Here are your parts
Parts for Whirlpool RF315PXDN0 Range - AppliancePartsPros.com
I would unplug the unit and remove the back just to be sure that an oven wire has not shorted out to the frame etc.
If OK then odds are that the control board (item 7 in the Control Panel Parts section) is toast.
Unfortunately it looks like it is only available in Almond.
Which you may or may not be able to live with.
The other possibility is to Google "appliance timer repair" and find a company that will fix the board.
Or replace the stove.