A two-stage bayesian procedure for failure count data assuming a non-constant failure intensity function

Abstract

Reliability analysis is essential in high-risk industries like Oil and Gas (O&G) for predicting equipment lifespan, anticipating costs, planning maintenance, and estimating system availability. However, failure data is often limited due to proprietary restrictions, high acquisition costs, or challenges in data collection. Bayesian inference addresses this limitation by enabling the integration of generic data, which can be updated with new specific data to generate a posterior distribution. The Offshore & Onshore Reliability Data (OREDA) provides a valuable source of generic data, created through collaboration among O&G companies to share information on equipment operation and maintenance. Traditional analysis of OREDA data often assumes a constant failure intensity function, which is not always accurate. This work generalizes the analysis by incorporating a non-constant failure intensity function using the Weibull distribution. Given the lack of a conjugate prior to this model, posterior estimates are obtained via Markov Chain Monte Carlo (MCMC) sampling. The model was validated using simulated data, demonstrating robust performance across various test sets, particularly in terms of relevant performance metrics, despite some variability in the prior distribution estimation stage. Following this validation, the model was applied to a real-world industrial case involving booster pumps, extending traditional reliability methodologies by integrating non-constant failure intensity into the analysis. This model was incorporated into the Petrobayes software, which is presented in this work and enables streamlined execution to enhance accessibility and practical application.