Mean instantaneous performance of a system with weighted components that have arbitrarily distributed lifetimes

• Instantaneous performance of systems with weighted components is studied.
• Ordered lifetimes of components are used.
• The results are illustrated for proportional hazard model.

There are various systems consisting of components which may have different contribution to the performance of the system. Such systems can be modeled systems with weighted components. In this paper, we study the mean instantaneous performance of this type of systems after successive component failures. The mean instantaneous performance is a useful characteristic to take preventive action about the system. In particular, we obtain explicit expressions for the mean instantaneous performance of a system with weighted components that have arbitrarily distributed lifetimes. We illustrate the results when the lifetime distribution of components follow proportional hazard model. Some further results are also presented for the components having exponential lifetime distribution.