Dynamic k-out-of-n system reliability with component partnership

This paper describes a new k-out-of-n system reliability model that is appropriate for certain design problems when the minimum number of required components, k, changes dynamically in response to failures to maximize the utility of the available collection of functioning components. This new model shares some distinct similarities with weighted k-out-of-n models and for some problems they produce the same result. However, there are subtle and distinct differences, and in practice, there are some complex applications have not been properly explained or modeled by traditional or extended k-out-of-n system models. For this application, components are arranged in a k-out-of-n configuration of heterogeneous components with different performance levels. Component performance is indicated by a component-specific component partnership level; the fewer partners required to operate successfully implies higher performance. The components can work collectively with partners at the same level to maintain system reliability, or they can create a partnership group with components at higher performance levels which serve as replacements to provide the necessary number of working components. When components fail, the dynamic k-out-of-n configuration maintains reliability of the system with changing k by having components create partnerships with other components at the same level or above. To demonstrate the model, a system replacement maintenance policy based on a replacement interval variable is applied to an example system to obtain the optimal replacement time.