91Ó°ÊÓ

You are given a system with \(n\) components. The mean time between failures for each component is \(100 \mathrm{~h}\) and the mean time to repair is \(5 \mathrm{~h}\), and each component has its own repair facility. Derive expressions for the limiting availability of the system when (a) All \(n\) components are required for the system to function. (b) At least one of the \(n\) components should function for the system to function correctly. Now, assuming that the times to failure and the times to repair for each component are exponentially distributed, write down expressions for the instantaneous availability and the interval availability for both the cases above.