Long-term monitoring of delivered luminosity and calibration stability in CMS

Over the course of the year different detector-specific effects can appear, e.g. temporary instability or efficiency loses. As the calibration of the luminosity detectors (``luminometers'') is carried out only once per year, its long term stability monitoring is of crucial importance. The luminosity ratios measured by multiple luminometers as a function of time are used to identify regions of specific detector instability and to deliver the final luminosity uncertainty due to stability and linearity. Several times during the year so-called ``$\mu$ scans'' are performed to facilitate such detector comparisons over extended range of instantaneous luminosity. However, ratios between different detector measurements allow for measuring only relative nonlinearity, and new methods were required to measure nonlinearity for individual detectors and to derive the corrections to luminosity. From 2017 onwards CMS also explored the potential of ``emittance scans'', which were regularly performed and allowed for detector-independent stability and nonlinearity monitoring. Procedures used to measure the corrections and final luminosity uncertainty for 2018 data-taking period are reported.