The present paper deals with a stochastic model of a system consisting of two identical units. Initially, one unit is in operation and other is taken as spare in cold standby. The standby unit may fail after exceeding the maximum redundancy time. The failed standby unit undergoes for inspection immediately to check its possible renewal. If renewal of the unit is not possible, it is replaced by new one. The operative unit goes directly under repair without inspection, after failure. The failure time of unit follows exponential distribution while the inspection and repair times follow arbitrary distributions. The semi-Markov process and regenerative-point technique are used to derive expressions for different reliability and performance indices. The practical importance of the study is demonstrated by simulating   theoretical results for a particular case.