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Let's suppose there is a project which is expected to take a certain amount of time to complete. As certain jobs are done, we can quantifiably measure how much of the project has been completed at any time.

Consider a progress bar - it starts at 0%, and is updated at some discrete time values as parts of the project are completed, until it reaches 100%. It is expected that this completion percentage will increase linearly over time.

While the project has yet to be completed, it seems logical that the best way of estimating the final completion date based on this data is to plot the (time,%) values, calculate a line of best fit, and find where that intersects the 100% value. As time goes on, these approximations should get closer and closer to the true value, oscillating around it on both sides.

However, let's say some small part of the project (for example, a 5% range) gets delayed (or perhaps gets completed faster than expected). This period is going to drag down (or up) the line of best fit every single time it is calculated - meaning that our estimated completion date is going to be permanently too low, and will increase each time we calculate it, rather than oscillating about the true value like you'd expect.

Is there a better method of estimating the completion time that can take into account local periods of faster or slower increase?

Some sort of moving average may smooth the data, but doesn't seem logical with the variation not being cyclic. It is more like you'd want a piece-wise model - but how could you calculate the actual pieces and use this information appropriately without just looking at the graph and eyeballing where it 'seems' different?

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  • $\begingroup$ You don't have independence of sucessive points for the relationship between "time so far" and "% completed so far". You can't ignore that. But in any case I don't think linear regression is the tool you want. $\endgroup$
    – Glen_b
    Jul 14, 2013 at 0:10

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I can't see any way out of this without recalculating estimated time to completion at each waypoint of product development. PERT and critical path analysis deal are relevant to this topic and can be looked up on Wikipedia among other sources. Unless the delays or speedups can be forecast, then I can't see how you can expect to forecast their effect.

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  • $\begingroup$ I guess my main point is that I'm not trying to forecast the effect of delays - the forecasting should assume there will be no further delays at all. Suppose the percentage increases steadily (with minor random variation) at 1% a day for 30 days, then 0.1% per day for 10 days, then 1% a day for 30 days. Based on the entire data, and the assumption the progress should have been linear overall, it's logical to assume a 1% increase for the whole time. A linear trend which uses the entire data would predict a much later completion date. But I don't want to ignore the first 30 days altogether. $\endgroup$
    – Stephen
    Jul 14, 2013 at 0:46
  • $\begingroup$ The problem is really trying to separate intervals of a separate trend from simple random variation in the main trend, and determine exactly which parts should count as either type. What is the gradient of 'most' of the data? $\endgroup$
    – Stephen
    Jul 14, 2013 at 0:49

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