In this thesis we propose a two-stage periodic inspection model for maintaining the reliability of a system in long-term storage. There are two types of tests available; a fallible test and an error-free test. The system is overhauled at detection of failure or when the storage reliability after inspection becomes less than or equal to the prespecified value. The expected cost per unit time until overhaul is derived and a procedure for minimizing the expected cost is suggested. The two-stage periodic inspection model is compared with the one-stage periodic inspection model for various parameters of the cost function when the failure time follows exponential and Weibull distributions. The proposed model is then applied to an existing missile system for comparison with the current inspection policy.