  A search for singly produced vector-like quarks $Q$, where $Q$ can be either
a $T$ quark with charge $+2/3$ or a $Y$ quark with charge $-4/3$, is performed
in proton-proton collision data at a centre-of-mass energy of 13 TeV
corresponding to an integrated luminosity of $36.1 \text{fb}^{-1}$, recorded
with the ATLAS detector at the LHC in 2015 and 2016. The analysis targets $Q
\to Wb$ decays where the $W$ boson decays leptonically. No significant
deviation from the expected Standard Model background is observed. Upper limits
are set on the $QWb$ coupling strength and the mixing between the Standard
Model sector and a singlet $T$ quark or a $Y$ quark from a $(B,Y)$ doublet or a
$(T,B,Y)$ triplet, taking into account the interference effects with the
Standard Model background. The upper limits set on the mixing angle are as
small as $|\sin{\theta_{\text{L}}}|= 0.18$ for a singlet $T$ quark of mass 800
GeV, $|\sin{\theta_{\text{R}}}|= 0.17$ for a $Y$ quark of mass 800 GeV in a
$(B,Y)$ doublet model and $|\sin{\theta_{\text{L}}}|= 0.16$ for a $Y$ quark of
mass 800 GeV in a $(T,B,Y)$ triplet model. Within a $(B,Y)$ doublet model, the
limits set on the mixing parameter $|\sin{\theta_{\text{R}}}|$ are comparable
with the exclusion limits from electroweak precision observables in the mass
range between about 900 GeV and 1250 GeV.
