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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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.

A system consists of six independent components arranged as follows:

• Two components with reliabilities 0.9 and 0.8 connected in series.

• This series combination is connected in parallel with a component of reliability 0.7.

• The resulting subsystem is connected in series with two components of reliabilities 0.85 and 0.95.

Draw the reliability block diagram and calculate the overall reliability of the system.

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.

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

(c) In a series system, improving the reliability of the weakest component gives the maximum improvement in system reliability.

(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.

A factory purchases bolts in lots of 800. Acceptance is decided using a single-sampling plan with sample size n = 20 and acceptance number c = 3. Assume that 2% of defective items are considered acceptable quality and 7% defective items are considered unacceptable quality.

Find:

(i) The probability of accepting a lot when the incoming quality level is 5% defective.

(ii) The Average Outgoing Quality (AOQ), assuming rejected lots are completely screened and defectives are replaced.

(iii)The Average Total Inspection (ATI)

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