One from the archives. Our customer needed to alarm on thermocouple failure without shutting down the process.
Thermocouple instruments commonly include upscale burnout indication. If the thermocouple breaks or fails open-circuit the instrument's output goes high, just as if the temperature had gone out of control. This often is used to insure failsafe failure, shutting the process down and sounding an alarm.
Our customer, a utility, needed an overtemperature shutdown on a monitored water temperature. They also wanted to trip an alarm upon thermocouple failure but without interrupting the process. We were able to suggest a simple dual-trip alarm setup to do this.