You will not find any formula of this kind in ASME BPVC and many other mechanical codes, because it is out of their scope. You shall start the design once you have already defined the process.
Generally speaking it is obvious that the design pressure shall be above the operating pressure as the design temperature shall be above the operating temperature, but there are some considerations to take care of, for example:
- an internal pipe of a heat exchanger with 10bar of tube side design pressure and 6bar of shell side design pressure, could be calculated taking care only of the differential pressure of 4bar, if it is not to be pressurized from one side only while in service. In any case the design pressure of the tube side of the heat exchanger is always 10bar.
- also the mechanical design pressure, which in reality is a design stress (in fact has unit of MPa instead of bar) is never to be related to the absolute pressure of fluid, at least if you are not out in space. For example, if a fluid has absolute pressure 10bar (=1MPa), you shall make the system with a design pressure of at least 0.9MPa. This is you case also.