Abstract
Usually, the lifetimes of components in operation and in warm standby are assumed to be random variables. The probability distributions of the random variables have crisp parameters. In many practical situations, the parameters are difficult to determine due to uncertainties and imprecision of data. So it is appropriate to assume the parameters to be fuzzy variables. In this paper, the lifetimes of components in operation and in warm standby are assumed to have random fuzzy exponential distributions, then reliability and mean time to failure (MTTF) of the warm standby systems are given. Finally, a numerical example is presented.
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