Reliability Assessment of Random Uncertain Multi-State Systems

The random uncertain multi-state system is defined as a multi-state system consisting of multi-state components whose performance rates and the corresponding state probabilities are presented as uncertain variables. Reliability assessment of random multi-state systems with enough samples based on probability theory has been widely investigated. Nevertheless, in some real-world applications, only a few or even no samples are available to estimate the state probabilities and performance rates of multi-state components or systems. To overcome the problem, by joint employment of probability theory and uncertainty theory, the reliability of a random uncertain multi-state system is analyzed in this paper. The state probabilities and performance rates of multi-state components are considered as uncertain variables. The uncertain universal generating function is introduced to evaluate the state probabilities and performance rates of the random uncertain multi-state systems. The uncertainty distributions, inverse uncertainty distributions, expected values and variances of the state probabilities, and performance rates for the system are discussed. An assessment technique for system reliability is proposed to compute the system reliability under the crisp user demand. A numerical example is presented to illustrate how to assess the state probabilities, performance rates, and reliability of the system.