One step in the manufacture of large engines requires that holes of very precise
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Question
One step in the manufacture of large engines requires that holes of very precise dimensions be drilled. The tools that do the drilling are regularly examined and are adjusted to ensure that the holes meet the required specifications. Part of the examination involves measurement of the diameter of the drilling tool. A team studying the variation in the sizes of the drilled holes selected this measurement procedure as a possible cause of variation in the drilled holes. They decided to use a designed experiment as one part of this examination. Some of the data are given in the table below. The diameters in millimeters (mm) of five tools were measured by the same operator at three times (8:00 A.M., 11:00 A.M., and 3:00 P.M.). Three measurements were taken on each tool at each time. The person taking the measurements could not tell which tool was being measured, and the measurements were taken in random order.
Multiply each measurement by 0.04 to convert from millimeters to inches. Plot the means and run a two-way ANOVA using the transformed measurements. Summarize what parts of the analysis have changed and what parts have remained the same.
TABLE 13.2 Tool diameter data Tool Time Diameter 25.030 25.030 25.032 25.028 25.028 25.028 25.026 25.026 25.026 25.016 25.018 25.016 25.022 25.020 25.018 25.016 25.016 25.016 1 25.005 25.008 25.006 25.012 25.012 25.014 25.010 25.010 25.008 25.012 25.012 25.012 25.018 25.020 25.020 25.010 25.014 25.018 24.996 24.998 24.998 25.006 25.006 25.006 25.000 25.002 24.999 Table 13-2 to the Practice of Statistics, Fifth Edition o 200SW,H Freeman and CompanyExplanation / Answer
The result are obtained by using excel command
Anova: Two-Factor With Replication SUMMARY Time Diameter Diameter Diameter Total 1 Count 3 3 3 3 12 Sum 6 3.00336 3.00336 3.00344 15.01016 Average 2 1.00112 1.00112 1.001147 1.250847 Variance 1 6.4E-09 6.4E-09 1.49E-08 0.385902 2 Count 3 3 3 3 12 Sum 6 3.00216 3.00216 3.002 15.00632 Average 2 1.00072 1.00072 1.000667 1.250527 Variance 1 1.92E-08 6.4E-09 2.13E-09 0.386076 3 Count 3 3 3 3 12 Sum 6 3.00108 3.0012 3.001104 15.00338 Average 2 1.00036 1.0004 1.000368 1.250282 Variance 1 2.08E-08 6.4E-09 3E-08 0.38621 4 Count 3 3 3 3 12 Sum 6 3.0016 3.00184 3.002 15.00544 Average 2 1.000533 1.000613 1.000667 1.250453 Variance 1 2.77E-08 2.77E-08 2.77E-08 0.386116 5 Count 3 3 3 3 12 Sum 6 3.00008 3.00024 3.00012 15.00044 Average 2 1.000027 1.00008 1.00004 1.250037 Variance 1 4.05E-08 2.56E-08 3.04E-08 0.386344 Total Count 15 15 15 15 Sum 30 15.00828 15.0088 15.00866 Average 2 1.000552 1.000587 1.000578 Variance 0.714286 1.59E-07 1.38E-07 1.59E-07 ANOVA Source of Variation SS df MS F P-value F crit Sample 4.32E-06 4 1.08E-06 4.32E-06 1 2.605975 Columns 11.23713 3 3.745711 14.98284 1.1E-06 2.838745 Interaction 1.47E-06 12 1.23E-07 4.91E-07 1 2.003459 Within 10 40 0.25 Total 21.23714 59Related Questions
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