PMBok (page 221) mentions two formulas for estimation ETC based on previous project performance. These are:
(1) ETC = (BAC-EV) / CPI
(2) ETC = (BAC-EV) / (CPI * SPI)
While (1) is completly clear for me, I don't understand the motivation for including SPI in (2).
(There are other estimations too, like assuming the remaining work procceds like planed ETC = BAC - EV, or new bottom-up analysis if boundary conditions have changed strongly. These estimations are not considered in my question.)
Assuming that we can proportionaly reduce task duration by adding resources [ money / duration ] , i would expect the total remaining cost [ money / duration ] * [duration] to stay constant.
If the process cannot be speeded by additional resources due to its nature I don't see a point in adding resources.
So basically I don't see why in this case the factor time should be included in the ETC calculation. CPI = EV/AC, this definition is independent if we are ahead or behind shedule. And extrapolation should be indepentently if we increase burn rate or not.
Inspired by the answer of David, I did my own calculations. Also some test estimations showed that the first formula always gives the correct results, whilest the second formula only converges to the final value at the end of the project.
Formula (2) only seems to be correct if we would define CPI = PV / AC, which is not correct.
In this PMI publication I have found a third formula.
(3) ETC = (BAC-EV) / (CPI*0.8 + SPI*0.2)
I cannot find a mathematical justification for this. The weighting of 0.8 seems to be arbitrary. Instead of using the historic SPI, it would have more justification to include somthing like a To-complete-Scope-performance-index TSPI = (BAC-EV)/(BAV-PV).
I can only interpret it that this formulars are used in industry. They might seem to have higher accuracy in some cases, but I i expect this just due to compensation of inaccurate estimation of EV (project progress)
So my most important question is:
What are the criteria, to decide which formula to use in the PMI exam?