The present paper seeks to explore stochastic analysis of a cold standby system with conditional failure of server. The model consists of two identical units –one is initially operative and the other is kept as spare in cold standby. The operative unit may fail directly from normal mode and on the contrary, the cold standby unit may be out of order owing to remain unused for a longer period of time or due to any other reason. There is a single server, who may get tired while performing his assignment and goes for refreshment but he is not allowed to take refreshment in case of repair of cold standby unit (called conditional failure of server). The time taken to refreshment and repair activity by the server follows arbitrary distributions with different probability density functions whereas the distributions of unit and server failure are taken as exponential. The expressions of various reliability characteristics are analyzed in steady state using semi-Markov process and regenerative point technique. The behaviour of some measures of system effectiveness has been observed for arbitrary values of the parameters (l, µ, f & q) and also to examine the effect of repair strategies.