Some systems such as missiles and ammunitions are used only one time in combat or emergency situation. Predicting correct storage reliability is very important for those systems which are inspected periodically. Many researches have been done for predicting the storage reliability using generally exponential or Weibull failure distribution. However, recent studies show the hazard functions follow various types of failure distributions. So in this paper, we proposed a generalized model that measures the storage reliability regardless of type of failure distributions. And this model reflects inspection error and failures that might be occurred during periodical check and within storage term as well.