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Question
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
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Solution
| Sample number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Total |
| `bar"X"` | 49 | 45 | 48 | 53 | 39 | 47 | 46 | 39 | 51 | 45 | 462 |
| R | 7 | 5 | 7 | 9 | 5 | 8 | 8 | 6 | 7 | 6 | 68 |
The control limit for `bar"X"` chart is
`\overset{==}{"X"} = (sumbar"X")/"No. of samples" = 462/10` = 46.2
`bar"R" = (sum"R")/"No. of samples" = 68/10` = 6.8
UCL = `\overset{==}{"X"} + "A"_2 bar"R"`
= 46.2 + (0.58)(6.8)
= 46.2 + 3.944
= 50.144
= 50.14
CL = `\overset{==}{"X"}` = 46.2
LCL = `\overset{==}{"X"} + "A"_2 bar"R"`
= 46.2 – (0.58)(6.8)
= 46.2 – 3.944
= 42.256
= 42.26
The control limits for Range chart is
UCL = `"D"_4 bar"R"`
= (2.115)(6.8)
= 14.382
= 14.38
CL = `bar"R"` = 6.8
LCL = `"D"_3bar"R"` = (0)(6.8) = 0
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RELATED QUESTIONS
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Name the control charts for variables
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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)
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 |
Choose the correct alternative:
Variations due to natural disorder is known as
The following are the sample means and I ranges for 10 samples, each of size 5. Calculate; the control limits for the mean chart and range chart and state whether the process is in control or not.
| Sample Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Mean | 5.10 | 4.98 | 5.02 | 4.96 | 4.96 | 5.04 | 4.94 | 4.92 | 4.92 | 4.98 |
| Range | 0.3 | 0.4 | 0.2 | 0.4 | 0.1 | 0.1 | 0.8 | 0.5 | 0.3 | 0.5 |
