Hi gentleman:
Once I had a generator problem after pushback ,then we backed to bay ,after maintenance procedure finished, they need eng idle run to verify everything was back to normal, I had my passenger deplaned, then it cause a lot of further delay, I wonder if it is OK to have Eng test run with passenger on board?

Yes, so long as you keep your passengers informed about the reasons for the run....assuming company procedures allow it. Any engine runs done at the gate will of course be at low power only, a high power run would need to be completed away from the gate, and most likely without passengers.

Disembarking and re-boarding 400 passengers would not make you popular with the Ground Staff..........perhaps your plane was slightly smaller?

I've done it before, passengers wont know any different unless there is the obvious signs of engineers crawling all over the engine bay. Also, if its only an idle test then its a 2-3 minute penalty ('ish) as compared to a possible 30+mins penalty for boarding etc. no big deal.

Depends on the airline's procedures, local aviation regulators regulations and the nature of the problem.

Agree completely, but I doubt any company would be in their right mind to allow pax onboard for a power assurance run. All it takes is something as simple as a stall at power and the aircraft jumps chocks swinging around. There are many things that could go wrong. The lawers would have a hayday with the company.

I believe that nobody in their right mind would even contemplate PA or MPA runs with pax on board.
As previous comments Airport and Maintenance SOP,s would dictate if allowed, that a ground idle run could be carried out. No problem to do so, I have as maintenance a few times.
I totally agree with the prior statement to de plane a B747-400 causes to say the least, major difficulties for Airport and Airline staff, imagine a high density A380.

From an Engineering point of view. If the eng run is carried out by the flight crew with all cabin crew present then as long as local and company procedures are followed it is ok with pax on board.

My present employer insists that if engineering staff are carrying out the run then all pax and crew are off, doors closed, bridges off etc. Minimum of two Licensed Engineers on the flight deck and numerous Mechs/techs outside. Tricky at a line station...

My company allows engineers to carry out an idle ground run on the gate with passengers on board.
At least one member of the tech crew must be in the flight deck, cabin crew must be on board and at their stations. Plus the usual announcement to let the customers know what's going on.