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On the q-Weibull distribution for reliability applications: An adaptive hybrid artificial bee colony algorithm for parameter estimation

机译：关于可靠性应用的q-Weibull分布：参数估计的自适应混合人工蜂群算法

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摘要

The q-Weibull model is based on the Tsallis non-extensive entropy [22] and is able to model various behaviors of the hazard rate function, including bathtub curves, by using a single set of parameters. Despite its flexibility, the q-Weibull has not been widely used in reliability applications partly because of the complicated parameters estimation. In this work, the parameters of the q-Weibull are estimated by the maximum likelihood (ML) method. Due to the intricate system of nonlinear equations, derivative-based optimization methods may fail to converge. Thus, the heuristic optimization method of artificial bee colony (ABC) is used instead. To deal with the slow convergence of ABC, it is proposed an adaptive hybrid ABC (AHABC) algorithm that dynamically combines Nelder-Mead simplex search method with ABC for the ML estimation of the q-Weibull parameters. Interval estimates for the q-Weibull parameters, including confidence intervals based on the ML asymptotic theory and on bootstrap methods, are also developed. The AHABC is validated via numerical experiments involving the Weibull ML for reliability applications and results show that it produces faster and more accurate convergence when compared to ABC and similar approaches. The estimation procedure is applied to real reliability failure data characterized by a bathtub-shaped hazard rate.
机译：q-Weibull模型基于Tsallis非扩展熵[22]，并且能够通过使用一组参数来建模危害率函数的各种行为，包括浴盆曲线。尽管q-Weibull具有灵活性，但由于参数估计复杂，因此尚未在可靠性应用中广泛使用。在这项工作中，q-Weibull的参数通过最大似然（ML）方法估算。由于非线性方程组的复杂性，基于导数的优化方法可能无法收敛。因此，代之以使用人工蜂群（ABC）的启发式优化方法。为了解决ABC的收敛速度慢的问题，提出了一种自适应混合ABC（AHABC）算法，该算法将Nelder-Mead单纯形搜索方法与ABC动态结合起来，用于估计q-Weibull参数的ML。还开发了q-Weibull参数的区间估计，包括基于ML渐近理论和自举法的置信区间。通过涉及Weibull ML的数值实验验证了AHABC在可靠性方面的应用，结果表明，与ABC和类似方法相比，它产生更快，更准确的收敛。该估计程序应用于以浴缸形危险率为特征的真实可靠性故障数据。

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