Anomaly distribution acquisition method for probabilistic damage tolerance assessment of hole features

Abstract

Anomaly distribution is an essential input for the probabilistic damage tolerance assessment, which is required by the airworthiness certification criteria Federal Aviation Regulation (FAR) 33.70. The default anomaly distribution of hole features has been established and published in airworthiness advisory circular 33.70-2 based on historical anomaly data collected from cracked or ruptured parts recorded in laboratory analysis reports of the special industries before 2005. However, for other industries, this default anomaly distribution fails to reflect the machining level of these industries. Besides, insufficient historical maintenance anomaly data makes the mathematical model of the default distribution inapplicable, and few models can deal with the production data. Therefore, this paper proposes a model for achieving the anomaly distribution of hole features induced by machine or maintenance process, including collecting anomaly data, deriving the exceedance number by the probability of detection (POD), conducting the curve fitting process, and calibrating and modifying the anomaly distribution. The anomaly distribution and the probability of failure (POF) are dependent on defect numbers as well as confidence levels. To recommend the number of collected data and the correction factor for the POFs with different sample numbers and confidence levels, the sensitivity analysis is conducted by quantifying the influence of the anomaly distributions of different anomaly numbers on the POFs. Results show that when the anomaly number is 25, the differences between the POFs are less than 32.9%, and a 1.329 correction factor $z_P$ is supposed to modify the POF. When the anomaly number is larger than 50, a 1.2 correction factor $z_P$ is supposed to obtain the most conservative risk value with a 95% confidence level.