Fuzzy Availability Based on Affine Arithmetic and Markov Process

This paper proposes a novel approach of fuzzy availability modeling based on probabilistic approach, employs affine arithmetic together with Markov process. Availability models based on Markov process allow failure, maintenance to be specified in a concise manner. Under a Markov model from which transient availability and steady-state availability can be easily obtained. In practice, sometimes we can´t have the exact values of failure rate, repairing rate or other system parameters but with some uncertainty about these values. This is quite common for systems in modern large-scale monitor system and the control system, where many system parameters are not normalized. For the deviation explosion of fuzzy dependability analysis based on fuzzy set or interval arithmetic, affine forms of bounded uncertain quantities and affine arithmetic are introduced into modeling and calculating the dependability index. Using Markov process and affine arithmetic, the probability of each state at moment t can be calculated and then the fuzzy dependability curve of system will be built.