Failure rate of a Cold- or Hot-Spared Lognormal Component.

The failure rate is deduced for a pair of components with lognormal lifetimes when one component acts as a back-up (spare) for the other. Specifically, an assembly (e.g., a regenerator in an undersea optical communication cable) is said to be cold- spared if its degrading component (e.g., a laser) is backed up by a second such component which is activated (begins to degrade) when the first component fails. Alternatively, if the back-up component degrades concurrently with the primary component, then the assembly is said to be hot-spared. Under the assumptions that the assembly fails if and only if both statistically equivalent components fail and that the component life is lognormally distributed, the failure rate of the assembly is deduced for both the cold-spared and hot-spared cases.