Bayesian reliability assessment of legacy safety-critical systems upgraded with fault-tolerant off-the-shelf software

This paper presents a new way of applying Bayesian assessment to systems, which consist of many components. Full Bayesian inference with such systems is problematic, because it is computationally hard and, far more seriously, one needs to specify a multivariate prior distribution with many counterintuitive dependencies between the probabilities of component failures. The approach taken here is one of decomposition. The system is decomposed into partial views of the systems or part thereof with different degrees of detail and then a mechanism of propagating the knowledge obtained with the more refined views back to the coarser views is applied (recalibration of coarse models). The paper describes the recalibration technique and then evaluates the accuracy of recalibrated models numerically on contrived examples using two techniques: u-plot and prequential likelihood, developed by others for software reliability growth models. The results indicate that the recalibrated predictions are often more accurate than the predictions obtained with the less detailed models, although this is not guaranteed. The techniques used to assess the accuracy of the predictions are accurate enough for one to be able to choose the model giving the most accurate prediction.