# Equation model for project effort.

It is my first time here, so I hope I'm keeping on topic.

I wanted to find an equation where I could use the variables which affect the amount of work, in a way that feeling it the variables, I'd have the length of the task.

Note that this is not something used to calculate the length of the whole project, but just one particular task for an agile step which won't last more than a few days. Should be straightforward enough, I an just not familiar enough with mathematical modelling to get it right, thus my cry for help :)

I want to define how long it would take to analyse the solution for a particular problem, affecting a system that monitors other systems. A problem can be of many types, nonetheless one typical example could be an update in one or more of the systems monitored. In such case, the variables I'd have to deal to figure the problem would be:

• s[] (an array containing with an entry for each system): The complexity of each system affected.
• c[] (an array containing with an entry for each system): The complexity of the changes affecting each of the systems.
• The number of monitored systems affected by the issue being analysed, which would be just the length of either of the arrays.

(ps. I come from programming, sorry if I make everything look like code)

Lets not worry where does the values for s[] and c[] come from. They are actually subjective values we give by ourselves. The important thing is that they range from 0 to 1, being 1 the most complex.

Now, I reckon the formula would break down in two parts: a complexity factor, calculated from these variables which then is send to something that yields a logarithmic looking curve for values also ranging from 0 to 1, which I could multiply by the maximum effort allowed for this kind of project thus having the expected effort for the issue.

I got lost in how to represent this mathematically, specially the part of the arrays. Also, how to control the logarithmic part of it...

Sorry for the newbness and thanks for the help :)

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The formula could be something like:

F(S,K)=(1/L)sum(Si*Ksi); from i=1 to i=L

where Si=factor complexity for system i (between 0 and 1);

Ksi=factor complexity for change K in system i (between 0 and 1);

L=number of systems

That gives you a factor between 0 and 1 to be multiplied by the max of the time to execute the task.

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