This is a common dilemma that we face these days, as our pets are living longer and therefore developing chronic old age issues like your lass's arthritis. Instead of conditions that lead to clear cut decisions of when to let them go, health issues like arthritis leads us balance between the good and bad days and we often struggle to know when it is time.
First, whenever we are considering this type of situation, we have to ask ourselves if we are having more good days or bad days. If she is only have the occasional bad day, then it would be worth speaking to her vet about additional pain relief (ie tramadol, gabapentin, etc) to have on hand for those days. But if those days are starting to arise more often or overtake the number of good ones, then we'd have to consider whether we'd want to try and improve her pain relief regimen (by adding further medications) or take this as our sign that her condition is progressing to a level that we may struggle to manage well enough for her to be pain-free (which is very important for dogs).
Otherwise, in regards XXXXX XXXXX girl's situation, the key to deciding when it is her time will be based on her daily activities and her interaction with you. We do have to appreciate that at her age and with her condition, she will likely have some discomfort but the question is whether the pain medication is addressing that adequately for her (a real concern after Tuesday). Therefore, what you need to consider is whether she is doing those things that make her life worth living. This will, of course, vary by dog but you need to consider whether she is playing, eating, going for walks, snuggling, chewing her toys, or whatever gives her pleasure in life like she used to. Because if she is not able to do those things that have made her doggie life worth living for these past 15 years, then that is our sign that this arthritis is taking too big a toll on her and that we need to consider letting her go.
So, do look to your lass and her daily routine at the moment. Is she still keen to do the things she loves? Is she up and greeting you at the door (if that is something she has always done)? Or is she curled up sleeping the day away? Are the bad days coming more frequent or starting to out weigh the good ones? Depending on your answers to these questions, you will be able to appreciate what is right for her at this stage. And if you think she isn't doing those things she loves and is just existing, then we'd have to consider letting her go before this progresses any further for her.
Please take care,