It depends on your local supplement, which varies from region to region. However, generally its based om how many hours you worked. When I started part time in 1999 we were required to work 400 hours to recieve our health and wealthfare benefits. At that time the economy was humming along and I was allowed to double and triple shift and reached the 400 hours in well under 6 months. Today, you're lucky to get 5 hours a day at UPS. Still, if your goal is benefits from the job I would stick with it because you can't get these benefits anywhere else.
Man, how have times changed! In 1999 they were literally begging me to double and triple shift. As a part-timer I could work as many as 12-14 hours/day over 3 sorts if I wanted to. The shifts always lasted more than 4 hours and closer to 5. Now, they are lucky to get 4 hours and double shifting is almost non-existent. I really miss those days!
I hope this helps...