Log-logistic distribution is a flexible distribution that can model a wide range of failure patterns in the field of electrical, electronic and mechanical engineering and is often used in reliability inference. However, the inference of the parameters and reliability function of the log-logistic distribution can be challenging, especially in small sample scenarios. In this paper, we propose a new inference framework based on the least squares estimator-based generalized pivotal quantities (LSE-GPQ) for the parameters and reliability functions of the log-logistic distribution, which can provide better coverage in small sample scenarios. We will compare the performance of our proposed method with traditional methods such as the MLE and parametric bootstrapping through simulation studies and real data applications.

翻译：对数逻辑分布是一种灵活的分布，能够建模电气、电子和机械工程领域中广泛的失效模式，并常用于可靠性推断。然而，对数逻辑分布的参数及可靠性函数的推断具有挑战性，尤其是在小样本场景下。本文提出一种基于最小二乘估计广义枢轴量（LSE-GPQ）的新型推断框架，用于对数逻辑分布的参数和可靠性函数，该框架能在小样本场景下提供更优的覆盖率。我们将通过模拟研究和实际数据应用，将所提方法的性能与传统方法（如MLE和参数自助法）进行比较。