Hierarchical modelling of orthopaedic hip replacement damage accumulation and reliability
We describe the modelling of crack initiation and growth in a group of orthopaedic hip replacements. A hierarchical model is proposed and fitted with Bayesian methods, implemented by the Gibbs sampler. Our interest is in predicting the failure of the replacements, which is predominately caused by crack activity in the cement that fixates the metal prosthesis to the bone. Simulation from the model based on posterior distribution samples allows us to approx-imate the reliability function and to assess the effect on reliability of the properties of the replacement. We discuss the ideas behind this approach, which can be generalized to any group of physical systems and any function of their state that interests us.