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प्रश्न
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)
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उत्तर
We first find the sample mean and range for each of the 8 given samples.
| Sample Number | Observations | `bar"X"` | R | ||
| 1 | 32 | 36 | 42 | 36.67 | 10 |
| 2 | 28 | 32 | 40 | 33.33 | 12 |
| 3 | 39 | 52 | 28 | 39.67 | 24 |
| 4 | 50 | 42 | 31 | 41 | 19 |
| 5 | 42 | 45 | 34 | 40.33 | 11 |
| 6 | 50 | 29 | 21 | 33.33 | 29 |
| 7 | 44 | 52 | 35 | 43.67 | 17 |
| 8 | 22 | 35 | 44 | 33.67 | 22 |
| Total | 301.67 | 144 | |||
The control limits for `bar"X"` chart is
`\overset{==}{"X"} = (sumbar"X")/"Number of samples" = 301.67/8` = 37.71
`bar"R" = 144/8` = 18
UCL = `\overset{==}{"X"} + "A"_2 bar"R"`
= 37.71 + (0.58)(18)
= 37.71 + 10.44
= 48.15
CL = `\overset{==}{"X"}` = 37.71
LCL = `\overset{==}{"X"} - "A"_2 bar"R"`
= 37.71 – (0.58)(18)
= 37.71 – 10.44
= 27.27
The control limits for Range chart is
UCL = `"D"_4 bar"R"` = 2.115(18) = 38.07
CL = `bar"R"` = 18
LCL = `"D"_3 bar"R"` = 0(18) = 0
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संबंधित प्रश्न
Mention the types of causes for variation in a production process
Define chance cause
What do you mean by product control?
Define a control chart
A machine is set to deliver packets of a given weight. Ten samples of size five each were recorded. Below are given relevant data:
| Sample number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| `bar"X"` | 15 | 17 | 15 | 18 | 17 | 14 | 18 | 15 | 1 | 16 |
| R | 7 | 7 | 4 | 9 | 8 | 7 | 12 | 4 | 11 | 5 |
Calculate the control limits for mean chart and the range chart and then comment on the state of control, (conversion factors for n = 5, A2 = 0.58, D3 = 0 and D4 = 2.115)
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
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)
Choose the correct alternative:
The assignable causes can occur due to
Choose the correct alternative:
`bar"X"` chart is a
Choose the correct alternative:
The LCL for R chart is given by
