A fuzzy based approach for the design and evaluation of dependable systems using the Markov model

Dependability is a subject of great importance in the development of critical systems and may be quantified in terms of various factors, such as reliability, maintainability and availability, whose significance may vary between different applications. A generic technique based on the Markov model is proposed in this paper, using fuzzy theory, for the reliability and safety assessment of fault-tolerant computational systems, composed of replicated modules. As the Markov model requires some parameters which may not be precisely known during the calculation, this method allows uncertainty-based parameters that are represented as fuzzy numbers. As a consequence, the reliability and the safety time response are composed by several curves which have associated degrees of confidence. This result may be used to estimate the reliability and safety value range at a given instant of time where each value has an associated possibility degree in which the developer believes the system has.