712 CHAPTER 14 Statistical Process Control Quarters. In Exercises 9–12, refer to the accompanying table of weights (grams) of quarters minted by the U.S. government. This table is available in Data Set 44 “Weights of Minted Quarters” in Appendix B. Day Hour 1 Hour 2 Hour 3 Hour 4 Hour 5 x s Range 1 5.543 5.698 5.605 5.653 5.668 5.6334 0.0607 0.155 2 5.585 5.692 5.771 5.718 5.720 5.6972 0.0689 0.186 3 5.752 5.636 5.660 5.680 5.565 5.6586 0.0679 0.187 4 5.697 5.613 5.575 5.615 5.646 5.6292 0.0455 0.122 5 5.630 5.770 5.713 5.649 5.650 5.6824 0.0581 0.140 6 5.807 5.647 5.756 5.677 5.761 5.7296 0.0657 0.160 7 5.686 5.691 5.715 5.748 5.688 5.7056 0.0264 0.062 8 5.681 5.699 5.767 5.736 5.752 5.7270 0.0361 0.086 9 5.552 5.659 5.770 5.594 5.607 5.6364 0.0839 0.218 10 5.818 5.655 5.660 5.662 5.700 5.6990 0.0689 0.163 11 5.693 5.692 5.625 5.750 5.757 5.7034 0.0535 0.132 12 5.637 5.628 5.646 5.667 5.603 5.6362 0.0235 0.064 13 5.634 5.778 5.638 5.689 5.702 5.6882 0.0586 0.144 14 5.664 5.655 5.727 5.637 5.667 5.6700 0.0339 0.090 15 5.664 5.695 5.677 5.689 5.757 5.6964 0.0359 0.093 16 5.707 5.890 5.598 5.724 5.635 5.7108 0.1127 0.292 17 5.697 5.593 5.780 5.745 5.470 5.6570 0.1260 0.310 18 6.002 5.898 5.669 5.957 5.583 5.8218 0.1850 0.419 19 6.017 5.613 5.596 5.534 5.795 5.7110 0.1968 0.483 20 5.671 6.223 5.621 5.783 5.787 5.8170 0.2380 0.602 9. Quarters: Notation Find the values of x and R. Also find the values of LCL and UCL for an R chart, then find the values of LCL and UCL for an x chart. 10. Quarters: R Chart Treat the five measurements from each day as a sample and construct an R chart. What does the result suggest? 11. Quarters: x Chart Treat the 5 measurements from each day as a sample and construct an x chart. What does the result suggest? 12. Quarters: Run Chart Treat the 100 consecutive measurements from the 20 days as individual values and construct a run chart. What does the result suggest? 13. s Chart In this section we described control charts for R and x based on ranges. Control charts for monitoring variation and center (mean) can also be based on standard deviations. An s chart for monitoring variation is constructed by plotting sample standard deviations with a centerline at s (the mean of the sample standard deviations) and control limits at B4s and B3s, where B4 and B3 are found in Table 14-2 on page 707 in this section. Construct an s chart for the data of Table 14-1 on page 701. Compare the result to the R chart given in Example 3 “R Chart of Earth Global Temperatures.” 14. x Chart Based on Standard Deviations An x chart based on standard deviations (instead of ranges) is constructed by plotting sample means with a centerline at x and control limits at x + A3s and x - A3s, where A3 is found in Table 14-2 on page 707 and s is the mean of the sample standard deviations. Use the data in Table 14-1 on page 701 to construct an x chart based on standard deviations. Compare the result to the x chart based on sample ranges in Example 4 “x Chart of Global Earth Temperatures.” 14-1 Beyond the Basics
RkJQdWJsaXNoZXIy NjM5ODQ=