Identifying a faulty diode in a series of LEDs.

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This simulation only uses a triangle AC source to illustrate the Source, normal diode and failed diode voltage drops while each have the same current.
The SCR diode needs to be selected for proper threshold eg 2V. It could even be a 5 cent red LED. (sim link)
This SCR diode bypass approach "could" be considered as a cost penalty for fault protection, but I would strongly advise you select suppliers who use Zener protected LEDs. That what I do. Just ask if you need.

Improved Falstad Simulation ( forgot collector SCR wire link
 
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