Hybrid reliability modelling under general uncertainty

The real world phenomena are often facing the co-existence reality of different formality of uncertainty and thus the probabilistic reliability modeling practices are very doubtful. Under complicated uncertainty environments, hybrid variable modeling is important in reliability and risk analysis, which includes Bayesian distributional theory, random fuzzy distributional theory, as well as fuzzy random distributional theory as special distribution families. In this paper, we define a new hybrid lifetime which is specified by a random lifetime distribution with an uncertain distributed parameter, which is called as random uncertain hybrid lifetime. We furthermore define the average chance distribution as a quality index for quantifying the hybrid lifetime and accordingly the average chance reliability is derived.