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Question
The following data gives the average life(in hours) and range of 12 samples of 5lamps each. The data are
| Sample No | 1 | 2 | 3 | 4 | 5 | 6 |
| Sample Mean | 1080 | 1390 | 1460 | 1380 | 1230 | 1370 |
| Sample Range | 410 | 670 | 180 | 320 | 690 | 450 |
| Sample No | 7 | 8 | 9 | 10 | 11 | 12 |
| Sample Mean | 1310 | 1630 | 1580 | 1510 | 1270 | 1200 |
| Sample Range | 380 | 350 | 270 | 660 | 440 | 310 |
Construct control charts for mean and range. Comment on the control limits.
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Solution
| Sample No | Sample Mean `bar"X"` |
Sample Range R |
| 1 | 1080 | 410 |
| 2 | 1390 | 670 |
| 3 | 1460 | 180 |
| 4 | 1380 | 320 |
| 5 | 1230 | 690 |
| 6 | 1370 | 450 |
| 7 | 1310 | 380 |
| 8 | 1630 | 350 |
| 9 | 1580 | 270 |
| 10 | 1510 | 660 |
| 11 | 1270 | 440 |
| 12 | 1200 | 310 |
| Total | `sum"X"` = 16410 | `sum"R"` = 5130 |
The control limits for `bar"X"` chart is
`\overset{==}{"X"} = (sum"X")/"Number of sample" = 16410/12` = 1367.5
`bar"R" = (sum"R")/"n" = 5130/12` = 427.5
UCL = `\overset{==}{"X"} + "A"_2 bar"R"`
= 1367.5 + 0.577(427.5)
= 1367.5 + 246.6675
= 1614.1675
= 1614.17
CL = `\overset{==}{"X"} ` = 1367.5
LCL = `\overset{==}{"X"} + "A"_2 bar"R"`
= 1367.5 – 0.577(427.5)
= 1367.5 – 246.6675
= 1120.8325
= 1120.83
The control limits for Range chart is
UCL = `"D"_4bar"R"`
= 2.115(427.5)
= 904.1625
= 904.16
CL = `bar"R"` = 427.5
LCL = `"D"_3bar"R"`
= 0(427.5)
= 0
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