Control ChartsControl Charts

Training SlidesTraining Slides02/19/0102/19/01

Control ChartsControl Charts

• Definition:Definition:- A statistical tool to - A statistical tool to

determine if a process is in determine if a process is in control.control.

History of Control History of Control ChartsCharts

• 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 Types of Variable Control ChartsControl Charts

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

Variable Control ChartsVariable Control Charts

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

• R chart: takes into count the R chart: takes into count the range of the valuesrange of 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 Types of Attribute Control ChartsControl Charts

• 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 defects per unit in each sample set.set.

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

Reasons for using Reasons for using Control ChartsControl Charts

• 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 Determine if process is “in” or

“out of control“out of control

Real World Use of Real World Use of Control ChartsControl Charts• Example from “Managing Example from “Managing

Quality” by Foster.Quality” by Foster.– The Sampson company develops special The Sampson company develops special

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

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

• Possible Goals when using Possible Goals when using Control Charts in your Company:Control Charts in your Company:– Line reengineeringLine reengineering– Increased Employee motivationIncreased Employee motivation– Continually improve of your Continually improve of your

processprocess– Increased profitsIncreased profits– Zero defectsZero defects

Control Chart Key TermsControl Chart Key Terms

• Out of Control: the process may Out of Control: the process may not performing correctlynot performing 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 Process is OUT of control if:control if:

• One or multiple points outside One or multiple points outside the control limitsthe control 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 sample points fall between the control limitsthe control limits

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

Calculating Major Lines Calculating Major Lines in a Control Chartin a Control Chart• Average Value: take the average of Average Value: take the average of

the sample datathe sample data• UCL: Multiply the Standard deviation UCL: Multiply the Standard deviation

by three. Then add that value to the by three. Then add that value to the Average Value.Average Value.

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

Examples of Control Examples of Control ChartsCharts

Examples of Control Examples of Control ChartsCharts

Control ChartsControl Charts

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

Example of Control Example of Control ChartsCharts

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

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

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

ExampleExample• First Step: Determine what First Step: Determine what

type of data you are working type of data you are working with.with.

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

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

ExampleExample

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

ProblemProblem• You have gathered a sample set of You have gathered a sample set of

data for your company. The data is data for your company. The data is in the form of percents. Your in the form of percents. Your company wants your company wants your recommendation, is the process in 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 What type of specific control chart should you use with that chart should you use with that type of sample set? (X-bar, R-type of sample set? (X-bar, R-chart, MA-chart, P-chart, R-chart, MA-chart, P-chart, R-chart, or U-chart)chart, or U-chart)

ProblemProblem

• Now that you have determined Now that you have determined the control chart to use, you the control chart to use, you have to calculate the average have to calculate the average and standard deviation. Use the and standard deviation. Use the data on the following slide. data on the following slide. Take notice to the amount of Take notice to the amount of sample data. (n>28)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 Now that you have calculated the three important lines for the the three important lines for the control chart, plot the data and control chart, plot the data and determine if the process is determine if the process is capable. (i.e. The data falls capable. (i.e. The data falls mostly inside the UCL, and the mostly inside the UCL, and the LCL)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 The variations are normal in the

system and we must accept them.system 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 determine the capability of a process.process.

– The different types of control The different types of control charts.charts.

– How to calculate the control limits How to calculate the control limits for a control chart.for 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 31 January 2001.January 2001.

Foster, S. Thomas. Foster, S. Thomas. Managing Quality.Managing Quality. Upper Saddle River: Prentice Hall, Inc. Upper Saddle River: Prentice Hall, Inc. 2001.2001.

““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.