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Find overall reliability for product

Answer these following Questions:

Question: 1. Suppose you want to inspect a lot of 10,000 products to see whether or not they meet requirements.

Design a sampling plan used to test these products.

Question: 2. Suppose a product is made of 100 components, each with a 97% reliability. What is the overall reliability for the product?

Question: 3. Suppose a product is made of 1,000 components, each with .999 reliability. What is the unreliability of

this product? Is this acceptable? Why or why not?

Question: 4. A product consists of 45 components. Each component has an average reliability of .97. What is the overall reliability for this product?

Question: 5. A radio is made up of 125 components. What would have to be the average reliability for each component for the radio to have a reliability of 98% over its useful life?

Question: 6. List five products with low reliability. List five that have high reliability. What are the elemental design differences between these products? In other words, what are the factors that make some products reliable and others unreliable?

Question: 7. An assembly consists of 240 components. Your customer has stated that your overall reliability must be at least 99%. What needs to be the average reliability factor for each component?

Question: 8. A product is made up of six components. They are wired in series with reliabilities of .95, .98, .94, .96, .98, and .97. What is the overall reliability for this product?

Question: 9. Suppose that redundant components are introduced for each of two components in Problem 8 with the lowest reliability. What is now the overall reliability for this product?

Question: 10. Suppose that redundant components are introduced for all of the components in Problem 8. What is now the overall reliability for the product?

Question: 11. A product is made up of components A, B, C, and D. These components are wired in series. Their reliability factors are .98, .999, .97, and .989, respectively. Compute the overall reliability for this product.

Question: 12. A product is made up of components A, B, C, D, E, F, G, H, I, and J. Components A, B, C, and F have a 1>10,000 chance of failure during useful life. D, E, G, and H have a 3>10,000 chance of failure. Components I and J have a 5>10,000 chance of failure. What is the overall reliability for this product?

Question: 13. For the product in Problem 12, if parallel components are provided for components I and J, what is the overall reliability for the product?

Question: 14. A product is made up of 20 components in a series. Ten of the components have a 1>10,000 chance of failure. Five have a 3>10,000 chance of failure. Four have a 4>10,000 chance of failure. One component has a 1>100 chance of failure. What is the overall reliability for this product?

Question: 15. For the product in Problem 14, if parallel components are used for any component with worse than a 1>1,000 chance of failure, what is the overall reliability? How many components will the new design have? What will be the average component reliability for the redesigned product?

Question: 16. An inspector visually inspects 200 sheets of paper at a time for aesthetics. Using trained judgment, the inspector will either accept or reject sheets based on whether they are flawless. Following are the

results of recent inspections:

Sample 1 2 3 4 5 6 7 8 9 10

Defectives 10 15 12 14 26 3 10 14 12 11

a. Given these results, using a p chart, determine if the process is stable.

b. What would need to be done to improve the process?

Question: 17. Using the data in Problem 16, compute the limits for an np chart.

Question: 18. Suppose a company makes the following product with the following numbers of defects. Construct ap chart to see if the process is in control. n ! 100

Question: 19. Using the data from Example 12-3 , evaluate the Demis using a u chart and evaluate the Streakless using a c chart. Assume that the Demis are twice the size of the Streakless on average.

Question: 20. Politicians closely monitor their popularity based on approval ratings. For the previous 16 weeks, Governor Johnny's approval ratings have been (in percentages):

Sample Defectives

4 32

5 30

6 48

7 32

8 24

9 25

10 27

11 28

12 29

13 65

14 66

15 69

16 70

17 26

18 13

19 45

20 46

21 47

22 48

23 28

24 29

25 75

Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Approval % 65 62 59 64 61 60 58 52 51 53 54 52 62 65 66 67

a. Prepare a report for the governor outlining the results of your analysis. Use control charts to analyze the data ( n = 200).

b. What action would you propose to the governor based on your analysis?

Question: 21. Construct and interpret a c chart using the following data:

Sample Defects

1 6

2 5

3 7

4 6

5 8

6 5

7 6

8 7

9 6

10 8

11 7

12 6

13 7

14 8

15 7

Sample Defects

16 6

17 5

18 2

19 1

20 0

21 12

22 4

23 6

24 7

25 8

26 3

27 2

28 3

29 2

30 3

Question: 22. Construct and interpret a u chart using the following data. Assume that the average size is two times the original product.

Sample Defects

16 6

17 5

18 2

19 1

20 0

21 12

22 4

23 6

24 7

25 8

26 3

27 2

28 3

29 2

30 3

Sample Defects

1 4

2 7

3 6

4 7

5 4

6 5

7 7

8 4

9 5

10 7

11 5

12 3

13 5

14 6

15 3

16 7

17 6

18 8

19 4

20 5

21 6

22 7

23 3

24 2

25 3

26 2

27 3

Question: 23. Dellana company tested 50 products for 75 hours each. In this time, they experienced four breakdowns. Compute the number of failures per hour. What is the mean time between failures?

Question: 24. The Collier company tested 200 products for 100 hours each. In this time, they experienced 12 breakdowns. Compute the number of failures per hour. What is the MTBF?

Question: 25. Crager company tested 100 products for 50 hours each. During the test, three breakdowns occurred. Compute the number of failures per hour and MTBF.

Question: 26. Suppose a product is designed to function for 10,000 hours with a 3% chance of failure. Find the average number of failures per hour and the MTTF.

Question: 27. Suppose a product is designed to function for 100,000 hours with a 1% chance of failure. Suppose six of these are in use at a facility. Find the average number of failures per hour and the MTTF.

Question: 28. Suppose there are 42 pumps used in a refinery. These pumps are continuously being used with a 2% chance of failure over 50,000 hours. If repair time is 10 hours to install a new rebuilt pump, how many pumps should be kept on hand to keep the chance of a plant shutdown to less than 1%. (Hint: Treat this problem as a traditional safety stock problem and use a z table.)

Question: 29. Suppose a product is designed to work for 1,000 hours with a 2% chance of failure. Find the average number of failures per hour and the MTTF. Question: 30. A product has been used for 5,000 hours with 1 failure. Find the mean time between failures (MTBF)

Question: 31. You are to decide between three potential suppliers for an assembly for a product you are designing. After performing life testing on several assemblies, you find the following:

Supplier MTBF (hr) MTTR (hr)

A 45 2

B 100 6

C 150 9

Supplier MTBF (hr) MTTR (hr)

1 45 2

2 90 2

3 120 6

4 200 6

Based on system availability, which supplier should you choose?

Question: 32. You are to choose a supplier of a copier based on reliability and service. After gathering data about the Supplier MTBF (hr) MTTR (hr)

1 45 2

2 90 2

3 120 6

4 200 6

alternatives, here is what you found. What do you recommend?

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