Khan Faridoon, Ahmad Zubair, Khosa Saima K, Alomair Mohammed Ahmed, Alomair Abdullah Mohammed, Alsharidi Abdulaziz Khalid
Pakistan Institute of Development Economics, Islamabad 44000, Pakistan.
Department of Statistics, Quaid-e-Azam University, Islamabad 44000, Pakistan.
Heliyon. 2023 Jun 16;9(6):e17238. doi: 10.1016/j.heliyon.2023.e17238. eCollection 2023 Jun.
Statistical modeling is a crucial phase for decision-making and predicting future events. Data arising from engineering-related fields have most often complex structures whose failure rate possesses mixed state behaviors (i.e., non-monotonic shapes). For the data sets whose failure rates are in the mixed state, the utilization of the traditional probability models is not a suitable choice. Therefore, searching for more flexible probability models that are capable of adequately describing the mixed state failure data sets is an interesting research topic for researchers. In this paper, we propose and study a new statistical model to achieve the above goal. The proposed model is called a new beta power very flexible Weibull distribution and is capable of capturing five different patterns of the failure rate such as uni-modal, decreasing-increasing-decreasing, bathtub, decreasing, increasing-decreasing-increasing shapes. The estimators of the new beta power very flexible Weibull distribution are obtained using the maximum likelihood method. The evaluation of the estimators is assessed by conducting a simulation study. Finally, the usefulness and applicability of the new beta power very flexible Weibull distribution are shown by analyzing two engineering data sets. Using four information criteria, it is observed that the new beta power very flexible Weibull distribution is the best-suited model for dealing with failure times data sets.
统计建模是决策和预测未来事件的关键阶段。来自工程相关领域的数据通常具有复杂的结构，其故障率呈现混合状态行为（即非单调形状）。对于故障率处于混合状态的数据集，使用传统概率模型并非合适的选择。因此，寻找能够充分描述混合状态失效数据集的更灵活概率模型，对研究人员来说是一个有趣的研究课题。在本文中，我们提出并研究了一种新的统计模型以实现上述目标。所提出的模型称为新的贝塔幂非常灵活的威布尔分布，它能够捕捉故障率的五种不同模式，如单峰、先降后升再降、浴盆形、下降、先升后降再升的形状。新的贝塔幂非常灵活的威布尔分布的估计量通过最大似然法获得。通过进行模拟研究来评估估计量。最后，通过分析两个工程数据集展示了新的贝塔幂非常灵活的威布尔分布的实用性和适用性。使用四个信息准则，可以观察到新的贝塔幂非常灵活的威布尔分布是处理失效时间数据集的最合适模型。
