Reliability estimation of Lomax distribution with fuzziness

Abstract

This paper considers the problem of estimating the reliability function for Lomax distribution with the presence of fuzziness through two procedures. The first procedure depends on fuzzy reliability definition that uses the composite trapezoidal rule in order to find the numerical integration and the second is Bayesian procedure which includes different cases depends on sample data and hyper-parameters of prior gamma distribution with squared error as a symmetric loss function and precautionary as an asymmetric loss function. In the Bayesian procedure, we proposed to consider three cases to estimate the fuzzy reliability with fuzzy observations, precise observations with fuzzy hyper-parameter, and fuzzy observations with fuzzy hyper-parameter.