IGNOU MSCAST MST 14 Statistical Quality Control and Time Series Analysis Solved Assignment ENGLISH

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MST 014 (January 2026 - July 2026) - ENGLISH

M 4. Statistical Qu and Time senes

Course Code: MST-014

Assignment Code: MST-014/TMA/2026

Maximum Marks: 100

Note: Attempt all questions. Answer in your own words.

1. 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.

2. 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).

3. 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. (10)

4. 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

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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.

5. 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.

6. 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

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(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.

7. Differentiate between the autoregressive and moving average models of time series.

 

MST 014 (January 2025 - July 2025) - ENGLISH

TUTOR MARKED ASSIGNMENT

MST-014: Statistical Quality Control and Time Series

Course Code: MST-014

Assignment Code: MST-014/TMA/2025

Maximum Marks: 100

Note: All questions are compulsory. Answer in your own words.

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

(i) The R-chart is suitable when subgroup size is greater than 

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

(iii) 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.

(iv) If a researcher wants to find the relationship between today's unemployment and that of 5 years ago without considering what happens in between then the partial autocorrelation is the better way in comparison to autocorrelation.

(v) A system has four components connected in parallel configuration with reliability 0.2, 0.4, 0.5, 0.8. To improve the reliability of the system most, we have to replace the component which reliability is 0.2.

(b) Differentiate between the autoregressive and moving average models of time series.

2 A manufacturer of men's jeans purchases zippers in lots of 500. The jeans manufacturer uses single-sample acceptance sampling with a sample size of 10 to determine whether to accept the lot. The manufacturer uses c = 2 as the acceptance number. Suppose 3% nonconforming zippers are acceptable to the manufacturer and 8% nonconforming zippers are not acceptable. Find

(i) Probability of accepting a lot of incoming quality 0.04.

(ii) Average outing quality (AOQ), if the rejected lots are screened and all defective zippers are replaced by non-defectives.

(iii) Average total inspection (ATI).

3 A system has seven independent components and reliability block diagram of it shown as follows:

Find reliability of the system.

4. At a call centre, callers have to wait till an operator is ready to take their call. To monitor this process, 5 calls were recorded every hour for the 8-hour working day. The data below shows the waiting time in seconds:

Time	Sample Number
	1	2	3	4	5
9 a.m	8	9	15	4	11
10	7	19	7	6	8
11	11	12	10	9	10
12	12	8	6	9	12
1 p.m	11	10	6	14	11
2	7	7	10	4	11
3	10	7	4	10	10
4	8	11	11	11	7

 

(i) Use the data to construct control charts for mean and comments about the process. If process is out of control, then calculate the revised control limits.

(ii) If the specification limits as the 8±2, then calculate the process capability index Cpk and impetrate the result

5. Consider the time series model

(i) Is this a stationary time series?

(ii) What are the mean and variance of the time series?

(iii) Calculate the autocorrelation function.

(iv)Plot the correlogram.

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