I have a 1 year old home. The bathroom outlet is a GFCI outlet on a circuit protected by a 15 amp ARC FAULT BREAKER. Today my wife plugged her hair blowdryer and the base of the cord lit up like an arc welder. This lasted for 5-8 seconds before the cord completely melted and the fireworks stopped. Apparently the cord was frayed and shorted out? Neither the GFCI or ARC FAULT BREAKER tripped!! Does this indicate that we have some kind of wiring problem?

The GFCI should not have tripped. They don't trip on short circuits.

The AFCI, I believe, should have tripped on two conditions:

1) The AFCI condition of sparks
2) The breaker should likely have tripped on overload.

Maybe I have been doing this wrong but the arc faults are required by code for new construction bedrooms. They can be used in other circuits but are only designed to prevent a fire caused by arcing. Your arc fault should have tripped but did not for some reason so it needs replacing. You can buy a combination GFCI and ARCI breaker and protect the hole line from the panel.

A GFCI is a ground fault current interrupter, meaning if there is a short to ground it will pop. The breaker is designed to prevent too much current from being pulled on the line and to stop a hard hit, in this case it was probably on a 15amp breaker.

What happened to you is essentially a bad dryer. Typical new homes use #12 thhn supplied to the outlets. The amps being pulled by the dryer was enough to melt down the smaller gauge cord feeding the dryer but not enough to overload the breaker. The reason it took so long for the sparks is that the insulation on the cord had to melt away exposing the live line wire to the ground. Once this occurs, spark, bang pop!

The GFCI should have tripped at this point. Replace the dryer, double check the electrical.

Sand Daddy:

A typical hair dryer has no ground. Only a hot and neutral, thus there can be no short to ground. There could, however, be a leakage path through the body, but there is no way of knowing. That path only needs to be a few milliamps.

KeepItSimpleStupid, this is true. There is a neutral however which will yield the same results. Short to the Neutral or ground will cause the above scenario.

Does the Test Button on any GFI or Arc Fault breakers trip the breaker?

This test is to be done once a month.

The AFCI breaker should have sensed the arcing occurring between the two wires of the cord.

That was my read on the situation yesterday, the ARCI should have picked up the arcing in the dryer. The reason you should test your faults each month is obvious, they do break down.