Reliability analysis is a specific field of statistics that studies failure time and its probability on a system. This branch of statistics takes an important place in many domains, especially in aeronautics. One of the most commonly used methods of reliability analysis is the hazard function which is defined for a specific instance in time, given the information up to that moment. Commonly, the most used parametric proportional hazard model is Weibull proportional hazard model. Weibull distribution makes restrictive assumptions of the baseline hazard function like monotonicity and gives average values, which can cover a large type of failures due to aircraft age and fatigue in life operation. The present work deals with an unusual phenomena, especially in the aircraft entrance in a turbulence area, see Zbrozek (Weather R Meteorol Soc 13(7):215–227, 1958). This type of situation can lead to the need of increasing–decreasing proportional hazard models, taking into account harsh conditions during the flight. The functions which could model these non-monotone phenomena are scarce in literature but remain very crucial due to their impact on flight safety. In this paper, we propose a new baseline hazard function using extreme values theory in proportional hazard model and we adjusted the flexible Weibull increasing–decreasing baseline hazard function proposed by Park* and Park (Commun Stat Theory Methods 47(4):767–778, 2018) to the proposed baseline hazard function. This function could be implemented in control system of navigation particularly the take-off and landing phase and used as a support tool for pilot or aviation controller running turbulence area. The newly suggested function is non-monotone and will be named generalized extreme values baseline hazard function and we prove that this function satisfies hazard properties and could be used as a tool in the prediction of system operations. An application on aircraft flights is done and the effects of environmental factors are studied in aircraft performance modeling with the proposed model.

可靠性分析是统计的特定领域，用于研究故障时间及其在系统上的概率。统计的这一分支在许多领域中都占有重要地位，尤其是在航空领域。可靠性分析中最常用的方法之一是危险函数，该危险函数是在特定时刻根据给定的信息为特定实例定义的。通常，最常用的参数比例风险模型是Weibull比例风险模型。威布尔分布对诸如单调性之类的基线危险函数进行了限制性假设，并给出了平均值，该平均值可以涵盖由于航空器老化和生命运行中的疲劳而导致的大量故障。当前的工作处理的是一种不寻常的现象，尤其是在湍流区域的飞机入口处，参见Zbrozek（Weather R Meteorol Soc 13（7）：215–227，1958年）。考虑到飞行过程中的恶劣条件，这种情况可能导致需要增加或减少比例危害模型。可以对这些非单调现象进行建模的功能在文献中很少，但是由于它们对飞行安全性的影响而仍然非常关键。在本文中，我们在比例风险模型中使用极值理论提出了一个新的基准风险函数，并调整了Park *和Park提出的灵活的Weibull增减基准风险函数（公共统计理论方法47（4）：767-778 （2018年）。该功能可以在导航控制系统中实现，特别是在起飞和降落阶段，并可以用作飞行员或航空控制器在湍流区域运行的辅助工具。新建议的功能是非单调的，将被称为广义极值基准危险函数，我们证明该函数满足危险属性，可以用作预测系统运行的工具。完成了在飞机飞行中的应用，并在所提出的模型的飞机性能建模中研究了环境因素的影响。