Control charts are statistical tools used to determine if a process is in or out of control. There are variable control charts that measure continuous variables like weight or volume, and attribute control charts that measure quality attributes. Common variable charts include X-bar, R, and MA charts. Common attribute charts are P, C, and U charts. An example control chart using percent defective data is presented to demonstrate calculating the average, standard deviation, and control limits to determine if the process is in control.

1. Control ChartsControl Charts
• Definition:Definition:
- A statistical tool to determine if a- A statistical tool to determine if a
process is in control.process is in control.

2. History of Control ChartsHistory of Control Charts
• Developed in 1920’sDeveloped in 1920’s
• By Dr. Walter A. ShewhartBy Dr. Walter A. Shewhart
• Shewhart worked for Bell Telephone LabsShewhart worked for Bell Telephone Labs

3. Two Types of Control ChartsTwo Types of Control Charts
• Variable Control ChartsVariable Control Charts
• Attribute Control ChartsAttribute Control Charts

4. Variable Control ChartsVariable Control Charts
• Deal with items that can be measured .Deal with items that can be measured .
• ExamplesExamples
1) Weight1) Weight
2) Height2) Height
3) Speed3) Speed
4) Volume4) Volume

5. Types of Variable ControlTypes of Variable Control
ChartsCharts
• X-Bar chartX-Bar chart
• R chartR chart
• MA chartMA chart

6. Variable Control ChartsVariable Control Charts
• X chart: deals with a average value in aX chart: deals with a average value in a
processprocess
• R chart: takes into count the range of theR chart: takes into count the range of the
valuesvalues
• MA chart: take into count the movingMA chart: take into count the moving
average of a processaverage of a process

7. Attribute Control ChartsAttribute Control Charts
• Control charts that factor in the qualityControl charts that factor in the quality
attributes of a process to determine if theattributes of a process to determine if the
process is performing in or out of control.process is performing in or out of control.

8. Types of Attribute ControlTypes of Attribute Control
ChartsCharts
• P chartP chart
• C ChartC Chart
• U ChartU Chart

9. Attribute Control ChartsAttribute Control Charts
• P Chart: a chart of the percent defective inP Chart: a chart of the percent defective in
each sample set.each sample set.
• C chart: a chart of the number of defectsC chart: a chart of the number of defects
per unit in each sample set.per unit in each sample set.
• U chart: a chart of the average number ofU chart: a chart of the average number of
defects in each sample set.defects in each sample set.

10. Reasons for using ControlReasons for using Control
ChartsCharts
• Improve productivityImprove productivity
• Make defects visibleMake defects visible
• Determine what process adjustments needDetermine what process adjustments need
to be madeto be made
• Determine if process is “in” or “out ofDetermine if process is “in” or “out of
controlcontrol

11. Real World Use of ControlReal World Use of Control
ChartsCharts
• Example from “Managing Quality” byExample from “Managing Quality” by
Foster.Foster.
– The Sampson company develops special equipment forThe Sampson company develops special equipment for
the United States Armed Forces. They need to usethe United States Armed Forces. They need to use
control charts to insure that they are producing acontrol charts to insure that they are producing a
product that conforms to the proper specifications.product that conforms to the proper specifications.
Sampson needs to produce high tech and top of theSampson needs to produce high tech and top of the
line products, daily so they must have a process thatline products, daily so they must have a process that
is capable to reduce the risks of defects.is capable to reduce the risks of defects.

12. How Will Using Control Charts help yourHow Will Using Control Charts help your
Company?Company?
• Possible Goals when using Control ChartsPossible Goals when using Control Charts
in your Company:in your Company:
– Line reengineeringLine reengineering
– Increased Employee motivationIncreased Employee motivation
– Continually improve of your processContinually improve of your process
– Increased profitsIncreased profits
– Zero defectsZero defects

13. Control Chart Key TermsControl Chart Key Terms
• Out of Control: the process may notOut of Control: the process may not
performing correctlyperforming correctly
• In Control: the process may be performingIn Control: the process may be performing
correctlycorrectly
• UCL: upper control limitUCL: upper control limit
• LCL: lower control limitLCL: lower control limit
• Average value: averageAverage value: average

14. Process is OUT of control if:Process is OUT of control if:
• One or multiple points outside the controlOne or multiple points outside the control
limitslimits
• Eight points in a row above the averageEight points in a row above the average
valuevalue
• Multiple points in a row near the controlMultiple points in a row near the control
limitslimits

15. Process is IN control if:Process is IN control if:
• The sample points fall between the controlThe sample points fall between the control
limitslimits
• There are no major trends forming, i.e.. TheThere are no major trends forming, i.e.. The
points vary, both above and below thepoints vary, both above and below the
average value.average value.

16. Calculating Major Lines in aCalculating Major Lines in a
Control ChartControl Chart
• Average Value: take the average of the sample dataAverage Value: take the average of the sample data
• UCL: Multiply the Standard deviation by three. ThenUCL: Multiply the Standard deviation by three. Then
add that value to the Average Value.add that value to the Average Value.
• LCL: Multiply the Standard deviation by three. ThenLCL: Multiply the Standard deviation by three. Then
subtract that value from the Average Value.subtract that value from the Average Value.

17. Examples of Control ChartsExamples of Control Charts

18. Examples of Control ChartsExamples of Control Charts

19. Control ChartsControl Charts
• The following control chart shows theThe following control chart shows the
improvement of a process. The standardimprovement of a process. The standard
deviation decreases as the processdeviation decreases as the process
becomes more capable.becomes more capable.

20. Example of Control ChartsExample of Control Charts

21. How to Calculate theHow to Calculate the
standard deviationstandard deviation
• P chart:P chart:
– P= percent or rateP= percent or rate
– N= number of trailsN= number of trails

22. How to Calculate theHow to Calculate the
standard deviationstandard deviation
• C chart:C chart:
– X= the averageX= the average

23. How to Calculate the controlHow to Calculate the control
limitslimits
• X-bar Chart:X-bar Chart:
Lower Control Limit:Lower Control Limit:
• Mean – 3*sigmaMean – 3*sigma
n(1/2)n(1/2)
Center Line:Center Line:
• Process meanProcess mean
Upper Control Limit:Upper Control Limit:
• Mean + 3*sigmaMean + 3*sigma
n(1/2)n(1/2)

24. How to Calculate the controlHow to Calculate the control
limitslimits
• R chart:R chart:
– Lower Control Limit:Lower Control Limit:
• R-Bar – 3*d3*sigmaR-Bar – 3*d3*sigma
– Center Line:Center Line:
• R-BarR-Bar
– Upper Control Limit:Upper Control Limit:
• R-Bar + 3*d3*sigmaR-Bar + 3*d3*sigma

25. Sample SizeSample Size
• The sample set of data should be greaterThe sample set of data should be greater
than 28.than 28.
• The data should have been collectedThe data should have been collected
uniformlyuniformly
• The data should contain multiple capableThe data should contain multiple capable
points of data, or the information ispoints of data, or the information is
incorrect.incorrect.

26. ExampleExample
• First Step: Determine what type of dataFirst Step: Determine what type of data
you are working with.you are working with.
• Second Step: Determine what type ofSecond Step: Determine what type of
control chart to use with your data set.control chart to use with your data set.
• Third Step: Calculate the average and theThird Step: Calculate the average and the
control limits.control limits.

27. ExampleExample
• The following slides contain data andThe following slides contain data and
questions for your practice with controlquestions for your practice with control
charts. Please take the process step bycharts. Please take the process step by
step and look back to previous slides forstep and look back to previous slides for
help.help.

28. ProblemProblem
• You have gathered a sample set of data for yourYou have gathered a sample set of data for your
company. The data is in the form of percents. Yourcompany. The data is in the form of percents. Your
company wants your recommendation, is thecompany wants your recommendation, is the
process in control.process in control.
• What type of control chart should you use? (VariableWhat type of control chart should you use? (Variable
or Attribute)or Attribute)

29. ProblemProblem
• What type of specific control chart shouldWhat type of specific control chart should
you use with that type of sample set? (X-you use with that type of sample set? (X-
bar, R-chart, MA-chart, P-chart, R-chart, orbar, R-chart, MA-chart, P-chart, R-chart, or
U-chart)U-chart)

30. ProblemProblem
• Now that you have determined the controlNow that you have determined the control
chart to use, you have to calculate thechart to use, you have to calculate the
average and standard deviation. Use theaverage and standard deviation. Use the
data on the following slide. Take notice todata on the following slide. Take notice to
the amount of sample data. (n>28)the amount of sample data. (n>28)

31. Sample DataSample Data
DayDay PercentPercent DayDay PercentPercent
11 .056.056 1515 .068.068
22 .078.078 1616 .038.038
33 .064.064 1717 .077.077
44 .023.023 1818 .068.068
55 .067.067 1919 .053.053
66 .078.078 2020 .071.071
77 .067.067 2121 .037.037
88 .045.045 2222 .052.052
99 .034.034 2323 .072.072
1010 .045.045 2424 .047.047
1111 .062.062 2525 .042.042
1212 .051.051 2626 .051.051
1313 .070.070 2727 .064.064
1414 .039.039 2828 .071.071

32. • Now that you have calculated the threeNow that you have calculated the three
important lines for the control chart, plotimportant lines for the control chart, plot
the data and determine if the process isthe data and determine if the process is
capable. (i.e. The data falls mostly insidecapable. (i.e. The data falls mostly inside
the UCL, and the LCL)the UCL, and the LCL)
ExampleExample

33. Final StepFinal Step
• Make a recommendation to your company.Make a recommendation to your company.
– The process is capableThe process is capable
– The process is not capableThe process is not capable
• The following errors were found.The following errors were found.
• The process needs improvementThe process needs improvement
• The variations are normal in the system and weThe variations are normal in the system and we
must accept them.must accept them.

34. Control Charts ReviewControl Charts Review
• What have we learned?What have we learned?
– Control Charts are a useful way to determine theControl Charts are a useful way to determine the
capability of a process.capability of a process.
– The different types of control charts.The different types of control charts.
– How to calculate the control limits for a controlHow to calculate the control limits for a control
chart.chart.

35. Works CitedWorks Cited
““Control Charts as a tool in SQC.” Internet.Control Charts as a tool in SQC.” Internet. http://deming.eng.clemson.edu/pub/tutorials/qctools/ccmain1.htmhttp://deming.eng.clemson.edu/pub/tutorials/qctools/ccmain1.htm..
31 January 2001.31 January 2001.
Foster, S. Thomas.Foster, S. Thomas. Managing Quality.Managing Quality. Upper Saddle River: Prentice Hall, Inc. 2001.Upper Saddle River: Prentice Hall, Inc. 2001.
““Generating and Using Control Charts.” Internet.Generating and Using Control Charts.” Internet. http://www.hanford.gov/safety/upp/spc.htmhttp://www.hanford.gov/safety/upp/spc.htm.. 31 January 2001.31 January 2001.
““Quality and Statistical Process Control.” Internet.Quality and Statistical Process Control.” Internet. http://www.systma.com/tqmtools/ctlchtprinciples.htmlhttp://www.systma.com/tqmtools/ctlchtprinciples.html.. 1212
February 2001February 2001..
““Statistical Thinking Tools-Control Charts for the Average.” Internet.Statistical Thinking Tools-Control Charts for the Average.” Internet.
http://www.robertluttman.com/yms/Week5/page6.htmhttp://www.robertluttman.com/yms/Week5/page6.htm. 12 February 2001.. 12 February 2001.