We consider using Z-scores an advanced scheduling formula that most project managers are probably not expected to know by heart. However, it's good to know where to find this formula when you need it...
The Z-Score is a calculation that helps you answer "Given a desired completion date, what is the probability that this completion date is reachable?"
Statistically the Z-score is the number of standard deviations from the mean a particular value is. For project management purposes, the value of Z is the number of standard deviations that the desired project due date is from the expected completion time.
To determine the Z-Score you would take the proposed project completion time (T), subtract the expected project completion time (T_{E}) from it, and divide it by the project standard deviation (σ): Z = (T-T_{E})/σ
Once you determine the Z-Score, you can translate the z-score into the probability percentage by using a Z-Score table such as the one at http://www.statsoft.com/textbook/distribution-tables/#z.
This is the step-by-step process:
Step 1: Calculate the expected completion time (T_{E}) using PERT
T_{E} = (O+4M+P)/6
Step 2: Calculate the variance of the project by calculating the variance of each task
Task Variance = [(P-O)/6]^{2}
Step 3: Calculate the standard deviation
Standard Deviation = √ Task Variance1 + Task Variance2 + Task Variance3… .
Step 4: Calculate the Z-Score
To calculate the Z-Score use the equation:
Z = (T-T_{E})/σ
The Z-Score (z) is the differnce between the desired completion time and the project's expected time divided by the standard deviation for the project.
Step 5: Calculate the probability of success now that you have figured out the Z-Score.
Translate that score (sigma value) into an actual percentage. This translation is done using a Z-Score table. Note that a Z-Score table is not calculated by the project manager—it is a pre-existing table that statisticians have already calculated for use with Z-Scores. The Z-Score contains the same values regardless of the application or industry.