Earned Value Management – Application of PERT on EACs

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01:45 – Putting the Basic EVM Parameters SV and CV on the graph
04:15 – Calculating the SPI, CPI, and CSI
07:00 – Calculating the different Estimates at Completion
10:45 – Calculating the EAC @ 50% and the corresponding standard deviation using PERT
13:40 – Determining the borders of the confidence interval with 1 standard deviation (68%)
16:50 – Estimate at Completion @ 80% with z = 0.8416
19:50 – Conclusions

Using Earned Value Management, it is possible to calculate different estimates at completion: the mathematical, the CPI-based, and the CSI-based estimated. They are also called respectively the Optimistic, Probable, and Pessimistic Estimated at Completion.

When considering the terminology optimistic, probable, and pessimistic estimates, it reminds me of the PERT and 3Point formulas that introduce uncertainty and risk in our estimates. Remember that the formulas are:

PERT
(opt + 4 x prob + pess)/6
(pess – opt)/6

3Point
(opt + prob + pess)/3
(pess – opt)/5

In our application here, we will use the PERT formula to calculate the estimate at 50% and the corresponding standard deviation:

1. Calculating SV and CV
From the data, we know that BAC = 1,000k, PV(50%) = 500k, EV(50%) = 300k and AC(50%) = 450k
So, we find
SV = EV – PV = 300k – 500k = -200k
CV = EV – AC = 300k – 450k = -150k

2. Calculating SPI, CPI and CSI
Based on the previous values we can calculate the performance indices

SPI = EV/PV = 300/500 = 0.6
CPI = EV/AC = 300/450 = 1/1.5
CSI = SPI x CPI = 0.4

3. Calculating the Estimates at Completion
Based on the CPI and CSI, we can calculate the different EACs

Mathematical or Optimistic = AC + (BAC – EV) = 540 + (1,000 – 300) – 1,150k
CPI-based or Probable = BAC/CPI = 1.5 x 1,000 = 1,500k
SPI-based or pessimistic = AC + (BAC – EV)/CSI = 540 + 700/0.4 = 2,200k

4. Calculating the PERT estimates

[email protected]% = (opt + 4 x prob + pess)/6 = (1,150 + 4 x 1,500 + 2,200)/6 = 1,558k
SD = (pess – opt)/6 = (2,200 – 1,150)/6 = 117k

5. Confidence interval 68% and 1 Standard Deviation

EAC with a probability of 68% is between 1,441k and 1,657k

84% probability that EAC(80%) is smaller than 1,675k

6. Probability at 80%

EAC(80%) = [email protected]% + z x SD = 1,558 + 0.8416 x 117 = 1,656k

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