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15-2. + Twenty-five samples of size 5 are drawn from a pro- 15-19. + Twenty successive hardness measurements are made cess at one-hour intervals, and the following data are obtained: on a metal alloy, and the data are shown in the following table. Ex, = 362.75 En=8.60 Es, = 3.64 Observation Hardness Observation Hardness 51 (a) Calculate trial control limits for X and R charts. 52 52 (b) Repeat part (a) for X and S charts. 54 50 A W 55 51 15-8. + The copper content of a plating bath is measured 55 10 56 three times per day, and the results are reported in ppm. The (a) Using all the data, compute trial control limits for individ- and r values for 25 days are shown in the following table: ual observations and moving-range charts. Construct the chart and plot the data. Determine whether the process is in Day X Day statistical control. If not, assume that assignable causes can 5.45 1.21 14 7.01 1.45 15-46. A control chart for individual observations has 3-sigma 2 5.39 0.95 15 5.83 1.37 control limits UCL = 1.80 and LCL = 1.62. The process speci- 3 6.85 1.43 16 6.35 1.04 fication limits are (1.64, 1.84). (a) Estimate the process standard deviation. 4 6.74 1.29 17 6.05 0.83 (b) Calculate PCR and PCR, for the process. 5 5.83 1.35 18 7.11 1.35 6 7.22 0.88 19 7.32 1.09 15-56. The following data are the number of spelling errors 7 6.39 0.92 20 5.90 1.22 detected for every 1000 words on a news Web site over 20 weeks. 8 6.50 1.13 21 5.50 0.98 No. of Spelling No. of Spelling 9 7.15 1.25 22 6.32 1.21 Week Errors Week Errors 10 5.92 1.05 23 6.55 0.76 11 11 6.45 0.98 24 5.90 1.20 12 W N 0 13 12 5.38 1.36 25 5.95 1.19 14 13 6.03 0.83 9 15 5 16 (a) Using all the data, find trial control limits for X and k 2 13 charts, construct the chart, and plot the data. Is the process 17 N in statistical control? 18 3 19 10 15-13. Apply the Western Electric Rules to the following 20 control chart. The warning limits are shown as dotted lines. Describe any rule violations. (a) What control chart is most appropriate for these data? (b) Using all the data. compute trial control limits for the chart 32.5 in part (a). UCL = 30.82 30.0- 28.21 27.5- 25.60 25.0- 22.5- X = 22.98 20.0- 20.37 17.5 17.76 15.0 LCL = 15.15 1 3 5 7 9 11 13 15 17 19 21 23 25 Observation