Parameter inference for non-repairable multi-state system reliability models by multi-level observation sequences

Multi-state system reliability theory has received considerable attention in recent years, as it is able to characterize the multi-state nature and complicated deterioration process of systems in a finer fashion than that of binary-state system models. Parameter inference for multi-state system reliability models, which is a task that precedes reliability evaluation and optimization, is an interesting topic to be investigated. In this paper, a new parameter inference method, which aggregates observation sequences from multiple levels of a system, is developed. The proposed inference method generally consists of two stages: (1) compute the sequences of the posterior state probability distributions of units based on multi-level observation sequences by dynamic Bayesian network models and (2) estimate the unknown transition probabilities of units by converting the sequences of posterior state probability distributions into a least squares problem. Two illustrative examples, together with a set of comparative studies, are presented to demonstrate the effectiveness and efficiency of the proposed method.