Bayesian Reliability: Combining Information

July, 2016
IDA document: D-8136
FFRDC: Systems and Analyses Center
Type: Documents
Division: Operational Evaluation Division
Alyson Wilson, Kassandra Fronczyk See more authors

One of the most powerful features of Bayesian analyses is the ability to combine multiple sources of information in a principled way to perform inference. This feature can be particularly valuable in assessing the reliability of systems where testing is limited. At their most basic, Bayesian methods for reliability develop informative prior distributions using expert judgment or similar systems. Appropriate models allow the incorporation of many other sources of information, including historical data, information from similar systems, and computer models. We introduce the Bayesian approach to reliability using several examples, and point to open problems and areas for future work, including:

  • Reliability for various types of systems: on-demand with pass-fail testing (notional SDB-II data) and continuous lifetime data (viscosity breakdown times). These examples include definitions and illustrations of prior distributions, likelihood and sampling distributions, posterior distributions, and predictive distributions.
  • Additional discussion of how to specify prior distributions is provided, along with brief descriptions of methods and possible resources for more complex analyses like hierarchical modeling, system reliability with subsystem or component level testing, and implementation using Markov chain Monte Carlo techniques.
  • Finally, some open research areas are discussed regarding combining information across multiple tests for assessment purposes and to plan an appropriately sized follow-on test.