Sparing rules for duplexed units

Consider m offices with each operating a duplexed unit. Suppose a centrally located warehouse is to be provisioned with k spares to be used when offices experience failures. Assume that failed units are instantaneously replaced with spare units, provided a spare is available at the warehouse and the failed units are repaired and used to replenish the spare inventory. We consider two approaches for determining a suitable value for k. In the first approach, a network emergency is declared whenever the number of failed units in the network exceeds k. A simple expression for the mean time to a network emergency (MTNE) is obtained using a birth and death process model. The value of k is selected to make MTNE satisfactorily large. In this approach, it is conservatively assumed every network emergency will be service affecting. However, only when the number of failures exceeds k AND at least one office has two failures is the incident service affecting. Our second approach accounts for this distinction by evaluating the mean time to a service affecting incident (MTSI). The two approaches are compared by contrasting the different valves of k each requires to achieve a specified objective for MTNE and MTSI, respectively