IGNOU MSTE 1 SOLVED ASSIGNMENT

Ques 1.

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.

Ques 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)

Ques 3.

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:

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

Ques 4.

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.

Ques 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.

Ques 6.

In a manufacturing process, 4 items are inspected every hour for 10 consecutive hours. The measured quality characteristic (in mm) is given below:

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.

Ques 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.

Ques 8.

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.

Ques 9.

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)

Ques 10.

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:

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

Ques 11.

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.

Ques 12.

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.

Ques 13.

In a manufacturing process, 4 items are inspected every hour for 10 consecutive hours. The measured quality characteristic (in mm) is given below:

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.

Ques 14.

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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