An additive Chen‐Weibull distribution and its applications in reliability modeling
Tien Thanh Thach, Radim Briš
Abstract
Abstract In this article, we introduce a new lifetime distribution with increasing and bathtub‐shaped failure rates. Some statistical properties of the proposed distribution are studied. We use the method of maximum likelihood for estimating the model parameters and reliability characteristics and discuss the interval estimates using asymptotic confidence intervals and bootstrap confidence intervals on one hand, and we provide Bayes estimators and highest posterior density intervals for the parameters via Hamiltonian Monte Carlo simulation method on the other hand. We demonstrate the superiority of the proposed distribution by fitting two reliability data sets well‐known from references.
Topics & Concepts
Weibull distributionConfidence intervalEstimatorStatisticsReliability (semiconductor)Monte Carlo methodBayes' theoremMathematicsApplied mathematicsConfidence distributionBathtubComputer scienceBayesian probabilityPhysicsQuantum mechanicsArchaeologyHistoryPower (physics)Statistical Distribution Estimation and ApplicationsProbabilistic and Robust Engineering DesignReliability and Maintenance Optimization