A Scientific method to calculate the time limits of a task

[Tyto alba]

Is there a way to estimate the upper limit and lower limit of time for doing a work?
Suppose we are learning a page of facts and want to estimate the upper and lower limit of time taken to do so. If we start estimating the time we will find that the pages are learned in some variable periods of time: 17 min, 16:45 min ...so on (during the experiment different sets of facts are learned by the same person and it is assumed that no major distraction happens - like phone call or any person intruding and no other work is done in the process or the process is abruptly stopped).
Each page contains approximately 112 words.

How can the upper limit and lower limit of time required to do the work be calculate?

 

[jim mcnamara]

This is really difficult to quantify, mostly because what you describe is very poorly delimited. To me, it looks like you may not have really though what you are trying to ask.
Why?

Learning occurs very many ways. Let's define some possible learning tasks. (Note: I am not the best person to answer this)
1. learn a theorem in Mathematics
2. learn to play 'Fur Elise' on the piano
3. decrease your response time in a lab where you push button 'A' when your see a green light, 'B' when you see a red light.

#1 has a scope problem. Someone who can read math symbols can probably memorize what the theorem says in English words. If it is an area known to the person really well then generating a proof is possible, not guaranteed. Especially if you decide to time the event with a time limit. Otherwise, prove it? No. Explain what it means? Maybe. Recite it? yes. Someone not familiar with the math area will have a long task just getting enough background to get an accurate idea. A music major could recite by rote if someone wrote an English sentence for that person to memorize. Nothing more in most cases.

2. This has some scope issues and the issue of pupil background. Like many tasks, repetition for short periods a day over weeks is required. Playing it well may never happen. Unless the person is actively playing piano for a hobby, learning time will be inversely proportional to previous exposure to piano. For me, for example, I can read music, one of my hands is damaged. So answer is never.

3. Is a different kind of learning, somewhat related to #2 - primary motor skills. There are some 'brain training' software packages that do exactly this task - more fun though- and have been evaluated for dementia prevention. Normal people can in a few minutes become a lot more proficient, depending on how you define proficient. If repeated over days with days off, the skill really becomes improved, apparently more or less permanently.

So as asked I do not think I can give you a decent answer. The question belongs in another area. And the only person I know on PF that might be able to help : @DiracPool

 

[fresh_42]

How can the upper limit and lower limit of time required to do the work be calculate?

If you have a sample as result of your experiment, then it is simply the maximal and minimal value.
If you don't have data, then the lower limit is probably $0$ and the upper limit $\infty$.
It is part of your setup, and not a result of a calculation.

 

[jim mcnamara]

IMO, this question is more about experimental design, learning, and psychology and not necessarily straight away amenable to mathematics. The 'operations' under discussion are not closed necessarily - meaning duration of tasks is indeterminate as defined. This is a problem in scientific methods as well.

 

[berkeman]

Is there a way to estimate the upper limit and lower limit of time for doing a work?
Suppose we are learning a page of facts and want to estimate the upper and lower limit of time taken to do so. If we start estimating the time we will find that the pages are learned in some variable periods of time: 17 min, 16:45 min ...so on (during the experiment different sets of facts are learned by the same person and it is assumed that no major distraction happens - like phone call or any person intruding and no other work is done in the process or the process is abruptly stopped).
Each page contains approximately 112 words.

How can the upper limit and lower limit of time required to do the work be calculate?

Are you maybe asking how to best start to estimate the distribution of the times you are measuring and will measure as you continue to gather data?

https://en.wikipedia.org/wiki/Normal_distribution

Would your "limits" be 1-sigma or 3-sigma, or something else?

 

[jedishrfu]

Another approach related to these kinds of problems is through a pert chart. Its a graphical representation of the tasks and order they must be done. Some tasks were independent of others and could be done in parallel.

Project managers would use pert charts to optimize workflows and to manage a work crisis ie some task took longer than expected.

In your case though the tasks are of indeterminate length and rather sequential with one person accomplishing them so charting would be kind of silly.

With experience you might be able to develop a metric for yourself like the ones programmers use to estimate to complete a program. 30 lines of debugged code a day and 300 lines of ported code a day. However your mileage vary based on the complexity of the task.