Renewal Model of Reliability for Series Systems - Revisited

The fact that failures follow the exponential distribution is almost universally accepted in reliability analysis. Two reasons are given for this assumption: (1) It is commonly assumed that electronic components do not wear out but are subject to random shocks which may cause failure. If these shocks form a Poisson process the underlying failure distribution is exponential. (2) Sufficiently complex equipment run for a sufficiently long time (failed components being replaced by good ones) will follow the exponential distribution. These reasons are investigated, especially the latter one. In many cases, equipment does not last long enough to reach the steady state alluded to in (2). For the special case where the failure law of (n=64,256,infinity) identical components is given by the gamma distribution (alpha = 2 (2) 12) the distribution of the time to next system failure has been recalculated and tabled over a range in which the system failure law differs markedly from exponential. (Author) Prepared in cooperation with Oceanweather Inc., White Plains, NY. and Kentucky Univ., Lexington.