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MSTE 1 2025 - English

TUTOR MARKED ASSIGNMENT

MSTE-001: Industrial Statistics-I

Course Code: MSTE-001

Assignment Code: MISTE-001/TMA/2025

Maximum Marks: 100

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

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

(a) Statistical quality control (SQC) is a technique of process control only.

(b) Twenty pieces of different length of cloth contained 2, 4, 1, 3, 5, 4, 2, 7, 3, 5, 2, 2, 4, 5,6, 4, 2, 1, 2, 4 defects respectively. To check the process is under control with respect to the number of defects, we should use np-chart.

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

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

(e) A system has four components connected in parallel configuration with reliability  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.

2. Twenty saraples each of size 10 were inspected. The number of defectives detected in cach of them is given below: : 0, 1, 0, 3, 9, 2, 0, 7, 0, 1, 1, 0, 0, 3, 1, 0, 0, 2, 1, 0 Find the control limits for the number of defectives and establish quality standards for the future. Plot the graph and interpost.

3. 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 2 as the acceptance nuraber. Suppose 3% nonconforming zippers are acceptable to the manufacturer and 8% oncoming zippers are not acceptable. Let incoming quality be 4%

i) Construct an OC carve

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

i) Average total inspection (ATI).

4. An office supply company ordered a lot of 400 printers. When the lot arrives the company inspector will randomly inspect 12 printers. If more than three printers in the sample are non-conforming, the lot will be rejected. If fewer than two printers are non-conforming the lot will be accepted. Otherwise, a second sample of size 5 will be taken. Suppose the inspector finds two non-conforming printers in the first sample and two in the second saraple. Also AQI. and LTPD at 0.05 and 0.10 respectively. Let incoming quality be 4%

i) What is the probability of accepting the lot at the first sample?

ii) What is the probability of accepting the lot at the second sample?

iii) Find AQL and ATI

5. A two-person zero-sum game having the following payoff matrix for player A 

 

    

(i) Check whether saddle point exit or not.

(ii) If saddle point does not exit then determine optimal strategies for both the manufacturers and value of the game.

6.A system has seven independent components and reliability block diagram of it shown blow:

Find reliability of the system.

7. The failure data for 40 electronic components is shown below:

Operating Time (in hours)	0-5	5-10	10-15	15-20	20-25	25-30
Number of Failures	5	7	6	4	5	4
Operating Time (in hours)	30-35	35-40	40-45	45-50	≥50
Number of Failures	4	0	2	1	2

Estimate the reliability, cumulative failure distribution, failure density and failure rate functions.

8. At a call omtre, 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 S-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	10	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 variability and comments about the process. If process is out of control, then calculate the revised controllinis

ii) If the specification limits as the 812, then find the process capability. Does it appear that the process is capable of mecting the specification reques

MSTE 001 (January 2026 - July 2026) - ENGLISH

TUTOR MARKED ASSIGNMENT
MSTE-001: Industrial Statistics-I

Course Code: MSTE-001
Assignment Code: MSTE-001/TMA/2026
Maximum Marks: 100

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

1. State whether the following statements are True or False. Give reason in support of your answer: (5×2=10)

(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.

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% 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)

3. A company manufactures water pumps. The quality control inspector of the company takes a sample of 100 water pumps at regular intervals. The numbers of defective pumps for 15 samples are given below:

Sample No.	Defective Pumps	Sample No.	Defective Pumps	Sample No.	Defective Pumps
1	5	6	0	11	6
2	6	7	4	12	1
3	3	8	8	13	10
4	2	9	2	14	2
5	1	10	2	15	1

Use the data to construct a suitable chart. Observe the results and comment on the control of the process as indicated by the chart.

4. A two-person zero-sum game having the following payoff matrix for player A

	Player B
		I	II	III	IV	V
Player A	I	2	4	3	8	4
	II	5	6	3	7	8
	III	6	7	9	8	7
	IV	4	2	8	4	3

(i) Check whether saddle point exit or not.

(ii) If saddle point does not exit then determine optimal strategies for both the manufacturers and value of the game.

5. 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.

6. 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.

7. A restaurant produces fresh burgers for its customers every day. The company is known for supplying fresh burgers and never uses burgers prepared on the previous day. Demand for burgers is uncertain, preparation capacity is limited, and the restaurant has the option of producing 0, 100, 200, 300 and 400 burgers every day. It has been estimated that the cost of producing each burgers pack is Rs.15. Each burger is sold for Rs. 20. Prepare a payoff matrix when 0, 100, 200, 300 or 400 demands of the burgers turn up on any given day. Prepare an opportunity loss table and hence find the optimum strategy.

 

 

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