Question

In a manufacturing process, 4 items are inspected every hour for 10 consecutive hours. 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

Construct control chart for variability and mean and comment on the state of statistical control. If the process is out of control, obtain revised control limits.

19 Jan 2026
Answer :
Word Count : 517
For each hour, the sample size is n = 4. Hence an (\bar X)-chart and an R-chart are appropriate. First, compute the sample mean and range for each hour. Hour 1: values 50, 52, 51, 49 (\bar X_1 = (50+52+51+49)/4 = 50.5), (R_1 = 52-49 = 3) Hour 2: 51, 50, 53, 52 (\bar X_2 = 51.5), (R_2 = 53-50 = 3) Hour 3: 49, 50, 48, 51 (\bar X_3 = 49.5), (R_3 = 51-48 = 3) Hour 4: 52, 54, 53, 51 (\bar X_4 = ______ _______ ___ ______ ______.
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Related Questions

State whether the following statements are True or False. Give reason in support of your answer: 

(a) The c-chart is suitable for monitoring to proportion of defective.

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(d) If the probabilities are not associated with the occurrence of different states of nature, then the situation is known as decision making under risk.

(e) In single sampling plan, if we increase acceptance number then the OC curve will be steeper.

 

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  Player B
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(i) Check whether saddle point exit or not.

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In a manufacturing process, 4 items are inspected every hour for 10 consecutive hours. 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

Construct control chart for variability and mean and comment on the state of statistical control. If the process is out of control, obtain revised control limits.

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