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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?
Define a control chart
Define the mean chart
Write the control limits for the R chart
Ten samples each of size five are drawn at regular intervals from a manufacturing process. The sample means `(bar"X")` and their ranges (R) are given below:
| Sample number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| `bar"X"` | 49 | 45 | 48 | 53 | 39 | 47 | 46 | 39 | 51 | 45 |
| R | 7 | 5 | 7 | 9 | 5 | 8 | 8 | 6 | 7 | 6 |
Calculate the control limits in respect of `bar"X"` chart. (Given A2 = 0.58, D3 = 0 and D4 = 2.115) Comment on the state of control
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 |
Choose the correct alternative:
The assignable causes can occur due to
Choose the correct alternative:
A typical control charts consists of
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 |
