Extended block replacement policy with shock models and used items

This paper considers an extended block replacement policy with shock models and used items. A system is subject to shocks that arrive according to a non-homogeneous Poisson process. As shocks occur a system has two types of failures. Type 1 failure (minor failure) is removed by a minimal repair, whereas type 2 failure (catastrophic failure) is removed by an unplanned (or unscheduled) replacement. After a replacement the shock process resets at 0. Under such a policy, an operating system is preventively replaced by new ones at times iT (i = 1,2,...) independently of its failure history. If system fails in ((i - 1)T,iT - δ) it is either replaced by a new one or minimally repaired, and if in [iT - δ,iT) it is either replaced by a used one or minimally repaired. The choice of these two possible actions is based on some random mechanism which depends on the number of shocks since the last replacement. The expected cost rate is obtained, using the results of the renewal reward theory. Various special cases are considered. Our results are shown to extend many of the well-known results for the block replacement policies.