Optimal structure of series system with 1-out-of-n warm standby subsystems performing operation and rescue functions

This paper models an operation and rescue system where upon the failure of the operation system (if occurring), the rescue system is immediately activated to prevent the entire system loss or destruction. Both operation and rescue systems are series structures composed of 1–out-of-n warm standby subsystems. Different subsystems may have different redundancy levels, and components within each subsystem can be of heterogeneous types with different lifetime distributions and costs (due to purchasing from different vendors, different exploitation history or different work conditions). The operation system failure detection and switching system is not fully reliable. A numerical algorithm is first proposed to evaluate the mission success probability and survivability of the considered system. Further, we formulate and solve the optimal component allocation and sequencing problem (CASP), which finds the set of components from a pool of available component types for each warm standby subsystem and their activation sequence minimizing the total cost. The cost function optimized covers costs associated with mission failure, system loss or destruction, and system equipment. A chemical reactor example is provided to demonstrate the application of the proposed methodology as well as effects of different parameters on the evaluation and optimization results. A large example containing ten operation subsystems and four rescue subsystems is further analyzed to demonstrate computational efficiency of the proposed methodology. Example solutions show that the proposed methodology can facilitate a cost-effective design and operation of the considered operation/ rescue system while achieving a balance between mission success probability and system survivability.