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Artificial Bee Colony with Levy Flights for Parameter Estimation of 3-p Weibull Distribution
Iranian Journal of Science and Technology, Transactions A: Science ( IF 1.7 ) Pub Date : 2020-05-16 , DOI: 10.1007/s40995-020-00886-4
Aynur Yonar , Nimet Yapici Pehlivan

Three-parameter (3-p) Weibull distribution is widely used to model failure distribution in reliability studies, and so the estimation of the parameters of this distribution is very crucial. The maximum likelihood (ML) method is the most popular method among parameter estimation methods. However, likelihood equations do not have explicit solutions for the 3-p Weibull distribution. Therefore, using metaheuristic methods is logical to obtain the ML estimation of 3-p Weibull distribution. The artificial bee colony (ABC) is one of the very simple, robust and population-based stochastic metaheuristic algorithms. The aim of this study is to obtain ML estimations of parameters of 3-p Weibull distribution by suggesting ABC with Levy flights (LABC) which improve the exploitation ability of the ABC algorithm. Furthermore, the ML estimation results of the LABC algorithm are compared with other well-known metaheuristic algorithms, standard ABC, particle swarm optimization, particle swarm optimization with Levy flights, simulated annealing, differential evolution and genetic algorithm through simulation studies and a real-data application. The results show that the suggested LABC algorithm gives more accurate ML estimations than the other metaheuristic algorithms for the parameter estimation of 3-p Weibull distribution.

中文翻译:

人工飞行蜂群进行3-p Weibull分布参数估计

三参数(3-p)威布尔分布广泛用于可靠性研究中的故障分布建模,因此,估算此分布的参数非常关键。在参数估计方法中,最大似然(ML)方法是最流行的方法。但是,似然方程对3-p威布尔分布没有明确的解决方案。因此,使用元启发式方法在逻辑上获得3-p Weibull分布的ML估计是合乎逻辑的。人工蜂群(ABC)是一种非常简单,强大且基于群体的随机元启发式算法。本研究的目的是通过建议具有征费飞行的ABC(LABC)来提高3-p威布尔分布参数的ML估计,从而提高ABC算法的利用能力。此外,通过模拟研究和实际数据应用,将LABC算法的ML估计结果与其他著名的元启发式算法,标准ABC,粒子群优化,带Levy飞行的粒子群优化,模拟退火,差分进化和遗传算法进行了比较。结果表明,对于3-p Weibull分布的参数估计,建议的LABC算法比其他元启发式算法提供了更准确的ML估计。
更新日期:2020-05-16
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