If a system has one active and four redundant components, then the lower bound of the system's reliability can be calculated as $R_s=r+ \rho\sum_{n=1}^{4-1}\frac{e^{-\lambda t}(\lambda t)^n}{n!} $,where $r$ is component reliability, $\lambda$ is failure rate, and $\rho$ is the switch reliability. I have a doubt in the case of a system where one active component is parallelly connected with one cold standby component or a system where more than one redundant components are active and only one component is in cold standby redundancy. How will we calculate the sum in the above formula, or is there any other way to calculate system reliability?
2026-02-24 14:44:52.1771944292
Reliability of system with cold standby redundancy
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