In this work, we develop a General Entropy loss function (GE) to estimate the reliability function of the Weibull distribution based on complete data. We do this by merging a weight into GE to produce a new loss function called weighted General Entropy loss function (WGE). We then use WGE to derive the reliability function of the Weibull distribution. Consequently, we discuss the loss functions for three different types of loss function, including squared error (SE), GE, and WGE. By using WGE, the proposed method Bayesian (BWGE) and the approximate Bayesian estimation (BLWGE) are examined and compared with other methods including maximum likelihood estimation, Bayesian estimation, and approximate Bayesian estimation under SE and GE by using Monte Carlo simulation. It is found that the proposed methods of the BWGE and the BLWGE present the best performance in estimating reliability according to the smallest values of mean square error (MSE).

在这项工作中，我们开发了一个通用熵损失函数 (GE) 来估计基于完整数据的威布尔分布的可靠性函数。我们通过将权重合并到 GE 中来产生一个新的损失函数，称为加权通用熵损失函数 (WGE)。然后我们使用 WGE 推导出威布尔分布的可靠性函数。因此，我们讨论了三种不同类型的损失函数的损失函数，包括平方误差 (SE)、GE 和 WGE。通过使用WGE，对提出的方法贝叶斯(BWGE)和近似贝叶斯估计(BLWGE)进行了检验，并通过蒙特卡罗模拟与SE和GE下的最大似然估计、贝叶斯估计和近似贝叶斯估计等其他方法进行了比较。