Cumulative damage model with two kinds of shocks and its application to the backup policy

This paper considers an extended cumulative damage model with two kinds of shocks: one is failure shock at which a system fails and the other is damage shock at which it suffers only damage. Shocks occur at a nonhomogeneous Poisson process. A system fails when a failure shock occurs or the total damage has exceeded a threshold level K. A system is also replaced before failure at scheduled time T. Reliability measures of this model are derived, using the theory of cumulative processes. Further, this is applied to the backup of files in a database system. Optimal replacement times which minimize the expected cost are discussed and numerically computed for several cases.