Fuzzy system reliability analysis based on new aging indexes

The concept of aging plays an important role in reliability analysis. The aim of this paper is providing the novel method to definition aging indexes based on fuzzy random variables and using the concept of α-pessimistic in both parametric and non-parametric approaches. In parametric approach, the concepts of survival function, hazard rate function and mean residual function were extended for fuzzy random variables. After that, we obtain and analyse these indexes for fuzzy exponential and fuzzy two-parameter Weibull distributions as two frequently used lifetime distribution in reliability theory. Moreover, with the assumption that the distribution of fuzzy observations is unknown (non-parametric approach), first an estimate for the fuzzy distribution function is presented, and then an estimate for the aging indices of the system is investigated. To do this, the concept of fuzzy empirical distribution function is investigated as an estimator of cumulative distribution function. Moreover, some properties of investigated estimator have been established.