The Asymptotic Time to Failure of a Mechanical System of Parallel Members

Abstract

A mechanical system of parallel members differs from the usual parallel element model studied in reliability monographs in that the nonfailed members at any instant must share an applied system load according to some rule. The resulting dependence among members causes difficulty in deriving useful exact results. However under certain reasonable probabilistic assumptions regarding single member failure, system loading and member load sharing, it can be shown that the system failure time is asymptotically normally distributed as the number of members grows large. We give the asymptotic mean and variance as functions of the parameters of loading and single member behavior. We study several cases of practical importance and show that many of the behavioral features of single members carry over to the system. But on a load per member basis, the system is weaker than a single member in many respects. However the variance in system time to failure can be reduced by increasing the number of members.