Advertisements
Advertisements
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 |
Advertisements
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.
APPEARS IN
संबंधित प्रश्न
Define Statistical Quality Control
Mention the types of causes for variation in a production process
What do you mean by product control?
Define a control chart
Name the control charts for variables
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
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 |
Choose the correct alternative:
The upper control limit for `bar"X"` chart is given by
