Proceedings of the Eighth International Conference on Probabilistic Safety Assessment & Management (PSAM)
179 Applications of Bayes Linear Methods to Reliability (PSAM-0263)
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Bayesian methods are common in reliability and risk assessment, however, such methods can demand a large amount of specification, can be computationally intensive and hence impractical for practitioners to use. The Bayes Linear methodology is similar in spirit to a Bayesian approach but offers an alternative method of making inferences. Bayes linear methods are based on the use of expected values rather than probabilities, and updating is carried out by linear adjustment rather than by Bayes Theorem. The foundations of the method are very strong, based as they are in work of De Finetti and developed further by Goldstein. A Bayes Linear model typically requires less specification than a corresponding probability model, and therefore, for a given amount of model building effort one can model a more complex situation. This paper considers three types of modelling in a Bayes Linear framework.
• Modelling probabilities for on-demand systems to illustrate the difference in approach compared to modelling MTBF of continously operating systems.
• Modelling more than one generation of a previous system to capture aspects of reliability improvement.
• Modelling reliability within a reliability programme, i.e. modelling future reliability based on current reliability and expert opinion.
The first model is considered in detail, following on from work carried out by Goldstein and Bedford. The mathematics behind the theory is discussed in detail. The elicitation requirement and a short example using ‘trivial’ data is given and the benefits of using BL is discussed. The second and third model demonstrate the different problems that Bayes Linear methods can be applied to.
We view the output of a BL analysis as an approximation to “traditional” probabilistic models. In addition, the BL technique has the potential to allow us to build “broad-brush” models that enable us, for example, to explore different test setups or analysis methods and assess the benefits that they can give. We believe that this type of analysis is a first step to building a fully justified reliability programme.