Control ChartsTraining Slides02/19/01

Control Charts

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

History of Control Charts

Developed in 1920sBy Dr. Walter A. ShewhartShewhart worked for Bell Telephone Labs

Two Types of Control Charts

Variable Control ChartsAttribute Control Charts

Variable Control ChartsDeal with items that can be measured .Examples 1) Weight 2) Height 3) Speed 4) Volume

Types of Variable Control Charts

X-Bar chartR chartMA chart

Variable Control ChartsX chart: deals with a average value in a processR chart: takes into count the range of the valuesMA chart: take into count the moving average of a process

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

Types of Attribute Control ChartsP chartC ChartU Chart

Attribute Control ChartsP Chart: a chart of the percent defective in each sample set.C chart: a chart of the number of defects per unit in each sample set.U chart: a chart of the average number of defects in each sample set.

Reasons for using Control ChartsImprove productivityMake defects visibleDetermine what process adjustments need to be madeDetermine if process is in or out of control

Real World Use of Control ChartsExample from Managing Quality by Foster.The Sampson company develops special equipment for the United States Armed Forces. They need to use control charts to insure that they are producing a product that conforms to the proper specifications. Sampson needs to produce high tech and top of the line products, daily so they must have a process that is capable to reduce the risks of defects.

How Will Using Control Charts help your Company?Possible Goals when using Control Charts in your Company:Line reengineeringIncreased Employee motivationContinually improve of your processIncreased profitsZero defects

Control Chart Key TermsOut of Control: the process may not performing correctlyIn Control: the process may be performing correctlyUCL: upper control limitLCL: lower control limitAverage value: average

Process is OUT of control if:One or multiple points outside the control limitsEight points in a row above the average valueMultiple points in a row near the control limits

Process is IN control if:The sample points fall between the control limitsThere are no major trends forming, i.e.. The points vary, both above and below the average value.

Calculating Major Lines in a Control ChartAverage Value: take the average of the sample dataUCL: Multiply the Standard deviation by three. Then add that value to the Average Value.LCL: Multiply the Standard deviation by three. Then subtract that value from the Average Value.

Examples of Control Charts

Examples of Control Charts

Control Charts

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

Example of Control Charts

How to Calculate the standard deviation

P chart: P= percent or rateN= number of trails

How to Calculate the standard deviation

C chart:X= the average

How to Calculate the control limitsX-bar Chart: Lower Control Limit: Mean 3*sigma n(1/2) Center Line:Process mean

Upper Control Limit:Mean + 3*sigma n(1/2)

How to Calculate the control limitsR chart:Lower Control Limit:R-Bar 3*d3*sigmaCenter Line: R-BarUpper Control Limit:R-Bar + 3*d3*sigma

Sample SizeThe sample set of data should be greater than 28.The data should have been collected uniformlyThe data should contain multiple capable points of data, or the information is incorrect.

ExampleFirst Step: Determine what type of data you are working with.Second Step: Determine what type of control chart to use with your data set.Third Step: Calculate the average and the control limits.

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

ProblemYou have gathered a sample set of data for your company. The data is in the form of percents. Your company wants your recommendation, is the process in control.What type of control chart should you use? (Variable or Attribute)

Problem

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

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

Sample DataDayPercent Day Percent 1.056 15 .0682.078 16 .0383.064 17 .0774.023 18 .0685.067 19 .0536.078 20 .0717.067 21 .0378.045 22 .0529.034 23 .07210.045 24 .04711.062 25 .04212.051 26 .05113.070 27 .06414.039 28 .071

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

Final StepMake a recommendation to your company.The process is capableThe process is not capableThe following errors were found.The process needs improvementThe variations are normal in the system and we must accept them.

Control Charts ReviewWhat have we learned?Control Charts are a useful way to determine the capability of a process.The different types of control charts.How to calculate the control limits for a control chart.

Works Cited

Control Charts as a tool in SQC. Internet. http://deming.eng.clemson.edu/pub/tutorials/qctools/ccmain1.htm. 31 January 2001.

Foster, S. Thomas. Managing Quality. Upper Saddle River: Prentice Hall, Inc. 2001.

Generating and Using Control Charts. Internet. http://www.hanford.gov/safety/upp/spc.htm. 31 January 2001.

Quality and Statistical Process Control. Internet. http://www.systma.com/tqmtools/ctlchtprinciples.html. 12 February 2001.

Statistical Thinking Tools-Control Charts for the Average. Internet. http://www.robertluttman.com/yms/Week5/page6.htm. 12 February 2001.

A simple basic definition that can be built on to service your companys needs.http://deming.eng.clemson.edu/pub/tutorials/qctools/ccmain1.htm#History

Dr. Shewhart developed the control charts as an statistical approach to the study of manufacturing process variation for the purpose of improving the economic effectiveness of the process. These methods are based on continuous monitoring of processvariation. These are the main to types of control charts. Each type has several specific charts that deal with a specific sample set of data.Use variable charts should be used whenever the data is something that is measured. The data should be for example the weight of a piece of candy. The main types of variable control charts are listed above. These are the definitions of the specific types of variable control charts. This will help in determining what type of chart to use when you are collecting sample data.Definition of attribute control charts. Tests the quality of the specific attributes of a product.The main types of attribute control charts are listed above.The definitions of the attribute control charts, help in determining the correct chart to use given a sample set of data.Control charts can be a huge asset to a company if used correctly. The reason for using control charts are clear, they will help your company improve.Real world example of a company that uses control charts to sell products to the United States. The products must be defect free to save lives.Brainstorming Activity:This is to help your employees realize the need to improve. The goal with control charts is basically three fold:Reduce DefectsImprove processesImprove productivityThis is just a list of key terms that one should know and understand to create a control chart and understand its results.There are other extreme examples of when a control charts is out of control but these are the main three that you should focus one.If your process is currently in control continue to monitor it to insure that productivity remains at a high level to produce good quality products.The control chart basically consists of three main lines. The center of mean line, and then the two control limits. This lines are called the Upper Control Limit, and the Lower Control Limit. They both can be shortened (UCL,and LCL).http://www.robertluttman.com/vms/Week5/page6.htmStatistical Thinking Tools-Control Charts for the AverageDate:February 12, 2001 Bob Luttman, Robert Luttman & Associates

Example of a control chart that has points outside the UCL. This process may need to be reworked. The problem is becoming worse, you can see that the data is consistently above the mean towards the end of the data.Processes and Process Variability, Date accessed: Feb 12, 2001http://www.sytsma.com/tqmtools/ctlchtprinciples.htmlExample of a process that is in-control.

Process improvement.Processes and Process Variability, Date accessed: Feb 12, 2001http://www.sytsma.com/tqmtools/ctlchtprinciples.htmlThe control chart above shows the improvements that a firm made in their process to improve quality.

Formula for computing the standard deviation for a P-chart.The control limits can be computed by multiplying the standard deviation by +/- 3.The procedure to calculate the upper and lower control limits for a X-Bar chart. Follow the formula provided, your should remember to make sure that you are using a sample size greater than 28.

http://www.statlets.com/usermanual/sect7_3.htm 7.3 Control Charts for VariablesDate Accessed: February 13, 2001Building a R-chart. The slide helps in computing the three main lines in the chart.

http://www.statlets.com/usermanual/sect7_3.htm 7.3 Control Charts for VariablesDate Accessed: February 13, 2001The most important thing to remember when constructing a control chart is to have a sample set greater than 28. If your set is smaller that 28 you may not be able to represent a large enough portion of data to get accurate results.Follow the steps to insure that the control chart will produce the outcome that you are looking for. A control chart is useless if the wrong chart is used for the wrong type of data.Practice designing a chart. Use the steps outlined in slide show.You should use a Attribute control chart because the data is in percent form.

After determining that the sample set should use a attribute control chart? Determine the correct type of chart to use in creating a control chart. (p-chart) Because it is the percent defect or errors of a sample set.Reinforcing the idea that you sample set must be greater than 28.First: Notice the sample sizeSecond: Calculate the mean (.056786)Third: Use the mean to calculate the control limits (UCL: .07442 ), (LCL: .03914) )Plot the points and determine if you process is capable: I would say that this process is pretty much capable, only a few points are outside the control limitsDetermine if your process is capable by looking at your results and determining if your process needs changes. What to do after you design the chart and look at the results. Make the chart work for you. Like it help your company improve quality. Summary, the control chart can greatly improve your companys profits and process capability.