Modeling Reliability and Safety of Multistate Systems with Ageing Components

Basic notions of ageing multistate systems, reliability analysis are introduced. The system components and the system multistate reliability functions are defined. The mean values and variances of the multistate systems, lifetimes in the reliability state subsets and the mean values of their lifetimes in the particular reliability states are defined. The multistate system risk function and the moment of exceeding by the system, the critical reliability state, are introduced. The multistate series, parallel, “m out of n”, consecutive “m out of n: F”, series-parallel, parallel-series, series-“m out of k”, “ $$m_{i}$$ out of $$l_{i}$$ ”-series, series-consecutive “m out of k: F” and consecutive “ $$m_{i}$$ out of $$l_{i}$$ : F”-series reliability structures of the multistate systems with degrading (ageing) components are defined and their reliability functions determined. As a particular case, the reliability functions of the considered multistate systems composed of components having exponential reliability functions are determined. Moreover, the multistate approach to analysis and defining the basic notions of systems’ safety is proposed. The system safety function and risk function that allow to define the basic safety structures of the multistate systems composed of components with degrading safety states are introduced. Applications of the proposed multistate system reliability and safety models to the evaluation and prediction of the reliability characteristics of an exemplary system and a port oil transportation system and the safety characteristics of a maritime ferry technical system are presented as well.