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When solid-state relays start to short, they will almost always fail. Solid-state relays should be checked with an ohmmeter across the normally open (N.O.) terminals when control power is off.  The relays should be open, switched to OL, and closed (0.2 , the internal resistance of the ohmmeter) when control power is applied. You can further confirm that the relay is bad by taking a multi-meter, put it in diode test and checking across A1(+) and A2(-). The meter will apply a small voltage to make the semiconductor conduct and read that voltage on the screen. This will check the (typically NPN) transistor from the base(P) to the... emitter. If its bad, the meter will read 0 or OL, but if the relay is good it will read 0.7 for a silicon transistor (which almost all of them are) or 0.5 for a germanium transistor (which are relatively rare but not unheard of). Solid-state relays are easy to troubleshoot, cheap to replace and last a long time if they stay cool. Typically, new relays come in DIN rail packages and block mountings. There is also a special type of relay called an SCR that comes in two flavors for heating wires and IR lamps and ovens, usually for exquisite process temperature control. This is basically a fast switch on a much faster switch that can turn off and on, which fail often due to temperature fluctuations.
Use an ohmmeter to check solid-state relays. Use a multi-meter in diode-test mode to confirm your findings. Keep SSRs cool.