Interval reliability inference for multi-component systems

This thesis is a collection of investigations on applications of imprecise probability theory to system reliability engineering with emphasis on using survival signatures for modelling complex systems. Survival signatures provide efficient representation of system structure and facilitate several reliability assessments by separating the computationally expensive combinatorial part from the subsequent evaluations submitted to only polynomial complexity. This proves useful for situations which also account for the statistical inference on system component lifetime distributions where Bayesian methods require repeated numerical propagation for the samples from the posterior distribution. Similarly, statistical methods involving imprecise probabilistic models composed of sets of precise probability distributions also benefit from the simplification by the signature representation. We will argue the pragmatic benefits of using statistical models based on imprecise probability models in reliability engineering from the perspective of inferential validity and provision of objective guarantees for the statistical procedures. Imprecise probability methods generally require solving an optimization problem to obtain bounds on the assessments of interest, but monotone system structures simplify them without much additional complexity. This simplification extends to survival signature models, therefore many reliability assessments with imprecise (interval) component lifetime models tend to be tractable as will be demonstrated on several examples.