Math Is Fun Forum

thekashyap

Member

Registered: 2009-06-02

Posts: 3

Predictions based on history data

Hi,

My problem is to come up with a method to predict based on history data. Here is the problem:

I'm observing the % of work finished by a single employee everyday during working hours. E.g. if the employee is a postman, the employee is expected to deliver 100 letters to appropriate addresses every day then % work indicates how many letters were actually delivered during working hours. So my history data looks something like this:

Date         Working hrs    % work
01-Jan       8            95
02-Jan       8            50
03-Jan       8            80
04-Jan       8            40
05-Jan       8            60
...             ...                     ...
28-Feb       8            75

I need to come up with some formula / way by which based on this history data I can answer following question:
- What is the number of working hours needed to be X% sure (e.g. 95% probability) that employee would complete 100% work.
- If number of working hours is X then how much work is the employee likely to finish.

Could someone point me in the right direction ? We are currently trying to employ some technique but not much luck yet. I don't mention which technique to avoid influencing.

Thanks
Kashyap

PS: Reason to put working hours in input data although it's constant is because for different employees it could very.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Predictions based on history data

Hi thekashyap;

Since you have a sample size of ≈ 60 the analysis could be done with statistics. Just using the mean and the sample standard deviation.

Last edited by bobbym (2009-06-02 23:32:21)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thekashyap

Member

Registered: 2009-06-02

Posts: 3

Re: Predictions based on history data

Interesting you say that. I started off with a simple average and then moved onto std deviation. But couldn't really make any headway. Here is what I did so far. My basic problem is how to factor in the probability.

1. I started with a simple technique:
Calculate the average efficiency based on history:
         D=N
e = [    ∑ ( Wd / Hd )    ]  /    N
         D=1
Where
- Wd is %work done on day d.
- Hd is number of working hours on day d.
- N is total number of days for which history is available.

Now I can predict the number of hours needed (100 * e) to complete 100% of work ONLY WITH 100% probability. So I don't know how to factor in the probability.

2. I tried plotting the std deviation of % work done. I didn't really get much further. I simply don't know how to factor in the probability value as the plotted data only considers % of work done as dimension. Also in this case I don't see even the time playing any role, i.e. I don't see the correlation between std deviation graph and time dimension.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Predictions based on history data

Hi thekashyap;

  I can't take that idea any further either. I don't even really see an extrapolation method. Since everything is in 8 hours there is no way for me to see how the percentage of work varies with time.

   If you post all the data for each day that you have in 2 columns, like you did in the first post. Then I will go as far as I can using statistics.

Last edited by bobbym (2009-06-03 18:31:35)

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thekashyap

Member

Registered: 2009-06-02

Posts: 3

Re: Predictions based on history data

Hmm.. Actually the data I posted was just an example, there is no real data set.
If you think it helps to see a variation in column 2 as well please feel free to assume. E.g.:
Date   working hrs    % work
1             8                  80
2             2                  30
3             4                  60
4             10                100
5             8                  70
.....

PS: If I can manage somehow to observe the time taken for completing 100% work everyday, then using prob density function I can plot the distribution and then it's possible to anwer my question for any probability. But of course in my scenario I don't have that data.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Predictions based on history data

Hi thekashyap;

  I could fit various curves to the data that you have provided but I would require more points for a useful analysis. Also when fitting curves to arbitrary data it is mandatory to have some idea of the underlying law that has created the data, otherwise an infinite number of fits are possible.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.