Near-Optimal Design for Fault-Tolerant Systems with Homogeneous Components under Incomplete Information

In this paper, we study a fault-tolerant control for systems consisting of multiple homogeneous components such as parallel processing machines. This type of system is often more robust to uncertainty compared to those with a single component. The state of each component is either in the operating mode or faulty. At any time instant, each component may independently become faulty according to a Bernoulli probability distribution. If a component is faulty, it remains so until it is fixed. The objective is to design a fault-tolerant system by sequentially choosing one of the following three options: (a) do nothing at zero cost; b) detect the number of faulty components at the cost of inspection, and c) fix the system at the cost of repairing faulty components. A Bellman equation is developed to identify a near-optimal solution for the problem. The efficacy of the proposed solution is verified by numerical simulations.