STATISTICAL-RELIABILITY ANALYSIS FOR REPAIRABLE SYSTEMS

Abstract

A repairable system is a system which contains n components operating initially and m components standby. When any of the operating components fails,one of the standby

components

for repair.

is switched on and the failed unit is taken away

The system fails when the number of operating

units is less than a specific number.

The purpose of this thesis is to investigate the avail• ability and reliability of some repairable systems and inpart• icular that of the K-out-of-n system.

A system of N operating units and M standby units with repair facility is considered. using the ordinary birth-and-death process, a set of difference-differential equations is obtained. Solutions to the difference-differential equations are obtained in the cases N=l, M=l and N=2, M=l. In the case N=2 and M=l the problem becomes more complicated since a distinction between the three possible solutions:real roots;equal roots, and imaginary roots has to be done. The availability, average availability, reliability and mean time to system failure are calculated. More generally, the availability and reliability analysis of the K-out-of-n system is considered.