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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 process control?
Define R chart
Write the control limits for the R 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)
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 means and the ranges for ten samples of size 4 each. Construct the control chart for mean and range chart and determine whether the process is in control.
| Sample Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| `bar"X"` | 29 | 26 | 37 | 34 | 14 | 45 | 39 | 20 | 34 | 23 |
| R | 39 | 10 | 39 | 17 | 12 | 20 | 05 | 21 | 23 | 15 |
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:
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 |
