On the fuzzy reliability estimation for Lomax distribution

Al‐Noor, Nadia H.

doi:10.1063/1.5136219

Cited by 3 publications

(2 citation statements)

References 5 publications

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“…[27] estimated the parameters of Lomax distribution with fuzzy observations. Afterward, Al-Noor, N.H. [28] described the composite trapezoidal rule-based fuzzy reliability estimate for the Lomax distribution. As for the other life distribution, Baloui Jamkhaneh [29] and Kumar, P. [30] analyzed different life distributions such as Rayleigh and Weibull and gave fuzzy reliability and hazard function formulae, as well as their α-cut set.…”

Section: Introductionmentioning

confidence: 99%

Statistical Fuzzy Reliability Analysis: An Explanation with Generalized Intuitionistic Fuzzy Lomax Distribution

Kalam,

Cheng,

et al. 2023

Symmetry

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To illustrate data uncertainty, intuitionistic fuzzy sets simply use membership and non-membership degrees. However, in some cases, a more complex strategy is required to deal with imprecise data. One of these techniques is generalized intuitionistic fuzzy sets (GIFSs), which provide a comprehensive framework by adding extra factors that provide a more realistic explanation for uncertainty. GIFSs contain generalized membership, non-membership, and hesitation degrees for establishing symmetry around a reference point. In this paper, we applied a generalized intuitionistic fuzzy set approach to investigate ambiguity in the parameter of the Lomax life distribution, seeking a more symmetric assessment of the reliability measurements. Several reliability measurements and associated cut sets for a novel L-R type fuzzy sets are derived after establishing the scale parameter as a generalized intuitionistic fuzzy number. Additionally, the study includes a range of reliability measurements, such as odds, hazards, reliability functions, etc., that are designed for the Lomax distribution within the framework of generalized intuitionistic fuzzy sets. These reliability measurements are an essential tool for evaluating the reliability characteristics of various types of complex systems. For the purpose of interpretation and application, the results are visually displayed and compared across different cut set values using a numerical example.

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Section: Introductionmentioning

confidence: 99%

Statistical Fuzzy Reliability Analysis: An Explanation with Generalized Intuitionistic Fuzzy Lomax Distribution

Kalam,

Cheng,

et al. 2023

Symmetry

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“…In recent years, some scholars have extended the fuzzy set theory to reliability analysis. Hashim [18] considered the problem of the fuzzy reliability estimation for the Lomax distribution. The first step was to use the composite trapezoidal rule to estimate the fuzzy reliability based on its definition.…”

Section: Introductionmentioning

confidence: 99%

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

Hu,

Ren

2023

Axioms

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As a commonly used model in reliability analysis, the inverse Weibull distribution (IWD) is widely applied in various scientific fields. This paper considers the reliability estimation of the IWD based on intuitionistic fuzzy lifetime data. Firstly, the related concepts of the fuzzy set theory are reviewed, and the concepts of the intuitionistic fuzzy conditional density, intuitionistic fuzzy likelihood function, and intuitionistic fuzzy conditional expectation are obtained by extension. In classical estimations, the maximum likelihood estimators of parameters and reliability are derived. Due to the nonlinearity, the EM algorithm is used to obtain the maximum likelihood estimates. In the Bayesian estimation, the gamma prior is selected, and the Bayesian estimation of the parameters and reliability is conducted under the symmetric entropy and the scale square error loss function, respectively. Since the integrals are complicated, the Lindley approximation is used to approximate the Bayesian estimates. Then, the performance of these estimators is evaluated by the Monte Carlo simulation. The simulation results show that the Bayesian estimation is more suitable than the maximum likelihood estimation for the reliability estimation. Finally, a set of real data is used to prove the effectiveness of these proposed methods. Through these methods, the reliability of the intuitive fuzzy life data is accurately estimated, which provides an important reference for the reliability analysis in the scientific field.

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

Roohanizadeh

Jamkhaneh

Deiri

2022

Complex Intell. Syst.

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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.

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On the fuzzy reliability estimation for Lomax distribution

Cited by 3 publications

References 5 publications

Statistical Fuzzy Reliability Analysis: An Explanation with Generalized Intuitionistic Fuzzy Lomax Distribution

Statistical Fuzzy Reliability Analysis: An Explanation with Generalized Intuitionistic Fuzzy Lomax Distribution

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

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

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