Two that really come to mind, I was called in at 2:00 am where some engineers had gone to a conveyor not running, they had replaced the dual channel safety relay 3 times using all the spares we had, first thing I noticed is that the 3 replacement ones had blown internal fuses, signs they had crossed the channels over or had a short, turns out they had crossed them, checked the e-stop loop it was open circuit so no short, went to one of the e-stops it was pressed in, replaced the relay with the original all worked, yes it was just someone had pressed the e-stop. Another was a call to a packaging machine, would not start, the engineers had been on it for about 5 hours, I went to the machine, called up the alarm page, Air pressure low, turns out the pressure switch was faulty, temporary fix was to short out the pressure switch, so it appears that instead of doing simple faultfinding ( probably due to lack of good training on diagnostics) 5 hours of lost production there were some very embarassed faces, I ended up doing training on fault finding with all engineers the first thing I taught them was look at the alarms if there is an HMI.
So, I think logical faultfinding is a valuable skill.