If your electric stove or oven is tripping the earth leakage or lightly shocking you when you operate it then it means that one of the plates has burnt out or is becoming dangerous to use. This usually happens when the stove is very old or when pots regularly boil over. This allows water and moisture to get into the electrical wiring of the stove which causes rust. Over a period of time the rust will cause an electrical short circuit which would create a "shocking experience" for the person operating the appliance.
It is very common for an oven element to just stop working. This is usually due to old age but can also be the result of a faulty element. With most makes of oven it is possible to replace the elements but this kind of repair should be done by a qualified electrician or authorized repair specialist. If the oven continually burns the food or doesn't switch off then it is usually the thermostat which needs replacing.