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प्रश्न
In a production process, eight samples of size 4 are collected and their means and ranges are given below. Construct mean chart and range chart with control limits.
| Samples number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| `bar"X"` | 12 | 13 | 11 | 12 | 14 | 13 | 16 | 15 |
| R | 2 | 5 | 4 | 2 | 3 | 2 | 4 | 3 |
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उत्तर
| Samples number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | Total |
| `bar"X"` | 12 | 13 | 11 | 12 | 14 | 13 | 16 | 15 | 106 |
| R | 2 | 5 | 4 | 2 | 3 | 2 | 4 | 3 | 25 |
Let us A2 = 0.73 and D4 = 2.282 and D3 = 0
The control limits for `bar"X"` chart is
`\overset{==}{"X"} = (sum"X")/"No. of samples" = 106/8` = 13.25
`bar"R" = (sum"R")/"No. of samples" = 25/8` = 3.125 = 3.12
UCL = `\overset{==}{"X"} - "A"_2 bar"R"`
= 13.25 + (0.73) (3.12)
= 13.25 + 2.2776 = 15.5276
= 15.53
CL = `\overset{==}{"X"}` = 13.25
LCL = `\overset{==}{"X"} - "A"_2 bar"R"`
= 13.25 – (0.73) (3.12)
= 13.25 – 2.2776 = 10.972
= 10.97
The control limits for Range chart is
UCL = `"D"_4 bar"R"`
= 2.28(3.12) = 7.11984
= 7.12
CL = `bar"R"` = 3.12
LCL = `"D"_3bar"R"` = 0(3.12) = 0
| UCL | CL | LCL | |
| Mean Chart | 15.53 | 13.25 | 10.97 |
| Range Chart | 7.13 | 3.125 | 0 |
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संबंधित प्रश्न
Define Statistical Quality Control
What do you mean by product control?
Write the control limits for the mean 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)
The following data show the values of sample mean `(bar"X")` and its range (R) for the samples of size five each. Calculate the values for control limits for mean, range chart and determine whether the process is in control.
| Sample Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Mean | 11.2 | 11.8 | 10.8 | 11.6 | 11.0 | 9.6 | 10.4 | 9.6 | 10.6 | 10.0 |
| Range | 7 | 4 | 8 | 5 | 7 | 4 | 8 | 4 | 7 | 9 |
(conversion factors for n = 5, A2 = 0.58, D3 = 0 and D4 = 2.115)
A quality control inspector has taken ten samples of size four packets each from a potato chips company. The contents of the sample are given below, Calculate the control limits for mean and range chart.
| Sample Number | Observations | |||
| 1 | 2 | 3 | 4 | |
| 1 | 12.5 | 12.3 | 12.6 | 12.7 |
| 2 | 12.8 | 12.4 | 12.4 | 12.8 |
| 3 | 12.1 | 12.6 | 12.5 | 12.4 |
| 4 | 12.2 | 12.6 | 12.5 | 12.3 |
| 5 | 12.4 | 12.5 | 12.5 | 12.5 |
| 6 | 12.3 | 12.4 | 12.6 | 12.6 |
| 7 | 12.6 | 12.7 | 12.5 | 12.8 |
| 8 | 12.4 | 12.3 | 12.6 | 12.5 |
| 9 | 12.6 | 12.5 | 12.3 | 12.6 |
| 10 | 12.1 | 12.7 | 12.5 | 12.8 |
(Given for n = 5, A2 = 0.58, D3 = 0 and D4 = 2.115)
Choose the correct alternative:
The quantities that can be numerically measured can be plotted on a
Choose the correct alternative:
How many causes of variation will affect the quality of a product?
Choose the correct alternative:
`bar"X"` chart is a
Choose the correct alternative:
The upper control limit for `bar"X"` chart is given by
