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प्रश्न
In a certain bottling industry the quality control inspector recorded the weight of each of the 5 bottles selected at random during each hour of four hours in the morning.
| Time | Weight in ml | ||||
| 8:00 AM | 43 | 41 | 42 | 43 | 41 |
| 9:00 AM | 40 | 39 | 40 | 39 | 44 |
| 10:00 AM | 42 | 42 | 43 | 38 | 40 |
| 11:00 AM | 39 | 43 | 40 | 39 | 42 |
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उत्तर
| Time | Weight in ml | `bar"X"` | R | ||||
| 8:00 AM | 43 | 41 | 42 | 43 | 41 | 42 | 2 |
| 9:00 AM | 40 | 39 | 40 | 39 | 44 | 40.4 | 5 |
| 10:00 AM | 42 | 42 | 43 | 38 | 40 | 41 | 5 |
| 11:00 AM | 39 | 43 | 40 | 39 | 42 | 40.6 | 4 |
| Total | 164 | 16 | |||||
The control limits for `bar"X"` chart is
`\overset{==}{"X"} = (sumbar"X")/"Number of samples" = 164/4` = 41
`bar"R" = 16/4` = 4
UCL = `\overset{==}{"X"} - "A"_2 bar"R"`
= 41 + (0.58)(4)
41 + 2.32 = 43.32
CL = `\overset{==}{"X"}` = 41
LCL = `\overset{==}{"X"} - "A"_2 bar"R"`
= 41 – (0.58)(4)
= 41 – 2.32
= 38.68
The control limits for range chart is
UCL = `"D"_4 bar"R"` = 2.115(4)
= 8.46
CL = `bar"R"` = 4
LCL = `"D"_2 bar"R"` = 0(4) = 0
Conclusion: Since all the points of sample mean and Range are within the control limits, the process is in control.
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संबंधित प्रश्न
Define R chart
What are the uses of statistical quality control?
Write the control limits for the R chart
Construct `bar"X"` and R charts for the following data:
| Sample Number | Observations | ||
| 1 | 32 | 36 | 42 |
| 2 | 28 | 32 | 40 |
| 3 | 39 | 52 | 28 |
| 4 | 50 | 42 | 31 |
| 5 | 42 | 45 | 34 |
| 6 | 50 | 29 | 21 |
| 7 | 44 | 52 | 35 |
| 8 | 22 | 35 | 44 |
(Given for n = 3, A2 = 1.023, D3 = 0 and D4 = 2.574)
Choose the correct alternative:
How many causes of variation will affect the quality of a product?
Choose the correct alternative:
The assignable causes can occur due to
Choose the correct alternative:
R is calculated using
From the following data, calculate the control limits for the mean and range chart.
| Sample No. | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Sample Observations |
50 | 21 | 50 | 48 | 46 | 55 | 45 | 50 | 47 | 56 |
| 55 | 50 | 53 | 53 | 50 | 51 | 48 | 56 | 53 | 53 | |
| 52 | 53 | 48 | 50 | 44 | 56 | 53 | 54 | 549 | 55 | |
| 49 | 50 | 52 | 51 | 48 | 47 | 48 | 53 | 52 | 54 | |
| 54 | 46 | 47 | 53 | 47 | 51 | 51 | 47 | 54 | 52 |
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.
The following are the sample means and I ranges for 10 samples, each of size 5. Calculate; the control limits for the mean chart and range chart and state whether the process is in control or not.
| Sample Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Mean | 5.10 | 4.98 | 5.02 | 4.96 | 4.96 | 5.04 | 4.94 | 4.92 | 4.92 | 4.98 |
| Range | 0.3 | 0.4 | 0.2 | 0.4 | 0.1 | 0.1 | 0.8 | 0.5 | 0.3 | 0.5 |
