Capacity loss and residual capacity in weighted k-out-of-n:G systems

• Binary weighted-k-out-of-n:G system is studied from a dynamic perspective.
• Capacity loss and residual capacity are considered.
• The results are illustrated for exponential and Weibull distributions.

A binary weighted-k-out-of-n:G system is a system that consists of n binary components, and functions if and only if the total weight of working components is at least k. The performance of such a system is characterized by its total weight/capacity. Therefore, the evaluation of the capacity of the system is of special importance for understanding the behavior of the system over time. This paper is concerned with capacity loss and residual capacity in binary weighted-k-out-of-n:G systems. These measures are potentially useful for the purposes of preventive action. In particular, recursive and non-recursive equations are obtained for the mean capacity loss and mean residual capacity of the binary weighted-k -out-of-n:G system while it is working at a specific time. The mean residual capacity after the failure of the system is also studied.