The aim of this paper is to analyze a system, which consists of two components, working under a cost-free warranty policy. Past literature reflects that till now the focus of researchers is those systems which work without taking rest. But here authors emphasized on an industrial system which takes rest after working for a specific amount of time. This strategy helps the system to run for a long time with less failure. After taking rest, the system starts its working again. During the mathematical modeling of the system various state of the same are critically analyzed. Reliability of the considered system has been obtained for the different combinations of failure and repair rates. Also, the various parameters which affect the system performance have been evaluated.