A nonexponential approach to availability modeling

Most current state-of-the-art availability models are based on continuous-time Markov chains. This involves restrictive assumption about the probability distribution for both failure times and repair times being exponential. In many situations, the exponential distribution is not applicable for failure times and/or repair times. A general approach for calculating instantaneous availability is presented. It is applicable to systems or subsystems which are assumed to be returned to approximately their original state upon the completion of repair. It is based on the equation: A(t)=R(t)+∫^t₀R(t-s)m(s)ds. The first case study is a validation study since the uptimes and downtimes are both assumed to follow an exponential distribution. In this case, an analytical result for A(t) can be obtained. Thus, the results for the analytical approach and the proposed approach can be compared. An analysis of the results shows the proposed approach to be very reasonable. In the second case study, the uptimes are assumed to follow a Weibull distribution while the downtimes have a lognormal distribution