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प्रश्न
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)
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उत्तर
| Sample Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Total |
| Mean `bar"X"` | 11.2 | 11.8 | 10.8 | 11.6 | 11.0 | 9.6 | 10.4 | 9.6 | 10.6 | 10.0 | 106.6 |
| Range (R) | 7 | 4 | 8 | 5 | 7 | 4 | 8 | 4 | 7 | 9 | 63 |
The control limits for `bar"X"` chart is
`\overset{==}{"X"} = (sumbar"X")/"Number of samoles" = 106.6/10` = 10.66
`bar"R" = (sum"R")/"R" = 63/10` = 6.3
UCL = `\overset{==}{"X"} - "A"_2 bar"R"`
= 10.66 + (0.58)(6.3)
= 10.66 + 3.654 = 14.314
= 14.31
CL = `\overset{==}{"X"}` = 10.66
LCL = `\overset{==}{"X"} - "A"_2 bar"R"`
= 10.66 – (0.58)(6.3)
= 10.66 – 3.654
= 7.006
The control limits for Range chart is
UCL = `"D"_4 bar"R"` = 2.115(6.3)`
= 13.3245
= 13.32
CL = `bar"R"` = 6.3
LCL = `"D"_3 bar"R"` = 0(6.3) = 0
Conclusion: Since all the points of sample range is within UCL of R chart, the process is in control.
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संबंधित प्रश्न
Define assignable cause
Define R chart
What are the uses of statistical quality control?
A quality control inspector has taken ten samples of size four packets each from a potato chips company. The contents of the sample are given below, Calculate the control limits for mean and range chart.
| Sample Number | Observations | |||
| 1 | 2 | 3 | 4 | |
| 1 | 12.5 | 12.3 | 12.6 | 12.7 |
| 2 | 12.8 | 12.4 | 12.4 | 12.8 |
| 3 | 12.1 | 12.6 | 12.5 | 12.4 |
| 4 | 12.2 | 12.6 | 12.5 | 12.3 |
| 5 | 12.4 | 12.5 | 12.5 | 12.5 |
| 6 | 12.3 | 12.4 | 12.6 | 12.6 |
| 7 | 12.6 | 12.7 | 12.5 | 12.8 |
| 8 | 12.4 | 12.3 | 12.6 | 12.5 |
| 9 | 12.6 | 12.5 | 12.3 | 12.6 |
| 10 | 12.1 | 12.7 | 12.5 | 12.8 |
(Given for n = 5, A2 = 0.58, D3 = 0 and D4 = 2.115)
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 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 |
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:
The LCL for R chart is given by
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 |
