Bayesian methods for a growth-curve degradation model with repeated measures

Area of Science:

• Engineering
• Statistics
• Materials Science

Background:

• Increasing product reliability reduces observed failures in traditional survival analysis.
• Inference from degradation measurements is gaining traction due to limitations in failure time data.
• Existing degradation inference methods often rely on large-sample theory and approximations, especially for nonlinear models.

Purpose of the Study:

• To review current methods for inference from product degradation data.
• To introduce a fully Bayesian approach for approximation-free inference.
• To focus on predicting failure time distributions for new and in-test units.

Main Methods:

• Review of existing statistical methods for degradation analysis.
• Development and application of a fully Bayesian inference framework.
• Utilizing fatigue crack growth data for method illustration.

Main Results:

• The proposed Bayesian approach enables approximation-free inference from degradation data.
• Accurate prediction of failure time distributions for future and current units is achieved.
• Demonstrated effectiveness using real-world fatigue crack growth data.

Conclusions:

• The fully Bayesian approach offers a robust alternative to traditional methods for reliability analysis.
• Degradation modeling provides valuable insights when failure data is scarce.
• This method enhances predictive accuracy in reliability engineering.