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This paper introduces a new distribution based on extreme value distribution. Some properties and characteristics of the new distribution such as distribution function, moment generating function and skewness and kurtosis are studied. Finally, by computing the maximum likelihood estimators of the new distribution's parameters, the performance of the model is illustrated via two real examples.

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In this paper, some reliability concepts have been investigated based on the α-pessimistic and its relationship with the α-cut of a fuzzy number. For this purpose, if the lifetime distribution of the system components is known, using the definition of the scale fuzzy random variable, based on α-pessimistic, some reliability criteria have been investigated. Also, suppose the lifetime distribution of the components is unknown or only the fuzzy observations of the lifetime of the features are available. In that case, the empirical distribution function of the fuzzy data is used to estimate the reliability, and some examples are provided to illustrate the results.
 

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In this paper, fuzzy order statistics are expressed based on the concept of α-value, and some of its applications in reliability have been examined. For this purpose, if the lifetime distribution of the system components is known, some of the reliability criteria of the $i$th order statistic using the definition of a fuzzy random variable based on the α-value have been investigated. Also, if the lifetime distribution of the components is unknown or only the fuzzy observations of the lifetime of the components are available, the empirical distribution function of the fuzzy data is used to estimate the reliability based on ordinal statistics, and examples are provided to illustrate the results.