Here are the parts
Replacement parts for artsc8651ss models | AppliancePartsPros.com

Here is the tech sheet in case you do not have it.
http://www.servicematters.com/m...brary/docs/T232_34R1.pdf

Unfortunately it sounds like the control board is gone, especially as the errors are opposites one a short the other an open.

Is the control board, the ERC?
Yes

If it is, I've just replace it a year ago. Can it go out that quickly?
Yes if you are unlucky.
You have replaced the sensor. When you did this you probably had the power off to the unit for some time so if the board was going to reset it would have.
So it is my best guess.

It's expensive.
Yes it is at $207.44

"error f3 and f4, replaced temperature sensor but still have the same error"

But it was erroring F3, F4 before I've replaced the heating sensor
You said in your first post that it was giving the F3 and F4 errors and you replaced the temperature sensor but it is still giving the errors.
Or did I misunderstand this.

The tech sheet shows F3 as an open sensor and F4 as a shorted sensor.
This makes no sense as they are exact opposites and that is why I believe that something on the control board must be screwed up.

You could pull the sensor and check it with a meter should be approximately 1,100 ohms.

You could also check that the ground strap (if a 3 wire hook up)
and Neutral are tight. Sometimes a bad earth ground can do weird things.

Hopefully someone else will jump in with additional thoughts/solutions to this problem.

Very weird.

All I can suggests is that you try the stuff in may last post.

Also check to see if the connector for the temperature sensor on the board is OK. Check the pins for corrosion usually a light gray or tan coating. Also check that the pins are properly soldered in. Wiggle the pin while carefully watching the solder if the pin moves in the solder it is a bad solder joint. Also cold solder joints are usually a duller silver color or have pin holes.

All this of coarse is done with the unit unplugged.

I cannot explain why you get an open sensor fault and then a shorted sensor fault. This may just be the way they monitor the sensor re: if the sensor reading drops suddenly it may trip a shorted sensor error.