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Question
Define the mean chart
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Solution
The mean chart `(bar"X" "chart")` is used to show, the quality average of the samples taken from the given process.
The `bar"X"` charts are usually required for decision making to accept or reject the process.
Procedure for `bar"X"`
i. Let X1, X2, X3, etc. be the samples selected each containing “n” observations usually (n = 4.5 or 6)
ii. Calculate mean for each samples `bar"X"_1, bar"X"_2, bar"X"_3`, ......... by using `bar"X"_"i" = (sum"X"_"i")/"n"`, i = 1, 2, 3, 4, ….
Where `sum"X"_"i"` = Total f “n” values included in the sample X1.
iii. Find the mean `(bar"X")` of the sample means
`bar"X" = (sumbar"X")/"Number of samples"`
Where `sumbar"X"` = Total of all the sample means.
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RELATED QUESTIONS
Mention the types of causes for variation in a production process
What are the uses of statistical quality control?
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)
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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Variations due to natural disorder is known as
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The assignable causes can occur due to
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A typical control charts consists of
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`bar"X"` chart is a
The following data gives the average life(in hours) and range of 12 samples of 5lamps each. The data are
| Sample No | 1 | 2 | 3 | 4 | 5 | 6 |
| Sample Mean | 1080 | 1390 | 1460 | 1380 | 1230 | 1370 |
| Sample Range | 410 | 670 | 180 | 320 | 690 | 450 |
| Sample No | 7 | 8 | 9 | 10 | 11 | 12 |
| Sample Mean | 1310 | 1630 | 1580 | 1510 | 1270 | 1200 |
| Sample Range | 380 | 350 | 270 | 660 | 440 | 310 |
Construct control charts for mean and range. Comment on the control limits.
