You need to pull-in the schedule just to be able to meet the schedule. This is called "time banking." You accelerate to gain time now, since you know unexpected things will happen in the future where you will need to use that banked time (i.e. loose that saved time). What is certain is uncertainty!
When we say, "Accelerate the schedule," we are trying to hit the committed target date "on time." So you need to pull-in all the time, just to be on time. We are always trying to accelerate the schedule, regardless of being late or early. The larger discussion though is, "Should the committed target dates be accelerated?" This is real schedule acceleration. This thinking is characteristic of the best practice-fast teams. They were always trying to accelerate, they would accelerate even if they were not yet late, since they knew that they would need that "banked" time in the future.
Levels of "Pull-in" Process Maturity
Schedule acceleration has levels of process maturity. Each level represents increasing sophistication and program management skill. These are all predicated on having a good FTTM schedulein place in order to be able to accelerate the schedule. You can't pull-in the schedule if it does not reflect where you are today.
Some teams gain value in just putting a schedule together with the team involved and never update it (level 1). Next level is to update performance on a regular basis (at least weekly). This enables the team to see what has slipped and or pulled-in and will give them an indication of "where they are." Pull-back after slipping is the next maturity level. This is where most teams stop. Their focus is to regain lost ground and get back on schedule.
Fast teams did something different, they pulled-in before slipping. They knew if they tried to hit a schedule they would miss it. This means they banked-time, because they knew that they would need this time in the future for unanticipated events. It is not sufficient to only record the pull-ins in the schedule, you also have to implement them on the project by taking action.