  In this paper, we analyze the top-quark decay $t\to Wb$ up to
next-to-next-to-next-to-leading order (N$^{3}$LO) QCD corrections. For the
purpose, we first adopt the principle of maximum conformality (PMC) to deal
with the initial pQCD series. Then we adopt the Bayesian analysis approach,
which quantifies the unknown higher-order terms' contributions in terms of a
probability distribution, to estimate the possible magnitude of the
uncalculated N$^{4}$LO-terms. In our calculation, an effective strong coupling
constant $\alpha_{s}(Q_{*})$ is determined by using all non-conformal
$\{\beta_{i}\}$ terms associated with the renormalization group equation. This
leads to a next-to-leading-log PMC scale $Q_{*}^{(\rm NLL)}=10.3048$ GeV, which
can be regarded as the correct momentum flow of the process. Consequently, we
obtain an improved scale-invariant pQCD prediction for the top-quark decay
width, e.g. $\Gamma_{t}^{\rm tot} = 1.3120 \pm 0.0038$ GeV, whose error is the
squared average of the uncertainties from the decay width of $W$-boson $\Delta
\Gamma_{W} = \pm 0.042$ GeV, the coupling constant $\Delta \alpha_{s}(m_{Z}) =
\pm 0.0009$, and the predicted N$^{4}$LO-terms. The magnitude of the top-quark
pole mass greatly affects the total decay width. By further taking the PDG
top-quark pole mass error from cross-section measurements into consideration,
e.g. $\Delta m_{t} = \pm 0.7$ GeV, we obtain $\Gamma_{t}^{\rm tot} = 1.3120
^{+0.0194}_{-0.0192}$ GeV.
