Fiducial lower confidence limit for the reliability of cold standby system consists of geometric series components

This article is to discuss a cold standby system which consists of l series working components and n − 1 independent cold standby components. Suppose that the component follows geometric distribution. The precise Fiducial lower confidence limit for system reliability is obtained, when only a parameter is unknown. And when all of the parameters are unknown, a method is offered to resolve the Fiducial approximate lower confidence limit for system reliability. At the same time Monte Carlo simulation is carried out to verify the conclusions.