Your raw material is one piece. You need to familiarize yourself with your internal steel requirements. When ordering you should be stating a specification. You need to review the incoming material certifications to ensure they are reporting a chemistry that meets that specification. Periodically you should pull a sample and have a chemistry done to compare their reported chemistry to what you get. Now, remember your spectrometer and their spectrometer will vary and the chemistry may vary somewhat from their report. So, just because the report says .58% Cr and you get .55% Cr, that does not mean the report is not valid. Different elements will vary differently. When I do a chemistry check, I concentrate on cmparing Mn, Cr, Ni, Mo, and V. I look at Si, Al, P, S, Cu and other trace elements to ensure they are within spec. You can get a C on an optical emission spectrometer, but if I have a concern the carbon should be checked using a combustion method like a LECO.
Once you are sure you are getting the steel they say you are you can start comparing alloying elements with results. You can look at individual elements like C for hardness but things like Mn, Ni, Cr and Mo while they will affect hardness you probably would loose any correlation in the noise. So, a tool like a carbon equivalent or DI would help to you look at the overall hardenability of the steel and compare results. If you see that when you get some 8630 with a CE<60 gives you low hardness with your process you can start to tighten up the internal specifications. For example, ASTM A352 Grade LCC has a pretty lenient range for chemistry, however, if we got a carbon equivalent much below 36 we could not meet the elevated tensile requirements that one of our customers had so we put a lower C and Mn restriction for our internal requirements to ensure we would always have that CE.
This is assuming you have tight controls on the rest of the process. Your quench and temperature control in your ovens will have huge impacts on your final results. If you do not have a firm grip on these, nothing you do to control chemistry is going to help. Like Ed stated above, as quenched hardness can help you determine the effectiveness of your quench and if you need to adjust temper.