Control Charts for Variables Chapter 6 Les Jones

Control Charts for Variables Chapter 6 Les Jones IET 603

Chapter Summary • Shewhart Control Charts for: characteristics such as: length, width, temperature and volume. 1. Understand the statistical basis of Shewhart control charts for variables 2. Know how to design variables control charts 3. Know how to set up and use and R control charts 4. Know how to estimate process capability from the control chart information 5. Know how to interpret patterns on and R control charts 6. Know how to set up and use and s or s 2 control charts 7. Know how to set up and use control charts for individual measurements 8. Understand the importance of the normality assumption for individuals control charts and know how to check this assumption 9. Understand the rational subgroup concept for variables control charts 10. Determine the average run length for variables control charts

Setting Control Limits on the X Chart • Control of the process average or mean quality level is usually done with the control chart for means, or the x control chart. • Process variability can be monitored with either a control chart for the standard deviation, called the s control chart, or a control chart for the range, called an R control chart. • The X and R (or s) charts are among the most important and useful on-line statistical process monitoring and control techniques. (pg. 227).

Setting Limits For x-Charts when we don’t know s Upper control limit (UCL) = x + A 2 R Lower control limit (LCL) = x - A 2 R where R = average range of the samples A 2 = control chart factor found in Table S 6. 1 x = mean of the sample means hilo. hawaii. edu/uhh/faculty/. . . /361 Chapter. S. ppt Slide from: Pearson Publishers

R Limits For R-Charts Upper control limit (UCLR) = D 4 R Lower control limit (LCLR) = D 3 R where R = average range of the samples D 3 and D 4 = control chart factors from Table S 6. 1 Slide from Pearson Publishers at: hilo. hawaii. edu/uhh/faculty/. . . /361 Chapter. S. ppt

Mean and Range (a) (Sampling mean is shifting upward but range is consistent) These sampling distributions result in the charts below UCL x-chart LCL UCL R-chart LCL Figure S 6. 5 (x-chart detects shift in central tendency) (R-chart does not detect change in mean) Slide from Pearson Publishers at: hilo. hawaii. edu/uhh/faculty/. . . /361 Chapter. S. ppt