A Bayesian Framework for Reliability Assessment of Aeronautical Equipment with Small-Sample Right-Censored Lifetime Data Incorporating Historical Information Borrowing

Quantifying the extent to which historical information can be borrowed remains challenging in the reliability assessment of aeronautical equipment with small-sample right-censored lifetime data. This paper proposes a Bayesian reliability assessment framework that incorporates historical information and uses simulation to calibrate prior-borrowing boundaries. A two-parameter Weibull model is adopted. Weakly informative, historical empirical, discounted, and fixed-mixture priors are specified in the log-parameter space, and posterior distributions are updated using the right-censored likelihood. Independent historical and current fleets are simulated to examine compatible historical information, scale shifts, and prior misspecification. Under compatibility, the historical empirical Bayes method yields relative errors of 2.52%, 3.54%, and 3.12% for the shape parameter, scale parameter, and mean lifetime, respectively, with a mean absolute error of 1.28% for the reliability function. Using the relative error of the scale parameter and the mean absolute error of the reliability function as joint criteria, historical-information borrowing is divided into full-borrowing, discounted-borrowing, and fixed-mixture correction regions, thereby establishing engineering decision boundaries. The thresholds are simulation-calibrated for the sample size, censoring proportion, and parameter settings considered. The framework quantifies reliability uncertainty and supports prior selection and risk calibration for comparable equipment.