Calculating the math of the network diagram is a beginner project management skill. See this little 8-minute video on how that math calculation works. (Go to video now.)

Fast tracking: Changing the flow of the network diagram so that you are doing some work in parallel that you had previously planned on doing sequentially. This alters both the network diagram paths and possibly also the critical path.

Crashing: Adding resources (more equipment, people, or vendors) to the project activities to get them done faster than originally estimated. These keeps the sequence in the network diagram, but may alter the critical path.

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.

Read a good description of critical chain here. But when comparing this to normal project scheduling remember that critical chain eliminates the multi-tasking. It buffers all of the slack and contingency into a project pool, instead of building it in along the scheduling.

There are two types of budget reserves: contingency and management. Contingency reserves are allowances for unplanned but potentially required changes that can result from realized risks identified in the risk register. Management reserves, on the other hand, are budgets reserved for unplanned changes to project scope and cost. The PM may be required to obtain approval before obligating or spending the mgmt reserve, but generally this approval is not needed from the sponsor for the contingency reserve.

Management reserves are not part of the project cost baseline, but they may be included in the total budget for the project. Contingency reserves are ideally included in the cost baseline and budget.