SYSTEM FAILURE STATISTICS - SOME ASYMPTOTIC FORMULAS

We derive asymptotic formulae for the pdf and rail probability of a ra ndom variable D that arises as a summation of Gamma(nu,alpha)-distribu ted observations X-i occurring as a Poisson process with rate lambda. This is used to determine the reliability of a system that fails occas ionally and randomly and whose dominant failure modes give rise to Gam ma-distributed costs and/or down-times. It therefore provides accurate confidence intervals for the associated costs or down-times in some p eriod T of service or of observation.