The response of a GC will ideally only be affected by the concentration of your analyte in the sample. However, in reality this is never the case. The response will be affected by alot of external parameters that will cause the signal to drift over time. A response factor is therefore not a good way to measure purity.
The best way used to date for estimating Peak purity is the use of DAD (coupled with LC) or MS detectors. For GC MS detectable peaks, [1] Inject sample containing intact substance (or Derivative as TMS) containing impurity [2] inject pure standard sample [3] in ALL previous, use TIC [4] Extract MS of your compound (subtracting from Baseline MS. [5] get the most abundant m/z peak in your standard peak, extract this m/z as SIM, you shall get new chromatogram [6] go to GCMS injected sample using TIC, extract same most abundant m/z, you shall get your peak corresponds to the reference substance, and when you overlay two chromatograms (TIC, and SIM), now you should have decided if your impurities exist or not. Good Luck
Using a GC the use of an flame ionization detector is the best option for establishment of response factors as long as the identity of the single impurities is not known and as the detector response corresponds to the concentration and number of carbon atoms over a wide linear range. Assuming that the impurities are related to your main component response might be similar. Then the approach as explained before using area% is the best option. If impurities are known and you have standards of known content available for your main component and the main impurities the establishment of relative response factors (either relative to the main component or to an external or internal standard) is feasible. Then the detector is not of so high importance as long as the impurities and the main component give more or less similar responses. Otherwise sensitivity might be to low for some of the impurities.
In general,Rf is the ratio of the response value of the compound of interest and that of any standard compound whose identity and response value is established.
There are various methods to calculate response factor eg, (i) addition of internal standard,(ii) By external std. addition etc.
as Jean-Francois explained, purity (%) by GC is defined as the peak area of your main component of interest divided by the sum of all peak areas assuming that all impurities have the same detector response as your compound of interest and therefore a response factor equal to 1 (which is most probably not the case). Using this approach for purity determination it is very important that you do not consider peaks in the obtained chromatogram which do not origin from your sample (compound of interest) as you will inject a solution of your compound if your sample is not a liquid. In this case it is important to identify all peaks related to your solvent (solvent peak itself + impurities of the solvent) by an blank (injection of the used solvent) and not to integrate these peaks.
Furthermore it is useful to inject your sample solution several times over a certain time period to see, if your sample is stable in the solvent at the given conditions. Otherwise there will be the risk that you will consider degradants in solution which are not really impurities of your compound.
You should also test the linearity by injecting solutions of different concentrations of your sample to see, up to which range the detector response is linear. If you inject a solution for purity determination having a concentration out of the linear range, you will underestimate the main component related to the impurities. If the concentration is too low, the GC-FID might be not sensitive enough to detect all impurities.
Another important consideration to be made is the question, if your compound is stable and the sample and the related impurities are volatile enough at the applied injector temperature. Only in this case GC is applicable for a reasonable purity determination. However, the determined purity should not be accounted as content (% w/w) as there might be a lot of impurities not detected at all (water, non-volatiles etc.).