Reliability Analysis with Proportional Hazard Model in Aeronautics

Abstract

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.