Develop an X bar chart and an r-chart and plot the values. From the charts, what comments can you make about the process?
sample | 1 | 2 | 3 | 4 | Mean | Range | ||
1 | 1010 | 991 | 985 | 986 | 993 | 25 | ||
2 | 995 | 996 | 1009 | 994 | 998.5 | 15 | ||
3 | 990 | 1003 | 1015 | 1008 | 1004 | 25 | ||
4 | 1015 | 1020 | 1009 | 998 | 1010.5 | 22 | ||
5 | 1013 | 1019 | 1005 | 993 | 1007.5 | 26 | ||
6 | 994 | 1001 | 994 | 1005 | 998.5 | 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 | 28 | ||
11 | 996 | 1006 | 997 | 989 | 997 | 17 | ||
12 | 1019 | 996 | 991 | 1011 | 1004.25 | 28 | ||
13 | 981 | 991 | 989 | 1003 | 991 | 22 | ||
14 | 999 | 993 | 988 | 984 | 991 | 15 | ||
15 | 1013 | 1002 | 1005 | 992 | 1003 | 21 | ||
Average | 999.1 | 21.733 | ||||||
X chart control limits | N | A2 | D3 | D4 | ||||
UCL = x + A2R | 2 | 1.88 | 0 | 3.27 | ||||
LCL = x- A2R | 3 | 1.02 | 0 | 2.57 | ||||
4 | 0.73 | 0 | 2.28 | |||||
5 | 0.58 | 0 | 2.11 | |||||
R chart Control Limits | 6 | 0.48 | 0 | 2 | ||||
UCL = D4R | 7 | 0.42 | 0.08 | 1.92 | ||||
LCL = D3R | 8 | 0.37 | 0.14 | 1.86 | ||||
9 | 0.34 | 0.18 | 1.82 | |||||
10 | 0.31 | 0.22 | 1.78 | |||||
11 | 0.29 | 0.26 | 1.74 | |||||
X BAR CHART | ||||||||
UCL = X + A2R = 999.1 + 0.73(21.733) = 1014.965 | ||||||||
LCL = X - A2R = 999.1 - 0.73(21.733) = 989.235 | ||||||||
R CHART | ||||||||
UCL = D4R = (2.28)(21.733) = 49.551 | ||||||||
LCL = D3R = (0) (21.733) = 0 | ||||||||
CONCLUSION | ||||||||
All the points are well within control limits | ||||||||
The process is controlled | ||||||||
Develop an X bar chart and an r-chart and plot the values. From the charts, what...
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