control charts[1]

Control ChartsControl Charts

Training SlidesTraining Slides

02/19/0102/19/01


• Definition:Definition:

- A statistical tool to determine - A statistical tool to determine if a process is in control.if a process is in control.

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 Shewhart worked for Bell

Telephone LabsTelephone Labs

Two Types of Control Two Types of Control ChartsCharts

• Variable Control ChartsVariable Control Charts• Attribute Control ChartsAttribute Control Charts

Variable Control ChartsVariable Control Charts

• Deal with items that can be Deal with items that can be measured .measured .

• ExamplesExamples

1) Weight1) Weight

2) Height2) Height

3) Speed3) Speed

4) Volume4) Volume

Types of Variable Control Types of Variable Control ChartsCharts

• X-Bar chartX-Bar chart• R chartR chart• MA chartMA chart

Variable Control ChartsVariable Control Charts

• X chart: deals with a average value X chart: deals with a average value in a processin a process

• R chart: takes into count the range R chart: takes into count the range of the valuesof the values

• MA chart: take into count the MA chart: take into count the moving average of a processmoving average of a process

Attribute Control ChartsAttribute Control Charts

• Control charts that factor in the Control charts that factor in the quality attributes of a process to quality attributes of a process to determine if the process is determine if the process is performing in or out of control.performing in or out of control.

Types of Attribute Control Types of Attribute Control ChartsCharts

• P chartP chart• C ChartC Chart• U ChartU Chart

Attribute Control ChartsAttribute Control Charts

• P Chart: a chart of the percent P Chart: a chart of the percent defective in each sample set.defective in each sample set.

• C chart: a chart of the number of C chart: a chart of the number of defects per unit in each sample set.defects per unit in each sample set.

• U chart: a chart of the average U chart: a chart of the average number of defects in each sample number of defects in each sample set.set.

Reasons for using Control Reasons for using Control ChartsCharts

• Improve productivityImprove productivity• Make defects visibleMake defects visible• Determine what process Determine what process

adjustments need to be madeadjustments need to be made• Determine if process is “in” or “out Determine if process is “in” or “out

of controlof control

Real World Use of Control Real World Use of Control ChartsCharts

• Example from “Managing Quality” Example from “Managing Quality” by Foster.by Foster.– The Sampson company develops special The Sampson company develops special

equipment for the United States Armed Forces. equipment for the United States Armed Forces. They need to use control charts to insure that They need to use control charts to insure that they are producing a product that conforms to they are producing a product that conforms to the proper specifications. Sampson needs to the proper specifications. Sampson needs to produce high tech and top of the line products, produce high tech and top of the line products, daily so they must have a process that is capable daily so they must have a process that is capable to reduce the risks of defects.to reduce the risks of defects.

How Will Using Control Charts help How Will Using Control Charts help your Company?your Company?

• Possible Goals when using Control Possible Goals when using Control Charts in your Company:Charts 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

Control Chart Key TermsControl Chart Key Terms

• Out of Control: the process may not Out of Control: the process may not performing correctlyperforming correctly

• In Control: the process may be In Control: the process may be performing correctlyperforming correctly

• UCL: upper control limitUCL: upper control limit• LCL: lower control limitLCL: lower control limit• Average value: averageAverage value: average

Process is OUT of control Process is OUT of control if:if:

• One or multiple points outside the One or multiple points outside the control limitscontrol limits

• Eight points in a row above the Eight points in a row above the average valueaverage value

• Multiple points in a row near the Multiple points in a row near the control limitscontrol limits

Process is IN control if:Process is IN control if:

• The sample points fall between the The sample points fall between the control limitscontrol limits

• There are no major trends forming, There are no major trends forming, i.e.. The points vary, both above i.e.. The points vary, both above and below the average value.and below the average value.

Calculating Major Lines in Calculating Major Lines in a Control Charta Control Chart

• Average Value: take the average of the Average Value: take the average of the sample datasample data

• UCL: Multiply the Standard deviation by UCL: Multiply the Standard deviation by three. Then add that value to the three. Then add that value to the Average Value.Average Value.

• LCL: Multiply the Standard deviation by LCL: Multiply the Standard deviation by three. Then subtract that value from the three. Then subtract that value from the Average Value.Average Value.

Examples of Control Examples of Control ChartsCharts


• The following control chart shows The following control chart shows the improvement of a process. The the improvement of a process. The standard deviation decreases as standard deviation decreases as the process becomes more the process becomes more capable. capable.

Example of Control ChartsExample of Control Charts

How to Calculate the How to Calculate the standard deviationstandard deviation

• P chart: P chart: – P= percent or rateP= percent or rate– N= number of trailsN= number of trails

How to Calculate the How to Calculate the standard deviationstandard deviation

• C chart:C chart:– X= the averageX= the average

How to Calculate the How to Calculate the control limitscontrol limits

• 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)

How to Calculate the How to Calculate the control limitscontrol limits

• 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

Sample SizeSample Size

• The sample set of data should be The sample set of data should be greater than 28.greater than 28.

• The data should have been The data should have been collected uniformlycollected uniformly

• The data should contain multiple The data should contain multiple capable points of data, or the capable points of data, or the information is incorrect. information is incorrect.

ExampleExample

• First Step: Determine what type First Step: Determine what type of data you are working with.of data you are working with.

• Second Step: Determine what Second Step: Determine what type of control chart to use with type of control chart to use with your data set.your data set.

• Third Step: Calculate the average Third Step: Calculate the average and the control limits.and the control limits.

ExampleExample

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

ProblemProblem

• You have gathered a sample set of data You have gathered a sample set of data for your company. The data is in the for your company. The data is in the form of percents. Your company wants form of percents. Your company wants your recommendation, is the process in your recommendation, is the process in control.control.

• What type of control chart should you What type of control chart should you use? (Variable or Attribute)use? (Variable or Attribute)

ProblemProblem

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

ProblemProblem

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

Sample DataSample DataDayDay Percent Percent DayDay Percent Percent

11 .056.056 15 15 .068 .06822 .078.078 16 16 .038 .03833 .064.064 17 17 .077 .07744 .023.023 18 18 .068 .06855 .067.067 19 19 .053 .05366 .078.078 20 20 .071 .07177 .067.067 21 21 .037 .03788 .045.045 22 22 .052 .05299 .034.034 23 23 .072 .0721010 .045.045 24 24 .047 .0471111 .062.062 25 25 .042 .0421212 .051.051 26 26 .051 .0511313 .070.070 27 27 .064 .0641414 .039.039 28 28 .071 .071

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

ExampleExample

Final StepFinal Step

• Make a recommendation to your Make a recommendation to your company.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 The variations are normal in the system

and we must accept them.and we must accept them.

Control Charts ReviewControl Charts Review

• What have we learned?What have we learned?– Control Charts are a useful way to Control Charts are a useful way to

determine the capability of a process.determine the capability of a process.– The different types of control charts.The different types of control charts.– How to calculate the control limits for How to calculate the control limits for

a control chart.a control chart.

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 31 January 2001.2001.

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. . 12 February 200112 February 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.

control charts[1]

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