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Tutorial Solutions - C hapter 7 P roblem 7: Sample 1 2 3 4...

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Chapter 7 Problem 7: Sample 1 2 3 4 mean range 1 1010 991 985 986 993.00 25 2 995 996 1009 994 998.50 15 3 990 1003 1015 1008 1004.00 25 4 1015 1020 1009 998 1010.50 22 5 1013 1019 1005 993 1007.50 26 6 994 1001 994 1005 998.50 11 7 989 992 982 1020 995.75 38 8 1001 986 996 996 994.75 15 9 1006 989 1005 1007 1001.75 18 10 992 1007 1006 979 996.00 28 11 996 1006 997 989 997.00 17 12 1019 996 991 1011 1004.25 28 13 981 991 989 1003 991.00 22 14 999 993 988 984 991.00 15 15 1013 1002 1005 992 1003.00 21 999.1, = 21.733 Control limits for X-bar chart: UCL, LCL = , = 999.1 + .73(21.733) = 1014.965, 983.235 Control limits for R chart: UCL = = 2.28(21.7333) = 49.551 LCL = = 0(21.7333) = 0.00
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The process is in statistical control. Problem 11: = ( ) p defects from all samplesnumber of samples sample size = .008333 = .00287 UCL = + 1.96 = .008333 + 1.96(.00287) = .01396 LCL = - 1.96 = .008333 - 1.96(.00287) = .0027
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The process is in control. Therefore, it can be stated that the crime rate has not increased. However, there appears to be a gradual increase in the crime rate. Problem 12: = .015 = .00384 UCL = + 1.96 = .015 + 1.96(.00384) = .0225
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- 1.96 = .015 - 1.96(.00384) = .0075 Process is out of statistical control. Specifically, three areas outside of UCL warrant further investigation, and four areas below LCL warrant investigation. Problem 13: Sample number 1 2 3 4 5 Mean Range 1 .486 .499 .493 .511 .481 .494 .030 2 .499 .506 .516 .494 .529 .509 .035 3 .496 .500 .515 .488 .521 .504 .033 4 .495 .506 .483 .487 .489 .492 .023 5 .472 .502 .526 .469 .481 .490 .057 6 .473 .495 .507 .493 .506 .495 .034
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Tutorial Solutions - C hapter 7 P roblem 7: Sample 1 2 3 4...

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