Software development is not a stable process. Either a team is always building new things in which case there isn't a consistent process to measure, or there is a see-saw as people release new features, deal with the bugs in the features, then go back to building - that isn't a controlled process, it is going to oscillate in statistically weird ways.
If SPC is applied to bugs, it will be monitoring the relevant manager's habits. That is to say, if you show me a nice in-control timeseries of bug resolution, all that says is when a bug blows out horribly the manager splits it into 2x tickets or something similar. It isn't necessarily a bad outcome (small tickets are happy tickets and gently stressing managers is a good idea) - but don't expect the devs to behave differently.
It is good to have a grounding in SPC, just don't try to apply it to every timeseries that you see. Bugs are a timeseries, but they aren't expected to be a controlled process so SPC's assumptions break down and the logic doesn't work. If it does work, it is probably measuring something other than the software development aspect of the process.