This is the last in the series of posts on 7 different management tools that can be used on Six Sigma projects. This last tool of activity network diagramsi is used when you have decided on a Six Sigma Project, and you need to know how long it is going to take. Also, you need to be in a position to be able to figure out whether you can compress the schedule to reduce the time it takes to do the project. Finally, you need to plan on effective risk management to make sure that the project stays on schedule.
To do this, you need to create an activity network diagram. Once you create the diagram you need to figure out the critical path, which is the path from the start to the finish of the project with the longest cumulative duration. Those activities on the critical path may not be delayed without delaying the schedule as a whole. Other activities that are NOT on the critical path may be delayed for a certain period of time without affecting the schedule, and the amount of “wiggle room” in the schedule for any given activity is called the float of that activity.
First step is creating the activity network diagram.
Step  Description  
1.  Define Activities  Take the work breakdown structure or WBS, which takes the general objectives of the project and breaks them down into deliverables. Then take each deliverable and list all activities it will require to accomplish it. 
2.  Sequence Activities  Sequence the activities based on the precedence relationship between them. Some activities have to be completed before others are started, for example. Other activities may be able to be done simultaneously. Based on these relationships between activities, create a network diagram that looks like a flowchart with a box for each activity. 
3.  Estimate Activity Durations  Add a duration to each of the boxes containing the activities. 
4.  Critical Path Method  Calculate the duration of the various “branches” of the network in order to determine which branch is the critical path of the network. 
5.  Calculate “Float” or “Slack”  Using the forward pass and backward pass method, calculate the total float or slack of each of the activities. NOTE: An activity on the critical path will have ZERO float BY DEFINITION 
6.5.2. Critical path method
To determine how long a project will take, you need to find out the critical path, that is, the sequence of activities in the network diagram that is the longest. Other paths along the network will yield sequences of activities that are shorter than the critical path, and they are shorter by an amount equal to the float. This means that activities that have float could be delayed by a certain amount without affecting the schedule. Activities along the critical path have a float of zero. This means that any delay along the critical path will affect the schedule.
Here’s an outline of the critical path methodology.
a. You create a network diagram of all the activities.
b. You label each activity with the duration derived from process 6.4 Estimate Activity Durations.
c. You do a forward pass to determine the early start and early finish date of all activities, from the start of the project to the end of the project.
d. Once at the end of the project, you do a backward pass to determine the late start and late finish date of all activities, from the end of the project to the start of the project.
e. For each activity, you use the results of c and d to calculate the float of each activity.
f. All activities that have 0 float are on the critical
path for that project.
Let’s take a look at the methodlogy in general.
Step 1. For each activity, create a matrix which will contain the duration, the early start, the early finish, the late start, late finish, and float for a particular activity.
Activity Number 

Duration 

Early Start (ES)  Early Finish (EF) 
Late Start (LS)  Late Finish (LF) 
Float 
Here are the meanings of the numbers in the boxes:
Activity Number: you can label them A through Z, or 1 through N, just as long as each activity has a unique identifier.
Duration: this is the number that you should get as an output of the 6.4 Estimate Activity Durations process.
Early Start (ES): The Early Start is the number you begin the analysis with to do the forward pass. It is defined as 0 for the first activity in the project. The Early Start for subsequent activities is calculated in one of two different ways, which will be demonstrated below.
Early Finish (EF): This is the next number you go to in the forward pass analysis. It is taken by adding the number in the ES box plus the number in the Duration box.
Late Finish (LF): The Late Finish is the number you begin the analysis with to do the backward pass. It is defined to be equal to the number in the Early Finish box for the last activity in the project. The Late Finish for preceding activities is calculated in one of two different ways, which will be demonstrated below.
Late Start (LS): This is the next number you go to in the backward pass analysis. It is taken by subtracting the number in the Duration box from the number in the LF box.
Float: Once ES, ES, LF, and LS are determined, the float is calculated by either LS – ES or LF – EF. Just remember that a piece of wood will float to the top of the water, so the float is calculated by taking the bottom number and then going upward and subtracting the number that’s on the top of it.
Step 2.
For activity A, the first activity in the project, ES = 0.
A 

0 

Step 3.
Then EF for activity A is simply ES + duration. Let’s say activity A takes 5 days. Then EF = 0 + 5 = 5.
A 

5 

0 
5 
Step 4.
The forward pass for activity A is complete. Let’s go on to activity B.
Since activity B has only one predecessor, activity B, the ES for activity B is simply equal to the EF of activity A, which was 5.
B 

3 

5 

Then the EF for activity B is taken by adding the ES of to the duration of activity B or 3, giving EF = 5 + 3 = 8.
There’s one more situation that we have to discuss and that is if an activity has more than one predecessor.
Let’s assume the durations for each activity are as follows:
Activity  Duration 
A  5 
B  3 
C  6 
Assume Activity A and Activity B are both done concurrently at the start of the project, and both need to be done in order for Activity C to start. Well, before we do the formal forward pass analysis, what does logic tell us? Activity A takes 5 days; Activity B takes 3 days. Both activity A and B have to be done before Activity C can take place. In this case the start date of the project is considered to be 0. Can Activity C take place on day 3, when activity B is done? No, because Activity A isn’t completed yet, and you need BOTH A and B to be done. The earliest possible start date for Activity C will be day 5, because only on that date will both A and B be done.
So this illustrates the other way of calculating ES for an activity B. If there are multiple predecessors, then the ES is equal to the LARGEST of the ES of the predecessor activities.
Step 5.
Now, let’s assume we are at the end of the project at activity Z.
Z 

5 

95 
100 
EL = ES + duration gives us EL = 95 + 5 + 100. So the project will take 100 days according to our forward pass calculation.
Now, we have the backward pass.
We start this out by stating as a principle that the late finish or LF date for the last activity in the project is equal to the EF date.
Z 

5 

95 
100 
100 

Then, of course, the late start date or LS = LF – duration = 100 – 5 = 95.
Z 

5 

95 
100 
95 
100 
Step 6.
Now we go in the reverse direction towards the beginning of the network diagram, this time filling out the bottom LS and LF boxes for each activity.
If the activity has one successor, then the LF for the predecessor activity equals the LS for the successor of activity. But if there are more than one predecessor activity, then here’s what you do. For the forward pass, you take the highest EF of all predecessors.
For the backward pass, you take the lowest LS of all successors. Let’s see how this works.
Let’s assume the forward pass is done on A, B, and C. We do the backward analysis and we get to the following point. What is the LF of activity A?
A 
B 
C 

5 
3 
4 

0 
5 
5 
8 
5 
9 
6 
9 
5 
9 

Well, activity B and activity C are both successors of A. In this case, activity B has an LS of 6 and activity C has an LS of 5. The earliest LS is therefore 5, and so LS of activity A is 5.
A 
B 
C 

5 
3 
4 

0 
5 
5 
8 
5 
9 
0 
5 
6 
9 
5 
9 
Step 7.
What is the float? Take LF – EF (or LS – ES) for each of the activities.
A 
B 
C 

5 
3 
4 

0 
5 
5 
8 
5 
9 
0 
5 
6 
9 
5 
9 
0 
1 
0 
So the float of B is 1, and the float of A and C are 0. Therefore A and C are on the critical path.
If you were trying to shorten the length of the project you could do it by crashing or adding more resources to a specific activity to get it done in less time. Or you could fast track an activity so that if you have two activities that normally come one right after the other like this:
you can take the second activity and fast track it by starting it BEFORE the first activity is completed.
In this case, you don’t have increased cost like you do when you are crashing an activity, but you do have increased risk based on the need to coordinate the activities being done partly at the same time. The only time when fast tracking might cost additional resources would be if the people who are doing activity 1 and activity 2 are the same people.
In any case, you can see how the critical path lets you know what activities are critical to maintain the planned schedule, but it also shows you where you can compress the schedule most effectively, and gives you indications as to where the higher risk areas will be in the schedule. Those activities that have several predecessor activities that MUST be done first will need more scrutiny than those that only have one predecessor, for example.
This concludes the review of the 7 management tools that are used in Six Sigma. They are not exclusively used in Six Sigma, of course, but they are tools for brainstorming, for analyzing, and for planning a Six Sigma project.
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