Application of Supplementary Variables and Discrete Transforms in Availability and Reliability Analysis of a Parallel Redundant System with General Failure and Repair Time Distributions

Ilkka Virtanen

Abstract

The problem to be considered in this paper is as follows. A simple system consists of N (N>1) components that are redundantly connected in parallel. The running times of each individual component are identically and independently distributed random variables having a common general distribution. The repair times of the system are distributed according to another independent general distribution. The repair of the system starts when all the N components have failed, after completion of the repair of all the N components the system is put into operation again.

The object of the study is to find out both the transient state and steady state behaviour of the system, and, on the basis of this information to derive the most important reliability characteristics (i.e. reliability, availability and mean time to system failure MTSF) for the system. The behaviour of the system is described by state prababilities, a state (at time t) giving the number of failed components at that time. The system must have a little different state definition for availability analysis than for reliability analysis. This means that there also will be two separate models, one for the availability and another for the reliability and MTSF analysis of the system.

(Proceedings of The Turku School of Economics and Business Administration, Series A-12:1976, 15 p.)