Economic design of the mean prognostic distance for canary-equipped electronic systems

Canaries are a type of early warning device that can be embedded or mounted on electronic systems to issue a pre-failure warning to the host system. A canary is designed to fail faster than the host system. The distance from the time of canary failure to host system failure is called the prognostic distance of the canary. This distance is clearly random depending on the design and operating characteristics of each particular canary and host system, so in practice we often refer to the mean prognostic distance as the measure of prognostic distance. The mean prognostic distance is often determined during the design stage of the canary and the system without taking into account the cost associated with system failure. Clearly, if the consequence of system failure is severe, then the mean prognostic distance should be longer. This paper introduces an economic design for the mean prognostic distance in a canary-equipped system from the perspective of an economic analysis. We establish the necessary conditions for such an economic-based mean prognostic distance to exist and demonstrate it through numerical examples.