  As one of the key components of perturbative QCD theory, it is helpful to
find a systematic and reliable way to set the renormalization scale for a
high-energy process. The conventional treatment is to take a typical momentum
as the renormalization scale, which assigns an arbitrary range and an arbitrary
systematic error to pQCD predictions, leading to the well-known renormalization
scheme and scale ambiguities. As a practical solution for such scale setting
problem, the "Principle of Minimum Sensitivity" (PMS), has been proposed in the
literature. The PMS suggests to determine an optimal scale for the pQCD
approximant of an observable by requiring its slope over the scheme and scale
changes to vanish. In the paper, we present a detailed discussion on general
properties of PMS by utilizing three quantities $R_{e^+e^-}$, $R_\tau$ and
$\Gamma(H\rightarrow b\bar{b})$ up to four-loop QCD corrections. After applying
the PMS, the accuracy of pQCD prediction, the pQCD convergence, the pQCD
predictive power and etc., have been discussed. Furthermore, we compare PMS
with another fundamental scale setting approach, i.e. the Principle of Maximum
Conformality (PMC)... Our results show that PMS does provide a practical way to
set the effective scale for high-energy process, and the PMS prediction agrees
with the PMC one by including enough high-order QCD corrections, both of which
shall be more accurate than the prediction under the conventional scale
setting. However, the PMS pQCD convergence is an accidental, which usually
fails to achieve a correct prediction of unknown high-order contributions with
next-to-leading order QCD correction only, i.e. it is always far from the
"true" values predicted by including more high-order contributions.
