Estimation of Expected Lifetime of Highly Reliable Systems using Bayesian Analysis

Abstract

Nowadays, increasingly complex systems are critical due to the sectors and enterprises which they support. These are designed to be highly reliable and they are not expected to fail frequently. If a failure occurs, the safety, economical and operational consequences can be severe. Improvements and upgrades generate risk and uncertainty on their future performance. Therefore, there is a need for a procedure to estimate the expected lifetime of these highly reliable systems using a methodology based on available information. The aim of this thesis is to obtain highly accurate reliability estimations for highly reliable systems using Bayesian analysis when few or no historical data is available. For this purpose, a model for reliability estimations of expected lifetime based on Bayesian analysis was created and tested. The model estimates the probability of survival, probability of failure, histograms and plots for four predefined statistical distributions. The estimations are based on available historical data of performance and elicited expert knowledge to create posterior sample data of the system using Montecarlo simulations. Some relevant examples are included to compare the results with another estimation method such as Maximum Likelihood Estimation. Two main conclusions are derived; first, Bayesian analysis constitutes a powerful method to estimate the expected lifetime of highly reliable systems with high accuracy, compared to other methods such as Maximum Likelihood Estimation. Second, the model for reliability estimates provides decision support in a risk and operational context for maintenance or replacement.