A statistical approach to estimating the probabilistic distribution of composite damagesizes using aircraft service inspection data has been investigated. Bayesian updating methods were implemented to revise baseline composite damage size distributions using damage size data from the Federal Aviation Administration's Service Dif culty Reporting System. Updating was performed on the Boeing 757 and 767 wing composite trailing-edge devices, elevators and rudders, with the results demonstrating that the assumed baseline damage size estimates are conservative in nearly all cases. Component failure probabilities were recalculated using the updated damage size distributions, and these results show an overall improvement in reliability for the damage mechanisms analyzed. The results of the analysis demonstrate that an inspection and maintenance program that reports damage characteristics can be used to monitor the reliability of damage tolerant structures on a quantitative statistical basis. Recommendations are also made for improving current inspection data reporting systems, which would enhance the ability to gather detailed information on the characteristics of each structural damage event. Nomenclature A= random variable for damage size a = sample damage size from domain A a c = critical damage size a 50 = median detection probability for probability of detection models N a = sample mean of damage sizes D = binary random variable for damage detection state (1 indicates damage is detected) E[ ] = expected value of quantity in brackets f A .a/ = probability density function of A g = importance-sampled probability density function k = shape parameter for log-odds probability of detection model L = likelihood function a = sample mean of the log of damage sizes m = importance sample size n = sample size of damages used for updating P D .a/ = probability of detection for damage size a P.Y / = probability of Y N P D = sample mean of the log of probabilities of detection p.a/ = probability density function of actual damage size p 0 .a/ = probability density function of detected damage size R = reliability w = importance weight factor ® = shape parameter for prior distribution of gamma model parameter μ = shape parameter for Weibull distribution of damage sizes, or scale parameter for prior distribution of gamma model parameter µ µ = scale parameter for actual damage size distributions » = truncation value for detected damage size distribution ¾ = shape parameter for lognormal probability of detection model ¿ = shape parameter for gamma distribution of damage sizes Subscripts n = normalized values of importance weight factors u = updated distribution of model parameters 0= earlier distribution of model parameters

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