When you approach an instructor and ask: "How many repetitions should be in a set if I want to increase muscle strength?" The answer may vary: 6-8/10-12 or something else. Where are these numbers taken from?
Muscles don't count number of repetitions. The relevant parameter is set duration.
What should be the duration of set?
The answer to this question depends on what is your goal. Let's take a look at the most common target: micro injuries (according muscle damage theory, destructing old fibers for stronger new ones).
One of the most important outcomes of the used model is: micro injuries of muscle tissues are created when reservoirs of Creatine Phosphate are emptied and ATP's recreation speed (using Anaerobic Alactic&Lactic Energy Systems) is lower than its consumption speed.
Therefore, we should look for time boundaries that satisfy the aforementioned condition.
You probably know that there are two main types of muscle fibers: red (slow twitch) and white (fast twitch). We'll look for the conditions according to muscle type:
Within fast twitch (white) fibers after 7-10 seconds of max intensity work the Creatine level decreases till half of its original level. After 30-40 seconds anaerobic lactic energy system is at it high production, additionally acid products of metabolism are accumulated within the muscle. Therefore our boundaries are 7-40 seconds. Probably, optimal duration of set is somewhere in the middle of the mentioned interval and its 20-30 seconds.
After 60-120 seconds of set duration anaerobic alactic energy system (slow twitch fibers) reaches its high production. Note that when stress is higher than 30% of maximal one, blood circulation almost stops (makes it difficult for oxygen transportation, needed for alactic energy system). Therefore, set duration should be within 60-90 seconds duration.
A simple rule of thumb that's correct for many people: upper body muscles consist mainly from white fibers and lower body muscles from red ones.
There are also other tests to determine proportion between white/red fibers in your muscles.
General principle that you should keep in mind: if you want maximal advance both fiber types should be trained.
Exercise range is also something that should be taken into account. The bigger the range, the longer it will take you to make each repetition (unless you're keeping steady repetition duration, for example 2040 [2 seconds for positive phase, 4 seconds for negative and o seconds holding in each end]). In 20-30 seconds you'll probably make 6-8 squats, 8-10 bench press repetition and 10-15 calf raises.
In conclusion of this article I'd like to bring the following example: in workout a you've completed 7 reps in 30 seconds. In the next workout, you've finished 8 repetitions in 28 seconds (with the same weight). Some might tell that you've advanced. Instead of 7 reps 8 were completed, but in fact the duration of set decreased by 2 seconds (the intensity decreased) and that is what matters.