Exponentiated additive Weibull distribution

المجلة: Reliability Engineering & System Safety

سنة النشر: 2020

تاريخ النشر: 2020-01-01

Additive Weibull distribution combining two Weibull distributions was proposed by Xie and Lai [1]. In this paper, we propose a generalization of this distribution which is called exponentiated additive Weibull distribution. It includes a set of exponentiated distributions such as modified generalized linear failure rate, exponentiated Weibull and exponentiated exponential distributions in addition to some widely well known distributions such as additive Weibull, modified Weibull distributions, among others. It represents a flexible model for reliability analysis such as reliability engineering, firmware reliability, decision-making reliability, and cost analysis. Some statistical properties of the new distribution are presented. The estimation of five parameters by maximum likelihood is studied and the observed information matrix is computed. Finally, three real data sets are used to compare the proposed distribution to five of its sub-models. The results showed that the new distribution provides a better fit than its sub-models.

A new extension of the modified Weibull distribution with applications for engineering data

المجلة: Probabilistic Engineering Mechanics

سنة النشر: 2023

تاريخ النشر: 2023-10-01

In this study, a novel extension of the three-parameter modified Weibull distribution called the NMW3 distribution is proposed. The NMW3 distribution exhibits increasing or bathtub-shaped hazard rates, which can be beneficial in the context of reliability. The statistical characteristics of the NMW3 distribution are examined, including the difference between the change points of the hazard rate and the mean residual lifetime functions. Additionally, the sensitivities of the parameters and the flatness of the bathtub curve of the NMW3 distribution are discussed. The Weibull probability paper is utilized to characterize plots related to the NMW3 distribution. The parameters of the NMW3 distribution are estimated using both the graphical approach and the maximum likelihood method. Through the analysis of three real data sets, it is demonstrated that the NMW3 distribution outperforms existing extensions of the modified Weibull distributions, highlighting its practical importance. Finally, a reduced distribution of the NMW3 distribution is proposed, and it shows that the reduced distribution has almost the same advantageous characteristics as the NMW3 distribution.

Estimations from the exponentiated rayleigh distribution based on generalized Type-II hybrid censored data

المجلة: Journal of the Egyptian Mathematical Society

سنة النشر: 2017

تاريخ النشر: 2017-01-12

In this article, unknown parameters of exponentiated Rayleigh distribution based on generalized Type II Hybrid censored data, survival function, failure rate function and coefficient of variation are derived by applying the maximum likelihood, Bayes and percentile bootstrap methods. Approximate confidence intervals for the unknown parameters, survival function, failure rate function and coefficient of variation are obtained. We study Bayes estimates under gamma priors distributions depending on symmetric and asymmetric loss functions via the Gibbs within Metropolis-Hasting samplers procedure. Finally, the proposed methods can be understood through illustrating the results of the real data analysis.