Estimation of parameters of degradation growth rate distribution from noisy measurement data

• Existing methods do not deal correctly with random sizing error in degradation measurement data.
• A correct approach based on two stage probabilistic model and maximum likelihood method.
• The empirical Bayes method applied for the parameter estimation and prediction.
• Prediction of degradation, remaining life and reliability for fitness-for-service assessment.
• A comprehensive methodology applicable to both generic and flaw-specific reliability analyses.

An accurate estimation of the degradation growth rate is necessary for reliability analysis and fitness-for-service assessment of engineering components and structures. The growth rate analysis is based on repeated measurements of flaw sizes created by a degradation process over time in a component population. The flaw size measurements by inspection tools invariably include noise or sizing error, which complicates the estimation of growth rate. Most engineering models dealing with this issue do not properly account for the probabilistic structure of noisy data. Furthermore, the fact that the prediction of future degradation should be consistent with the model of underlying degradation process is often overlooked.This paper presents a comprehensive two-stage hierarchical model of noisy degradation measurement data, and formulates the associated maximum likelihood function. The parameter estimation is subsequently carried out in the spirit of well-known empirical Bayes method. The analysis is further extended to the prediction of the distributions of future degradation, remaining lifetime and reliability of components in both inspected and un-inspected component populations.