ETC calculation including SPI

Question

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.

Edit 1

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.

Edit 2

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?

Answer 1

The issue with using formula is that it will provide an extremely precise, deterministic value that lives in a range of probabilistic values. Although extremely precise, no single formula will give you a high degree of accuracy, i.e., all formula have varying degrees of accuracy and thus are useful. But that means you need to use several of them so that you can visualize the range of results that will give you the total risk. I am attaching a fake S Curve to show you the results of several different modeling approaches:

This project is supposed to take 16 periods with BAC of 2.650. EV is .620; PV is .663; AC is .672. I also did an Earned Schedule calculation and that suggests it'll take 18 periods, versus 16, to finish the work.

The orange line is the formula that includes SPI and the light blue is the formula that excludes the CPI. The ES trend line, the gray line, is an extrapolation from actual costs to get to period 18. The EV trend is an extrapolation from EV to get to period 18. You can see in this simple example that the ES trend line is closer to the formula result including the SPI. This suggests to me that the formula with SPI is reliable and those results are within the probable values. So if I were predicting an EAC and need to publish a single value, I'd likely choose a value between what both of those formulas are indicating. I'd go up or down based on other variables I know to be true.

Either way, don't reject any one formula. They all have usefulness and will help you visualize the probabilistic range that represents more reality than any single result would ever do.

(If you extend the blue line to period 18, you will intersect the orange line at the y-axis. So including SPI in the formula is consistent with what earned schedule suggests for a timeline.)

EDIT based on the updated question for the PMP exam: Table 7-1 on page 224 of the PmBOK shows four formulas for EAC. Those are the four you need to memorize. If you were to get a question asking for an EAC, run those four formula. One of the four multiple choice answers will coincide with the result of one of those four. In practice, there are an infinite number of predictive models, or formulas, you could use. The PMP test cannot administer a question using some obscure formula that is not resident in the PMBOK. Notwithstanding you found a weighting formula in their earned value book, the PMBOK would be a prevailing source for the PMP test.