Omitted], some results on stochastic comparisons of the two assembly systems are derived. From this result, some useful principles for assembling [Formula Omitted]-out-of-[Formula Omitted]-systems optimally are proposed. Two numerical examples are given to illustrate our results as well.