NEW 7 QC TOOLS

Arrow Diagram

Purpose

The purpose of an arrow diagram is to create a visual presentation of the steps of a process or tasks necessary to complete a project with special emphasis on the time taken for these activities. The diagram provides a clear understanding of the schedule of various steps in the process which helps one to monitor the process for ensuring its completion on time.

Procedure

The steps for preparing an arrow diagram are :

  1. List all tasks or activities that need to be accomplished before the completion of the process or the project.
  2. Decide which steps are undertaken in series and which steps can be run in parallel.
  3. Arrange the activities in a proper sequence.
  4. Prepare ‘Event Nodes’ at the completion of steps and number them. Where the process is bifurcating into two or more parallel streams, more lines will flow from a node and where the parallel streams are merging, two or more steps will lead to a node.
  5. Write the description of the step on top of the line or to the left of the line. Decide the time required for completing each step and write it under or to the right of the line.
  6. Calculate the earliest time to reach an event node for the start of the process. Where more than one streams are combining, the maximum time taken by a stream is taken into consideration. This time is entered on the top half of the rectangle. This time is related to the starting time of the process which is taken as zero.
  7. After the time for all event nodes including the completion of the process or the project is available, one calculates the latest time by which an event node must be reached. This is done by starting at the time of completion and going back step by step. The time is entered on the bottom half of the rectangle. The time indication at all event nodes will appear as :

    8. 15.JPG

    where X is the earliest time by which the event can be completed and Y is the latest time by which the event should be completed.

  8. Give a title to the diagram.

As the calculation of the time indications is extremely important in the construction of an arrow diagram it is necessary that we understand the procedure well. Let us understand the concept through diagram 13.

16.JPG

Let us calculate the time the events can be reached earliest by adding time for the step to the time of the earlier event starting with zero time at the start i.e. event-1. Where there are two streams one has to take the time for the longer or the critical path. The time to be put on the top half of the rectangle for the 15 event nodes are given in table 3.

For event node 7, we get two values. As the time for node 6 is 5 hours and

17.JPG

step from 6 to 7 takes one hour, the time for 7 would be 6 hours. But time for node 3 is 4 hours and the step from 3 to 7 takes 3 hours, the time for node 7 comes to 7 hours. The earliest both streams get ready is 7 hours and hence one has to take 7 hours as the time for node 7. The same principle has been applied for calculating the time for nodes 10 and 14.

Now let us see how to calculate the time to be put on the bottom half of the rectangle or the time by which the event must be reached to ensure 1 2 3 7 101114 15 8 9 2 52432 2 111

completion of the project on time. In this case one has to start with event 15 as 20 hours and calculate the time for the event by reducing the time taken for the step. Step from event 14 to 15 takes 2 hours. To complete the project at 20 hours, it is essential that one reaches event 14 by 18 hours. In this way we get the time by which the events must be accomplished. These are given in table 4.

18.JPG

In this case too, we get two values for some nodes. For instance for node 11, we get 14 hours if we consider the step form event 12 to 11 and 13 hours if we consider the step from event 14 to 11. Here the lower of the two values has to be taken. The same is true for events 7 and 2. If we combine the values given in tables 3 and 4, we get the time indication for all the event nodes as shown in table 5

19.JPG

The time indication for alternative nodes is shown on the arrow diagram as shown for event nodes 6 and 9 in diagram 14 a & b respectively.

20.JPG

A close look at the table shows that the time for all the events on the critical path, events 1, 2, 3, 7, 10, 11, 14 and 15, remains the same on both the top and the bottom halves of the rectangle. Where there is a difference between the two, there is a slack and the individual has a choice to schedule the steps within the limits of the two.

Applications

The most common application of an arrow diagram is in planning and scheduling projects which involve a large number of activities. The diagram is also useful in planning and scheduling steps in complicated processes. Once an arrow diagram is ready with time indications for all stages of the project or the process, referred as the event nodes in the procedure, one can look for opportunities to reduce the time taken for the project by concentrating on the steps on the critical path. It can then be used to monitor the progress of the project throughout its duration.