Bayesian Analysis of Lifetime Delayed Degradation Process for Destructive/Nondestructive Inspection

Degradation has become the dominant failure mode for highly reliable engineering systems. Cracking, a fatigue phenomenon composed of sequential phases of crack initiation and propagation, is a major concern for critical aircraft structures. Traditional fracture mechanics analysis cannot fully meet the requirements for assessing reliability indicators from a reliability analysis perspective. Alternatively, the empirical Lifetime Delayed Degradation Process (LDDP) provides an explanatory framework for sequential hard&soft failure mode. This study further generalizes the LDDP framework by introducing the Bayesian method as a Bayes-LDDP model, which incorporates a weakly informative prior derived from historical data of similar systems for both non-destructive and destructive inspections. Additionally, we compare our proposed method to the LDDP approach using specific inspection datasets. Two practical applications are conducted to demonstrate the effectiveness of the Bayes-LDDP model for reliability monitoring and remaining useful life (RUL) prediction in critical aircraft structures using field data. The crack inspection datasets of a transport aircraft and an aircraft core automated maintenance system (CAMS) are utilized for non-destructive and destructive inspections, respectively. The Markov Chain Monte Carlo (MCMC) sampling algorithm is adopted for the Bayes-LDDP, improving the computational efficiency of model parameters estimation compared to the stochastic expectation maximum (SEM) algorithm. Furthermore, the Bayes-LDDP model enables precise inference including the mean time to failure (MTTF) of cracks for destructive inspections and the RUL for non-destructive inspections under the selected optimal model. This extended novel framework provides a clear depiction of the lifetime delayed degradation process from a Bayesian perspective.