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 | 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 ________ ______ _______ ______ __________ ___.
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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.

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).

 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).

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.

 Consider the time series model

y₁=5+0.6y1-0.32 +8

where &, ~N[0,1]

(i) State whether the process is stationary, giving reasons.

(ii) Find the mean of the process.

(iii) Obtain the variance of the process.

(iv) Derive the autocorrelation function up to lag 2 and sketch the correlogram.

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. 

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

 

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

(i) The c-chart is suitable for moniterting to proportion of defective.

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

(iii) Autocorrelation measures the relationship between yt and yt-k after removing the effect of intermediate lags.

(iv) If the effect of summer and winter is not constant on the sale of AC then we use the additive model of the time series.

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

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