Bayesian Reliability Analysis for Non-Periodic Inspection with Estimation of Uncertain Parameters

The present study concentrates on the development of the Bayesian reliability analysis for estimating appropriate values of several uncertain parameters in probability distributions and generating appropriate non-periodic structural inspection schedules using small sample data gathered during in-service inspections. A pressurized fuselage structure of transport-type aircraft with multiple fatigue-critical elements is accepted as a structural model in this analysis. This element is a multiple component of two-bay fail-safe structure, designed by the damage tolerance principle, which consists of three frames and a skin panel subjected to cyclic stress due to differential pressure. Fatigue cracks are initiated and propagated from a hole for a rivet to connect the skin panel to the center frame. Probabilistic factors considered in this model are fatigue crack initiation and propagation, failure rates before and after crack initiation, yield stress, fracture toughness, cyclic stress range and crack detection capability of detailed visual inspection. Uncertain parameters estimated from inspection data such as the number of detected cracks, crack sizes and whether or not failures were detected are a scale parameter in a probability density function of fatigue crack initiation and a parameter in a simplified fatigue crack propagation equation. Both parameters can not be a priori estimated because of the paucity of pertinent data. Monte Carlo simulation techniques are utilized in order to generate a failure process in the structural element and to evaluate the validity of the proposed Bayesian reliability analysis.