The development of posterior probability models in risk-based integrity modeling

Area of Science:

• Engineering
• Reliability Engineering
• Materials Science

Background:

• Material degradation in process equipment poses risks to safety and reliability.
• Stochastic degradation mechanisms require risk-based integrity assessment.
• Probability distributions are essential for modeling degradation uncertainty.

Purpose of the Study:

• To develop accurate posterior probability models for material degradation.
• To enhance risk-based integrity assessment using updated degradation data.
• To improve the prediction of equipment failures.

Main Methods:

• Utilized a rejection sampling-based Metropolis-Hastings (M-H) algorithm for posterior distribution development.
• Employed the M-H algorithm, a Markov chain Monte Carlo method, to generate posterior samples without normalizing constants.
• Applied analytical Laplace approximation for validating posterior model parameters.

Main Results:

• The Metropolis-Hastings algorithm demonstrated superior performance in developing posterior distributions compared to conjugate pair estimations.
• Validated M-H algorithm results against Laplace approximations and conjugate pair estimations.
• Successfully applied the M-H algorithm for posterior development of priors for corrosion and cracking.

Conclusions:

• The Metropolis-Hastings algorithm is a robust method for updating material degradation models with new data.
• Accurate posterior models enhance the reliability and safety of process equipment.
• This approach provides a cost-effective means for mitigating risks associated with equipment degradation.