Control Charts Training Slides 02/19/01 Control Charts вЂў Definition: - A statistical tool to determine if a process is in control. History of Control Charts вЂў Developed in 1920вЂ™s вЂў By Dr. Walter A. Shewhart вЂў Shewhart worked for Bell Telephone Labs Two Types of Control Charts вЂў Variable Control Charts вЂў Attribute Control Charts Variable Control Charts вЂў Deal with items that can be measured . вЂў Examples 1) Weight 2) Height 3) Speed 4) Volume Types of Variable Control Charts вЂў X-Bar chart вЂў R chart вЂў MA chart Variable Control Charts вЂў X chart: deals with a average value in a process вЂў R chart: takes into count the range of the values вЂў MA chart: take into count the moving average of a process Attribute Control Charts вЂў Control 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 Charts вЂў P chart вЂў C Chart вЂў U Chart Attribute Control Charts вЂў P Chart: a chart of the percent defective in each sample set. вЂў C chart: a chart of the number of defects per unit in each sample set. вЂў U chart: a chart of the average number of defects in each sample set. Reasons for using Control Charts вЂў Improve productivity вЂў Make defects visible вЂў Determine what process adjustments need to be made вЂў Determine if process is вЂњinвЂќ or вЂњout of control Real World Use of Control Charts вЂў Example from вЂњManaging QualityвЂќ by Foster. вЂ“ 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? вЂў Possible Goals when using Control Charts in your Company: вЂ“ Line reengineering вЂ“ Increased Employee motivation вЂ“ Continually improve of your process вЂ“ Increased profits вЂ“ Zero defects Control Chart Key Terms вЂў Out of Control: the process may not performing correctly вЂў In Control: the process may be performing correctly вЂў UCL: upper control limit вЂў LCL: lower control limit вЂў Average value: average Process is OUT of control if: вЂў One or multiple points outside the control limits вЂў Eight points in a row above the average value вЂў Multiple points in a row near the control limits Process is IN control if: вЂў The sample points fall between the control limits вЂў There are no major trends forming, i.e.. The points vary, both above and below the average value. Calculating Major Lines in a Control Chart вЂў Average Value: take the average of the sample data вЂў UCL: Multiply the Standard deviation by three. Then add that value to the Average Value. вЂў 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 вЂў 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 вЂў P chart: вЂ“ P= percent or rate вЂ“ N= number of trails How to Calculate the standard deviation вЂў C chart: вЂ“ X= the average How to Calculate the control limits вЂў X-bar Chart: Lower Control Limit: вЂў Mean вЂ“ 3*sigma n(1/2) Center Line: вЂў Process mean Upper Control Limit: вЂў Mean + 3*sigma n(1/2) How to Calculate the control limits вЂў R chart: вЂ“ Lower Control Limit: вЂў R-Bar вЂ“ 3*d3*sigma вЂ“ Center Line: вЂў R-Bar вЂ“ Upper Control Limit: вЂў R-Bar + 3*d3*sigma Sample Size вЂў The sample set of data should be greater than 28. вЂў The data should have been collected uniformly вЂў The data should contain multiple capable points of data, or the information is incorrect. Example вЂў First Step: Determine what type of data you are working with. вЂў Second Step: Determine what type of control chart to use with your data set. вЂў Third Step: Calculate the average and the control limits. Example вЂў The 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. Problem вЂў You 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. вЂў What type of control chart should you use? (Variable or Attribute) Problem вЂў What type of specific control chart should you use with that type of sample set? (X-bar, Rchart, MA-chart, P-chart, Rchart, or U-chart) Problem вЂў Now 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 Data Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Percent .056 .078 .064 .023 .067 .078 .067 .045 .034 .045 .062 .051 .070 .039 Day 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Percent .068 .038 .077 .068 .053 .071 .037 .052 .072 .047 .042 .051 .064 .071 Example вЂў 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) Final Step вЂў Make a recommendation to your company. вЂ“ The process is capable вЂ“ The process is not capable вЂў The following errors were found. вЂў The process needs improvement вЂў The variations are normal in the system and we must accept them. Control Charts Review вЂў What have we learned? вЂ“ Control Charts are a useful way to determine the capability of a process. вЂ“ The different types of control charts. вЂ“ How to calculate the control limits for a control chart. Works Cited вЂњControl Charts as a tool in SQC.вЂќ 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. вЂњGenerating and Using Control Charts.вЂќ Internet. http://www.hanford.gov/safety/upp/spc.htm. 31 January 2001. вЂњQuality and Statistical Process Control.вЂќ Internet. http://www.systma.com/tqmtools/ctlchtprinciples.html. 12 February 2001. вЂњStatistical Thinking Tools-Control Charts for the Average.вЂќ Internet. http://www.robertluttman.com/yms/Week5/page6.htm. 12 February 2001.