A two-person zero-sum game having the following payoff matrix for player A
| Player B | |||||||||||||||||||
| I | II | III | IV | V | |||||||||||||||
| I | 2 | 4 | 3 | 8 | 4 | ||||||||||||||
| Player A | 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.
Let's break this problem into steps: ### Step 1: Check for a saddle point A saddle point is a situation where the element of the payoff matrix is the maximum in its row and the minimum in its column, or vice versa. #### Step 1.1: Identify the row minima and column maxima - Row Minima: For each row, identify the minimum value. - Column Maxima: For each column, identify the maximum value. #### Step 1.2: Compare the row minima with the column maxima - If a row minimum is equal to a column maximum, then that element is the saddle point. #### Step 2: If a saddle point does not exist, __________ _______ ______ _____ ______ ____ ______ ______.
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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.
Let incoming quality be 4%.
i) Construct an OC curve.
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)
A system has seven independent components and reliability block diagram of it shown blow:
Find reliability of the system.
A two-person zero-sum game having the following payoff matrix for player A
| Player B | |||||||||||||||||||
| I | II | III | IV | V | |||||||||||||||
| I | 2 | 4 | 3 | 8 | 4 | ||||||||||||||
| Player A | II | 5 | 6 | 3 | 7 | 8 | |||||||||||||
| III | 6 | 7 | 9 | 8 | 7 | ||||||||||||||
| IV | 4 | 2 | 8 | 4 | 3 | ||||||||||||||
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 8 will be taken. Suppose the inspector finds two non-conforming printers in the first sample and two in the second sample. Also AQL and LTPD are 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
Twenty samples each of size 10 were inspected. The number of defectives detected in each 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 interpret.
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 | |||||||||||||
State whether the following statements are True or False. Give reason in support of your answer:
(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 occurrence 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 0.2, 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.