Question
In a manufacturing process, 4 items are inspected every hour for 10 consecutive hours.
The measured quality characteristic (in mm) is given below:
The measured quality characteristic (in mm) is given below.
| Hour | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| 1 | 50 | 52 | 51 | 49 |
| 2 | 51 | 50 | 53 | 52 |
| 3 | 49 | 50 | 48 | 51 |
| 4 | 52 | 54 | 53 | 51 |
| 5 | 50 | 49 | 51 | 50 |
| 6 | 53 | 52 | 54 | 55 |
|---|---|---|---|---|
| 7 | 48 | 49 | 50 | 47 |
| 8 | 51 | 52 | 50 | 51 |
| 9 | 54 | 55 | 53 | 54 |
| 10 | 50 | 51 | 49 | 50 |
(i) Construct conreol chart for variability and mean and comment on the state of statistical control. If the process is out of control, obtain revised control limits.
(ii) Given specification limits 50 ± 3, compute the process capability index (Cpk) and interpret the result.
Answer :
Word Count : 961
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Skip in 10
Let's solve this step by step manually. We have a dataset of 10 hours, 4 items each hour. We'll construct X-bar and R control charts and then calculate process capability. --- ### Step 1: Organize data | Hour | X1 | X2 | X3 | X4 | | ---- | -- | -- | -- | -- | | 1 | 50 | 52 | 51 | 49 | | 2 | 51 | 50 | 53 | 52 | | 3 | 49 | 50 | 48 | 51 | | 4 | 52 | 54 | 53 | 51 | | 5 | 50 | 49 | 51 | 50 | | 6 | 53 | 52 | 54 | 55 | | 7 | 48 | 49 | 50 | 47 | | 8 | 51 | 52 | 50 | 51 | | 9 | 54 | 55 | 53 | 54 | | 10 | 50 | 51 | 49 | 50 | --- ### Step 2: Compute X-bar and Range (R) for each subgroup X-bar = (sum of 4 values)/4 R = max - min #### Calculations: 1. Hour 1: X-bar = (50+52+51+49)/4 = 202/4 = 50.5, R = 52-49 = 3 2. Hour 2: X-bar = (51+50+53+52)/4 = 206/4 = 51.5, R = 53-50 = 3 3. Hour 3: X-bar = (49+50+48+51)/4 = 198/4 = 49.5, R = 51-48 = 3 4. Hour 4: X-bar = (52+54+53+51)/4 = 210/4 = 52.5, R = 54-51 = 3 5. Hour 5: X-bar = (50+49+51+50)/4 = 200/4 = 50.0, R = 51-49 = 2 6. Hour 6: X-bar = (53+52+54+55)/4 = 214/4 = 53.5, R = 55-52 = 3 7. Hour 7: X-bar = (48+49+50+47)/4 = 194/4 = 48.5, R = 50-47 = 3 8. Hour 8: X-bar = (51+52+50+51)/4 = 204/4 = 51.0, R = 52-50 = 2 9. Hour 9: X-bar = (54+55+53+54)/4 = 216/4 = 54.0, R = 55-53 = 2 10. Hour10: X-bar = (50+51+49+50)/4 = 200/4 = 50.0, R = 51-49 = 2 Summary Table: | Hour | X-bar | R | | ---- | ----- | - | | 1 | 50.5 | 3 | | 2 | 51.5 | 3 | | 3 |
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