Improved Estimation of Aircraft Probability of Failure

Abstract

We report on estimating probability of failure (PoF) of an FA/18 bulkhead based on empirically obtained and published in open literature fatigue-crack growth and equivalent pre-crack size (EPS) distribution data. We demonstrate that the tail of the EPS distribution has a significant effect on PoF. Considering each flight to be a successful (i.e., no failure) fatigue test, we use a Bayesian approach to obtain an updated (posterior) EPS distribution and provide more accurate estimates of PoF. We then consider monitoring fatigue cracks in high stress concentration areas using fatigue damage sensors and show that using such sensor data (notably "no crack found" response) leads to a significant reduction of uncertainty in estimating the PoF. We also show the effect of increasing sensor accuracy (i.e., reliable detection of smaller cracks) on PoF predictions and required sensor interrogation intervals. The reported approach allows us to perform tradeoff studies on sensor accuracy and interrogation frequency for maintaining required levels of PoF.

A review of equivalent pre‐crack sizes in aluminium alloy 7050‐T7451

“…The distribution of an EPS population in a structure is an important consideration for calculation of probability of failure due to fatigue crack growth (for example, see Refs [25,26]). Also by knowing the distribution of the EPS from the initiating discontinuities of interest, the EPS values at any given percentile level can be determined and applied for structural life evaluation.…”

Bayesian Updating of Aircraft Risk Assessments Using Results of Inspection

“…Risk assessment updates of a single aircraft. To illustrate how the probability of failure is updated using the inspection outcome, we use the risk analysis parameters used by Macheret and Teichman [6] to determine the probability of failure of a single aircraft. The critical stress intensity factor is assumed to be a normal distribution with a mean of 30 MPa 1/2 and a standard deviation of 2 MPa 1/2 .…”

Probabilistic risk analysis of fracture of aircraft structures using a Bayesian approach to update the distribution of the equivalent initial flaw sizes

“…The use of Bayesian sampling to update the EIFS distribution without the NDI and similar to the aircraft updating method introduced in this paper has been proposed by Macheret and Teichman . They considered each flight hour as a fatigue test with each no failure indication used to update the EIFS distribution.…”

“…Non‐destructive inspection (NDI) is an expensive procedure and necessitates grounding of aircraft for a considerable length of time. Macheret and Teichman used a Bayesian updating process to improve the estimate of the equivalent pre‐crack size distribution. They were able to show that the probability of failure (PoF) can be updated using only the successful flight hours of an aircraft, without using the inspection results themselves.…”

“…They also presented the methodology on updating the PoF using both the successful flight hours and the sensor accuracy during inspection. However, it has been noted that the formulation of the Bayesian updating method presented in Ref . is questionable, which will be detailed later in this paper.…”