A copula-based reliability modeling for nonrepairable multi-state k-out-of-n systems with dependent components

As k-out-of-n systems have widespread applications in engineering practices, their reliability modeling and evaluation are a great concern of reliability community. However, most reported works on k-out-of-n reliability modeling and evaluation are based on the premise that all the components are s-independent. Such simplified treatment may not be realistic as components in a system often suffer the same working or environmental conditions and/or interact with one another, resulting in dependency between their failure processes. To characterize such dependency in reliability modeling and evaluation, a copula-based reliability modeling for dependent multi-state k-out-of-n systems is developed in this work using copula functions and minimal paths of system states. The state probability and reliability functions of dependent multi-state k-out-of-n systems with identical components, nonidentical components, and partially dependent components are formulated. Two illustrative examples and a port oil transportation system are presented to demonstrate the implementation of the proposed method, and a sensitivity analysis is also conducted to examine how sensitive the reliability measures are with respect to the degree of dependency.