 
Summary: AVAILABILITY OF CONTINUOUS SERVICE
AND COMPUTING LONG RUN MTBF AND
RELIABILITY FOR MARKOV SYSTEMS
John E. Angus
Claremont Graduate University
Claremont, CA 91711
john.angus@cgu.edu
December 6, 2000
Abstract
Steady state availability has long been a popular descriptor of effectiveness
for repairable systems because it captures both operability and repairability
aspects of the system. A related measure of effectiveness is the availability of
continuous service, which is particularly relevant for safety critical applications.
In this paper two different measures of this quantity are described for a repairable
system whose state is described by an ergodic Ūnite state space continuous time
Markov chain. Using these ideas, formulas for computing system long run mean
time between failures and the long run system reliability function are derived.
1. Introduction and Background
Consider a repairable system that may be in any one of the states in S = {0, 1, ..., J},
J a non negative integer, and suppose that the system state at time t is given by
