  A measurement of the ratios of the effective decay widths of $D^0 \to
\pi^-\pi^+$ and $D^0 \to K^-K^+$ decays over that of $D^0 \to K^-\pi^+$ decays
is performed with the LHCb experiment using proton-proton collisions at a
centre-of-mass energy of $13 \, \mathrm{TeV}$, corresponding to an integrated
luminosity of $6 \, \mathrm{fb^{-1}}$. These observables give access to the
charm mixing parameters $y_{CP}^{\pi\pi} - y_{CP}^{K\pi}$ and $y_{CP}^{KK} -
y_{CP}^{K\pi}$, and are measured as $y_{CP}^{\pi\pi} - y_{CP}^{K\pi} = (6.57
\pm 0.53 \pm 0.16) \times 10^{-3}$, $y_{CP}^{KK} - y_{CP}^{K\pi} = (7.08 \pm
0.30 \pm 0.14) \times 10^{-3}$, where the first uncertainties are statistical
and the second systematic. The combination of the two measurements is $y_{CP} -
y_{CP}^{K\pi} = (6.96 \pm 0.26 \pm 0.13) \times 10^{-3}$, which is four times
more precise than the previous world average.
