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, etc. Usually, the field-testing data can be available, but the failure causes for a series system cannot be always known because of the masked information. In this paper, the storage reliability model with possibly initial failures is studied on the statistical analysis method when the masked data are considered. To optimize the use of the masked survival data from storage systems, a technique based on the least squares (LS) method with an EM-like algorithm, is proposed for the series system. The parametric estimation procedure based on the LS method is developed by applying the algorithm to update the testing data, and then the LS estimation for the initial reliability and failure rate of the components constituting the series system are investigated. The results should be useful for accurately evaluating the production reliability, identifying the production quality, and planning a storage environment.