Optimal Preventive Replacement for Cold Standby Systems With Elements Exposed to Shocks During Operation and Task Transfers

This article considers heterogeneous, cold standby systems performing missions with the fixed amount of work when a failure of an operating element results in a mission failure. A system is operating in a random environment modeled by the Poisson process of shocks. Each shock decreases the remaining lifetime of an operating element and, therefore, its preventive replacement (PR) is scheduled on experiencing the predetermined number of shocks. An important feature of the discussed model is that the failure can also occur during these PRs (task transfers) with two elements involved. The duration of the task transfer depends on the time from the start of a mission. The recursive equations for obtaining the mission success probability are derived and the corresponding numerical algorithm is developed. The number of shocks triggering elements’ replacements is obtained as a solution of the formulated optimization problem. The numerical example with the detailed analysis for a set of virtual machines operating in a cloud computing environment is presented.