Wrong Stair Tread Bracket
Using the wrong stair tread brackets even if they are bigger isn't always better as you can see in the picture above. The bracket side that attaches to the stringer has 4 lag screws which is fine but the side that attaches to the tread has only2 lag screws. 2 lags will not be enough to prevent the tread from loosening up over time causing it to wiggle becoming a safety hazard.
Here's a good example of a metal stair tread bracket that was specifically designed for an 11.5 inch wide stair tread and an 11.5 inch wide stair stringer. You can clearly see that this particular bracket required six lag screws to attach the stair tread to the stair stringer and they have been installed correctly.
You should inspect these types of stairways regularly for missing lag
screws or loose building hardware. It is not uncommon to find these types of
problems and if they aren't repaired in a timely manner could create loose
steps, causing someone to trip or fall.
Something like this might not seem like that big of a problem, but over time could be.
For example if you have one missing screw and the stairway seems to be relatively structurally stable, then it might not be a problem today, but what about when another screw falls out, or another, this is when it becomes a safety problem and liability issue.
The last thing you want is someone walking up one of your stairways that could've been repaired a little sooner than later and ending up with a lawsuit.