The hazard (failure) rate is a fundamental statistical indicator commonly used in both reliability and survival analyses. In practice, the hazard curve might exhibit a non-monotonic unimodal behavior. Thus, determining the highest point of the peak of a non-monotonic hazard function is indeed a point of interest in lifetime analysis. This study discusses the shape of the hazard function of the logistic Birnbaum-Saunders distribution and associate estimation. This model belongs to the generalized Birnbaum-Saunders family of positively skewed models with lighter and heavier tails than the conventional two-parameter Birnbaum-Saunders distribution. The latter model originated from a problem related to material fatigue, a phenomenon of interest in material sciences. In this paper, we establish that the hazard rate of the logistic Birnbaum-Saunders distribution is either unimodal or decreasing depending on the value of the shape parameter. We also estimate the critical value of the hazard rate, which is the highest point of the peak of the hazard function, using moment estimators. We perform extensive Monte Carlo simulations to examine estimation efficiency numerically; moreover, we analyze a data set for the sake of illustration.

风险（失败）率是可靠性和生存分析中常用的基本统计指标。在实践中，风险曲线可能表现出非单调的单峰行为。因此，确定非单调风险函数峰值的最高点确实是寿命分析中的一个兴趣点。本研究讨论了 Logistic Birnbaum-Saunders 分布和关联估计的风险函数的形状。该模型属于广义的 Birnbaum-Saunders 系列正偏斜模型，其尾部比传统的双参数 Birnbaum-Saunders 分布更轻更重。后一种模型源于与材料疲劳相关的问题，这是材料科学中的一种有趣现象。在本文中，我们确定 Logistic Birnbaum-Saunders 分布的风险率要么是单峰的，要么是下降的，这取决于形状参数的值。我们还使用矩估计量估计危险率的临界值，即危险函数峰值的最高点。我们进行了广泛的蒙特卡罗模拟，以数值方式检查估计效率；此外，为了说明起见，我们分析了一个数据集。