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.

24 Mar 2026
Answer :
Word Count : 961
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 | _________ _____ ____ _______ _________ ____ _________ ___ ________.
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Related Questions

 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% defective items are considered acceptable quality and 7% defective items are considered unacceptable quality.

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I’ve transcribed the table from your image exactly as it appears.

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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% 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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y₁=5+0.6y1-0.32 +8

where &, ~N[0,1]

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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: 

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

 

The marketing manager of a company recorded the number of mobiles sold quarterly for which are given in the following table:

I’ve transcribed the table from your image exactly as it appears.

Quarterly Data Table

Year / Quarter $Q_1$ $Q_2$ $Q_3$ $Q_4$
2018 48 41 60 65
2019 58 52 68 74
2020 60 56 75 78

 

 

(i) Find the quarterly seasonal indexes for the mobile sold using the ratio to trend method.

(ii) Do seasonal forces significantly influence the sale of mobile? Comment.

(iii) Also find the deseasonalised values.

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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. 

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