I work in the engineering department of a Canadian manufacturing SME. My responsibilities mostly consist of designing products and production support (answering questions, solving issues, etc.). I report to the engineering manager, which reports to the CEO.
Our production team has been severely understaffed for several months. Since leaving employees aren't being replaced, we're down to a core team of employees with very little margin. To compensate, the production manager (PM) has been taking on more and more responsibilities which leaves him working unreasonable hours and losing focus. We've been able to mostly avoid delays, but we're seeing a large number of mistakes and redoes. Things that should easily be caught by QA get shipped because the PM doesn't have/take the time to properly inspect products.
I discussed the issue with my manager who suggested I go talk the PM into assigning an employee to QA for a couple hours a day. When presented with the idea, he refused as that would leave one of the departments even more understaffed. I suggested that he should present the situation to upper management and stop overworking himself by taking on the work of 3-4 people (both of which I would gladly back him up on). I also told him that by doing everything, he is obscuring the situation from management (since they see orders fulfilled on time), but he said that if he doesn't, he'll be the one that gets shit or even fired. He then asked me to not do anything or tell upper management and that he'd take care of QA.
As he doesn't report to me, I don't have any hard recourse other than going to upper management, but that would likely damage our work relationship. Furthermore, even if I did, nothing stops him from saying everything is under control.
At this point I'm very concerned. If one or two employees get sick or quit, production will very likely grind to a halt, likewise if the PM burns out. Should that happen, the company will likely be in a very bad situation, which puts my own job in jeopardy. Given that I have a baby coming in a few months, changing jobs now would be very difficult.
Now to my question: What can I do to improve the situation given my position? I don't thing I should leave things as they are, but I'm not sure what actions I can take that won't alienate the PM in return.