This thesis presents a measurement of the neutral charm meson mixing parameters $y_{C\!P}^{KK} - y_{C\!P}^{K\pi}$ and $y_{C\!P}^{\pi\pi} - y_{C\!P}^{K\pi}$ using $D^0 \rightarrow K^-K^+$, $D^0 \rightarrow \pi^-\pi^+$ and $D^0 \rightarrow K^-\pi^+$ decays. These parameters correspond to the departure from unity of the ratio of the effective decay widths of $D^0 \rightarrow K^-K^+$ or $D^0 \rightarrow \pi^-\pi^+$ decays over the effective decay width of $D^0 \rightarrow K^-\pi^+$ decays.The measurement is done with the dataset collected in the Run 2 (2015-2018) of the Large Hadron Collider (LHC) by the LHCb experiment at CERN at a centre-of-mass energy of $13\mathrm{TeV}$, and corresponding to an integrated luminosity of $6 \, \mathrm{fb}^{-1}$. The $D^0$ mesons originate from $D^{\ast+}(2010) \rightarrow D^0 \pi^+$ decays. We measure \begin{equation} \begin{split} y_{C\!P}^{KK} - y_{C\!P}^{K\pi} & = (7.08 \pm 0.30 \pm 0.14) \times 10^{-3}\, , \\ y_{C\!P}^{\pi\pi} - y_{C\!P}^{K\pi} & = (6.57 \pm 0.53 \pm 0.16) \times 10^{-3}\, , \end{split} \end{equation} where the first uncertainty is statistical while the second is systematic. Neglecting final state dependent contributions, we obtain the combination \begin{equation} y_{C\!P} - y_{C\!P}^{K\pi} = (6.96 \pm 0.26 \pm 0.13) \times 10^{-3} \, . \end{equation} This measurement improves by a factor of four the precision of the current world average value of $y_{C\!P} - y_{C\!P}^{K\pi}$. In addition, the results allow for an improvement of the precision on the mixing parameter $y$ by a factor of two, where $y$ is connected to the width difference between the neutral charm meson mass eigenstates. The new world average value of $y$ is estimated to be \begin{equation} y = (6.45 \pm 0.24) \times 10^{-3} \, . \end{equation} This thesis also presents the work done for the EPFL fibre mat production as part of the LHCb Scintillating Fibre (SciFi) Tracker upgrade.