In this paper, we solve the problem of finding interval estimate for system reliability via the CHA algorithm (Chaudhuri et al., 2001) following the Easterling (1972) approach. We consider a coherent system composed of independent components. No distributional assumption is made for the component life times. A closed form expression for the standard error of the system reliability, for a given mission of duration, is obtained. The method of calculating the lower confidence limit for the system reliability is illustrated for a simple low-pressure coolant injection system (LPCI) with two pumps (Blischke and Murthy, 2000). Both the CHA algorithm and the usual variance method are used for calculations. Some simulation results are also reported. This paper basically extends the results of Easterling to any coherent system.