I assume that MTBF means the mean time between failures.
I'm not an expert in maintenance, however, I will answer considering the MTBF as an indicator that we want to improve by increasing the mean time between failures. Thus, I would apply the classic quality tools. I would start with a Pareto chart with the reasons for failure. Then, for the most frequent reasons, I would perform a cause analysis using, for example, the cause-effect diagram to determine the root causes. Then I would develop actions to eliminate those root causes.
I recommend consulting the following materials: