Search

   

 



 

Control Chart

A control chart is a statistical tool used to distinguish between variation in a process resulting from common causes and variation resulting from special causes. It presents a graphic display of process stability over time.

When should we use a control chart?

A stable process is one that is consistent over time with respect to the center and the spread of the data. Control charts help you monitor the behavior of your process to determine whether it is stable. Like run charts, they display data in the time sequence in which they occurred. However, control charts are more efficient than run charts in assessing and achieving process stability.

Your team will benefit from using a control chart when you want to:

  • monitor process variation over time;

  • differentiate between special cause and common cause variation;

  • assess the effectiveness of changes to improve a process; and

  • communicate how a process performed during a specific period.

How do we develop a control chart?

Developing a control chart consists of four major steps:

Step 1: Determine what to measure

Step 2: Collect the data

Step 3: Plot the data

Step 4: Calculate the control limits

The first step in constructing a control chart is to identify one key measure you want to track over time or against some base other than time. This measure should be a “quality/productivity” (external customer or internal process) indicator providing information useful in making decisions.

Possible measures include:

  • Volume (i.e., how much over a specified period of time)

  • Cycle time (i.e., how long something takes)

  • Errors and defects (i.e., how many are incorrect over a period of time)

  • Waste (i.e., how much is reworked or rejected)


The following example illustrates how you can use the Control Chart in a service-related situation.

A major hotel in large metropolitan area…recently embarked on a quality-improvement effort. Steve, the new Quality Manager, discovered through a customer survey that the billing process was rated “high” in importance and received the most complaints. He decided to collect data on the number and types of errors to determine if the billing process was “in control” (i.e., its variation was due to day-to-day or common causes of variation) and to see where improvements could be made. Steve decided to use P-chart, which would help him identify the percentage of billing statements that contained errors….

Step 2: Collect The Data

Collect data then calculate the percent defective in the space provided. Items to be included on your data collection form include, but are not limited to:

  • date;

  • number inspected;

  • number defective;

  • types of defects/errors; and

  • percent defective.

Some tips that will help you collect data include:

  • Use a sample containing at least 50 items (the sample should be big enough to give an average of three or more defects per sample)

  • Avoid taking samples over long periods of time (i.e., try to break large samples up into more manageable two or four-hour time periods versus sampling full 24-hour day)

  • Avoid varying sample sizes

  • Take a minimum of 20 sets of samples

The billing department…had completed basic statistics training, so it wasn’t difficult for Steve to find volunteers eager to test their newly acquired skills. Michelle, a billing analyst, offered to inspect 50 hotel bills on a daily basis to find out how many times there were problems with customers’ bills (the number one customer complaint). Steve asked her to use the data collection form to keep track of the information that would be used to determine the state of the billing process…(See Diagram 1)

Creating a control chart consists of four major steps:

Step 1: Determine what to measure

Step 2: Collect the data

Step 3: Plot the data

Step 4: Calculate the control limits


Step 1: Determine what to measure

The first step in constructing a control chart is to identify one key measure you want to track over time or against some base other than time. This measure should be a “quality/productivity” (external customer or internal process) indicator providing information useful in making decisions.

Possible measures include:

  • Volume, e.g., how much over a specified period of time

  • Cycle time, e.g., how long something takes

  • Errors and defects, e.g., how many are incorrect over a period of time

  • Waste, e.g., how much is reworked or rejected

The example below illustrates how you can use the control chart in a service-related situation.

A major hotel in a large metropolitan area recently embarked on a quality-improvement effort. Steve, the new Quality Manager, discovered through a customer survey that the billing process was rated “high” in importance and received the most complaints. He decided to collect data on the number and types of errors to determine if the billing process was “in control” (i.e., its variation was due to day-to-day or common causes of variation) and to see where improvements could be made. Steve decided to use P-chart, which would help him identify the percentage of billing statements that contained errors.



Step 2: Collect the data

Collect data then calculate the percent defective in the space provided. Items to be included on your data collection form include, but are not limited to:

  • date

  • number inspected

  • number defective

  • types of defects/errors

  • percent defective

 

Some tips that will help you collect data include:

  • Use a sample containing at least 50 items, i.e., the sample should be big enough to give an average of three or more defects per sample

  • Avoid taking samples over long periods of time, i.e., try to break large samples up into more manageable two or four-hour time periods versus sampling full 24-hour day

  • Avoid varying sample sizes.

  • Take a minimum of 20 sets of samples.

The billing department had completed basic statistics training, so it wasn’t difficult for Steve to find volunteers eager to test their newly acquired skills. Michelle, a billing analyst, offered to inspect 50 hotel bills on a daily basis to find out how many times there were problems with customers’ bills (the number one customer complaint). Steve asked her to use the data collection form to keep track of the information that would be used to determine the state of the billing process…(See Diagram 1 below.)

 

Diagram 1 – Sample Control chart data collection sheet
(3.5 recorded on 7-22, not a consensus on whether one was a real defect; count .5)
     
Types of Defects
  
Remarks
Date
No. of
inspected
Wrong
Room
Wrong
Name
Wrong
Address
Incomplete
Information
% Defective
 
7-14
50
8
1
1
 
20
 
7-15
50
13
 
  
1
28
 
7-16
50
11
 
1
  
24
 
7-17
50
10
3
1
1
30
 
7-18
50
12
 
1
1
28
 
7-21
50
14
1
 
 
30
 
7-22
50
3.5
1
2
1
15
 
7-23
50
13
7
2
2
48
 
2-24
50
9
 
1
1
22


Step 3: Plot the data

After you’ve taken at least 20 samples and calculated the percent defective for each, create the plotting scale on the vertical axis of the graph. The scale should reveal whatever is appropriate for your particular measurement. Create a horizontal axis with a point for each sample date.

Plot the individual percent defectives on the graph. Next, compute the average percent defective by adding all of the percent defectives for the individual samples and dividing the result by total number of samples taken (in this case 20). Draw a horizontal line at the appropriate value, and label it (=).

Michelle began the workday by spending 15 minutes checking the bills for room number errors, as well as address errors, name errors, and incomplete information. She also calculated the percentage of bills that were defective for 20 working days. She then plotted the individual percentages, connected the line, and calculated the average percent defective, or (View Diagram 2).

Step 4: Calculate the control limits

Control limits will tell you if your process is in statistical control (i.e., the process is exhibiting only common cause variation, or the usual amount of day-to-day variation you might expect from common reasons, such as slightly different materials, methods, machines etc.). Think of control limits as invisible boundary lines. As long as the data points are within the boundary lines, everything is “OK.” However, when data points are outside the boundary, alarms should go off, and you’ll need to investigate why the boundary has been crossed. Control limits are calculated by using the following formula:

Having plotted all the data points Michelle calculated the upper and lower control limits for the billing process (View Diagram 3) where:

        UCLP = Upper Control Limit
        LCLP = Lower Control Limit
= Square Root
   n = Sample Size
                      P = Average Percent Defective

She found the corresponding points on the vertical axis of the graph and drew the horizontal lines above and below the average line. She labeled them with the upper and lower control limit values. (View Diagram 4).

 

Follow-up: Decide On Next Steps

What you do next depends upon whether or not your points are within the control limits.

If all points are within the control limits:

  • Continue with no changes

  • Recreate the P-chart periodically to double-check process control

  • Make improvements to the process to reduce common variations

  • Review to ensure any changes have had a positive effect

 

If one or more points are outside the control limits:

  • Investigate and take steps to eliminate the cause(s)

  • Review to ensure changes have had a positive effect, i.e., uncommon causes have been eliminated

  • Take new samples, and create a new P-chart using limits based on the new information

Having found the billing process to be out of control, i.e., one or more points outside the control limits; (View Diagram 5), Michelle and two other billing analysts began an investigation into the causes. They knew process improvements could not take place until all special causes, those which caused the data to be outside the control limits, had been identified and eliminated. From recent training, they knew special causes could be assigned to several main categories, including:

  • Equipment

  • Materials

  • Methods, i.e., not having a consistent method for the process

  • People, e.g., not having the necessary training, etc.

  • Environment, i.e., literally: a heat wave, earthquake, etc., or new management, company direction, etc.

They also knew the investigation process wouldn’t be easy but were confident real improvements could be made after the process was “in control.” The next challenge would be reducing the average defect rate substantially, from 27.22% to less than 5%, within six months. With the right problem solving and quality improvement tools, they felt they could accomplish their goal.

 

In summary, use the control chart when:

  • Trying to determine if a process is in statistical control, i.e., a process is said to be “out of control” when a data points falls outside of the control limits

  • You and your team want to create a visual representation of process performance. Like the run chart, the control chart provides a picture of process performance that can be used as a process-tracking device.

  • You and your team want to distinguish between a special cause variation - a clear occurrence of something not normally part of the process, and a common cause variation - coincidental changes that are inherent in the process

  • You and your team know the process will not change while you are collecting data. The process must not be changed because the intent is to see how the process performs “naturally."

 

More Quality Tools

This is best viewed with MS Internet Explorer 5.5 or Netscape Navigator 4.78 and above.
You can set your video resolution to 800x600 pixels (16 bit/24 bit color/32 bit) for best results.
You may send your comments to the Web Development Team.
Copyright©2002 All Rights Reserved. DLSU-Manila