In a large facility where there is 22 traction elevator & 2 hydraulic ones, how could you integrate the elevators maintenance to the work order & work request system?....I mean how could the elevator operator send the work request to the maintenance dept? the only way is through phone as my guess, but how could the work request being recorded then? and how could the maintenance labor know the details of the breakdown to prepare his tools & the other requirements before attempt to go to the elevator location?. If I'm aiming to calculate the time between work request and repair start time, how?

There are more choices than you may choose to make.
First of all start with a written maintenance control program. If you think that is not worth while, then stop reading this post.

Secondly a program such as the following two choices would be a place to go for keeping track of the reports.

http://www.paradigminfosystems.com/
http://www.kingsiii.com/monitoring.html

You can also "invent" your own system, however, it would be simply better for you to go with an off the shelf proven system that already works.

The fact is simply that proper and proactive preventative maintenance works. Its important that you work with some one who has a proven knowledge of such systems (lord forbid, a consultant) not a salesman.

If you are not the person who has the purchase authority, my best suggestion is to simply find something else to focus your attention on to.

Work safe and contact me if I may be of service to you.

Robert L Krieger info@cctc.name

Every manufacturer publishes recommended maintenance tasks and frequency. Rest assured, no maintenance company can both be competitive and still afford to provide the recommended maintenance. And, if you don't have regular third party inspections, you're wasting tons of money; "You can't expect what you don't inspect."