We conducted a series of fundamental research-based experimentations to measure the X-ray production cross sections of K-, L-, and M-shells from thick samples of Cu, Ag and Au, respectively, for proton beam in a lower energy range of 0.7 - 3.5 MeV utilizing particle induced X-ray emission (PIXE) analysis. The measurement theories based on the Merzbacher-Lewis (ML) relationship and procedure for thick samples are described. The detector efficiency and system calibration were first measured from Fe-55 and Am-241 X-ray sources and the standard sample, respectively. The X-ray yields as a function of the proton energy were measured and fitted for finding the derivatives which were used for the cross section measurement. The obtained results were compared with published data and predictions from the theoretical models of Plane Wave Born Approximation (PWBA) and the advanced ECPSSR. The measured results from Cu were in good agreement with the theoretical predictions, especially in the lower energy regime, and most of the reported data, while for the higher energy regime deviated by a few times but still in the same order of magnitude with the theoretical data. The Ag and Au results were in excellent agreement with published and theoretical values.