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Systems in engineering usually not only have multiple states but also may be required to fulfill several functions, meaning the system has multiple performance variables in a specific state. In a multi-performance multi-state weighted  K− -out-of- n  system, the system consists of several multi-performance multi-state components for completing its different functions. As this system is more complicated than the general weighted  k -out-of- n  system, reliability evaluation of the system is time-consuming. A recursive approach is developed to evaluate the system reliability more efficiently, and comparison with the existing approach is carried out in various aspects. It is found the developed method is generally more efficient. To further understand the dynamic behavior of the multi-performance multi-state weighted  K− -out-of- n  system, two measures: capacity loss and residual capacity are introduced to investigate the system capacity evaluation over time. A method is provided for the computation of mean capacity loss and mean residual capacity of the system. A numerical example is presented to demonstrate the proposed method. The result shows the two measures can give an idea of how much capacity is lost and how much capacity is available, and provide effective information for system maintenance and optimization.

Reliability and capacity evaluation of multi-performance multi-state weighted K − -out-of- n systems