Parameters and reliability estimation for the weibull distribution based on intuitionistic fuzzy lifetime data

Abstract

In this paper, the definition of probability, conditional probability and likelihood function are generalized to the intuitionistic fuzzy observations. We focus on different estimation approaches of two-parameter Weibull (TW) distribution based on the intuitionistic fuzzy lifetime data including, maximum likelihood (ML) and Bayesian estimation methodology. The ML estimation of the parameters and reliability function of TW distribution is provided using the Newton–Raphson (NR) and Expectation–Maximization (EM) algorithms. The Bayesian estimates are provided via Tierney and Kadane’s approximation. In the Bayesian estimation approach, for the shape and scale parameters, the Gamma and inverse-Gamma priors are considered, respectively. Finally, a simulated data set is analyzed for illustrative purposes to show the applicability of the proposed estimation methods. The Monte Carlo simulations are performed to find the more efficient estimator in the intuitionistic fuzzy environment. The performances of the ML and Bayesian estimates of the parameters and reliability function are compared based on the mean biased (MB) and mean squared errors (MSE) criteria.

Reliability Estimation of a Degradable System using Intuitionistic Fuzzy Weibull Lifetime Distribution

“…The fuzzy set theory normally offers a suitable tool for modelling imprecise data known as fuzzy number (FN), which is much more effective than analyzing only a specific value or classification 23) . used the fuzzy sets method to measure the system's Reliability.…”

Reliability Estimation of Inverse Weibull Distribution Based on Intuitionistic Fuzzy Lifetime Data

“…One of its important concepts is the fuzzy random variable proposed by Huibert [29]. Zahra et al [30] extended the definitions of probability, conditional probability, and likelihood function to intuitionistic fuzzy observations, and considered the parameter and reliability function estimation problem of the two-parameter Weibull distribution based on intuitionistic fuzzy lifetime data. ML estimators were obtained using the Newton-Raphson and EM algorithms, and Bayes estimators were obtained using Lindley and Tierney-Kadane approximations.…”