Storage reliability is of importance for the products that largely stay in storage in their total life-cycle such as warning systems for harmful radiation detection, rescue systems, many kinds of defense systems, etc. The storage reliability of a product is commonly defined as the probability that the product can perform its specific function for a period of specific storage time under specific storage environment. Logically, the failures of the product in storage should be identified with the same criteria as in its operation process. However, the failure data in storage may be observed indirectly through the maintenance or inspection activities. Nevertheless, when the storage reliability is concerned in general, the reliability model should take into consideration the possibility that the operational reliability does not start at 100%, for example, the one-shot product may have only 96% operational reliability when they are newly produced. In this paper, the storage reliability model with possibly initial failures, which are usually neglected at the beginning of storage in most of storage models, is studied on the statistical analysis method when the masked data are observed. The parametric estimation procedure, based on the Least Squares method, is developed generally by applying an EM-like (Expectation and Maximization) algorithm for the storage data in which some information about which components have caused the system failures is not known, namely the failure data are masked. The estimates of the model parameters including the initial reliability are formalized. In the case of exponentially distributed storage lifetime and series system, a numerical example is provided to illustrate the method and procedure though the method is not limited to such case. The results should be useful for planning a storage environment, decision-making concerning the maximum length of storage, maintenance strategy optimization and identifying the production quality.