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.

中文翻译：

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Chen-Weibull可加分布及其在可靠性建模中的应用

在本文中，我们介绍了一种新的寿命分布，其故障率不断增加且呈浴缸状。研究了建议分布的一些统计性质。我们使用最大似然法估计模型参数和可靠性特征，并一方面讨论使用渐近置信区间和自举置信区间的区间估计，然后通过汉密尔顿蒙特卡洛模拟提供参数的贝叶斯估计和最高后验密度区间另一方面。我们通过拟合参考文献中众所周知的两个可靠性数据集来证明建议的分布的优越性。