Lesson 3

Question 1

What does RBD stand for?

Answer 1

Reliability Block Diagram

Question 2

What is a system defined as?

Answer 2

A set of elements, subsystems, or components connected to guarantee one or more functional performances.

Question 3

What does the reliability of a system depend on?

Answer 3

The characteristics of reliability and availability elements that make up the system.

Question 4

What is Combinatory Analysis?

Answer 4

The study of the relationships of the connections between subsystems.

Question 5

What is the purpose of the RBD method?

Answer 5

To determine the elements necessary for the fulfillment of the required function and which can fail without affecting item functioning.

Question 6

How is each Required Function represented in RBD?

Answer 6

By its own Reliability Block Diagram.

Question 7

What are the two main factors that system reliability depends on?

Answer 7

• Reliability of the components
• System structure or configuration

Question 8

In an RBD, how are elements necessary for the required function connected?

Answer 8

In series.

Question 9

What configuration represents elements that can fail without affecting the required function?

Answer 9

Parallel configuration.

Question 10

What happens to elements not relevant for the required function in an RBD?

Answer 10

They are removed after verifying their failure does not affect elements involved in the required function.

Question 11

What does the series functional configuration represent?

Answer 11

The simplest and most common reliability model in certain contexts.

Question 12

In a series configuration, when is the system considered to have failed?

Answer 12

When the first failure occurs.

Question 13

What assumption is made about the operation and failure of elements in a series configuration?

Answer 13

Each element operates and fails independently from every other item.

Question 14

What is the probability of system success in a series configuration expressed as?

Answer 14

Pr{W} = Pr{E1} * Pr{E2|E1} * Pr{E3|(E1 ∩ E2)} * … * Pr{En|(E1 ∩ E2 ∩ … ∩ En-1)}.

Question 15

What is the formula to calculate the reliability of a system with n elements in series?

Answer 15

Rs(t) = ∏ Ri(t) for i = 1 to n.

Question 16

How does the reliability of a system change with respect to the number of items considered for the required function?

Answer 16

The reliability of the system decreases.

Question 17

What does redundancy mean in the context of RBD?

Answer 17

The existence of more than one means for performing the required function.

Question 18

What are the three classifications of redundancy?

Answer 18

• Active (Hot)
• Warm Standby
• Cold Standby

Question 19

What is the difference between active and warm standby redundancy?

Answer 19

Active redundancy shares the load from the beginning, while warm standby is subjected to a lower load until an operating element fails.

Question 20

In a cold standby redundancy, what happens to the redundant elements until one of the operating elements fails?

Answer 20

They are subjected to no load.

Question 21

What is a parallel model in RBD?

Answer 21

A model that consists of n elements where the system works if at least one item works without failure.

Question 22

What theorem is used to solve the problem of system reliability in a parallel configuration?

Answer 22

The Addition Theorem.

Question 23

What is the reliability of a system composed of twenty identical items if the reliability of the single element is above 0.98?

Answer 23

Over 65% to a fixed time instant.

Question 24

What is pseudo redundancy?

Answer 24

When a redundant element fulfills only a part of the required function.

Question 25

In a series configuration, what is the expression for system reliability in terms of individual item reliability?

Answer 25

Rs(t) ≤ min{Ri(t)}.

Question 26

What is the significance of the weakest element in a series structure?

Answer 26

It determines the overall system reliability.

Question 27

What is the formula for Mean Time Between Failures (MTBF)?

Answer 27

MTBF = 1/R(t).

Question 28

What is the probability of the system functioning when all elements are operational?

Answer 28

Pr{A} + Pr{B} + Pr{C} - Pr{A ∩ B} - Pr{A ∩ C} - Pr{B ∩ C} + Pr{A ∩ B ∩ C} ## Footnote This formula calculates the combined probability of multiple events in a parallel configuration.

Question 29

What is the formula for system reliability in parallel configuration?

Answer 29

R_S(t) = 1 - ∏ F_i(t) ## Footnote F_i(t) represents the failure function of the i-th element.

Question 30

When is a system considered not functioning in a parallel configuration?

Answer 30

When all the elements are faulty.

Question 31

What does MTTF stand for?

Answer 31

Mean Time To Failure.

Question 32

What is the relationship between MTTF and failure rate?

Answer 32

MTTF = ∫ R_S(t) dt from 0 to +∞.

Question 33

How is system reliability calculated with respect to individual element reliability?

Answer 33

R_S(t) ≥ max{R_i(t)} for i = 1, ..., n.

Question 34

True or False: The probability of the system functioning decreases with the increase in the number of constituent elements.

Answer 34

False.

Question 35

What is the failure rate in a parallel configuration with redundancy?

Answer 35

λ_s(t) is an increasing function.

Question 36

In a parallel configuration of two identical items, what is the failure rate?

Answer 36

λ_s(t) = 2λ - e^(-2λt).

Question 37

What does the reliability value of a parallel structure depend on?

Answer 37

The reliability values of the individual items at a fixed time instant.

Question 38

If the reliability of three items in a parallel structure are E1 = 0.4, E2 = 0.7, E3 = 0.9, what is the probability of the system functioning?

Answer 38

0.982.

Question 39

Fill in the blank: The 787 Dreamliner uses more electricity instead of ______ to power airplane systems.

Answer 39

[pneumatics].

Question 40

What are the benefits of the 787's more-electric design?

Answer 40

* More efficient power generation * Better fuel efficiency * Lower maintenance costs * Less drag and noise.

Question 41

What does a k-out-of-n configuration mean?

Answer 41

A structure where n elements are in active redundancy and k are necessary to perform the required function.

Question 42

How is the reliability of a k-out-of-n configuration calculated?

Answer 42

Using binomial distribution.

Question 43

What does the reliability of the generic element R(t) indicate?

Answer 43

The probability of correct functioning.

Question 44

What is the formula for system reliability R_S(t) in a k-out-of-n configuration?

Answer 44

R_S(t) = ∑(n choose i) R(t)^i (1 - R(t))^(n - i) for i = k to n.

Question 45

True or False: The reliability of the system increases with the increase in the number of elements.

Answer 45

True.

Question 46

What is the formula for the failure rate of two items with different failure rates λ1 and λ2?

Answer 46

λ_s(t) = λ1 * e^(-λ1t) + λ2 * e^(-λ2t) - (λ1 + λ2)e^(- (λ1 + λ2)t).

Question 47

What is the expected reliability increment when increasing the number of elements?

Answer 47

Always positive.

Question 48

What is the formula for the reliability function R(t) in terms of failure rates?

Answer 48

R(t) = e^{-(λ_1 + λ_2 + ... + λ_n)t} ## Footnote This formula represents the reliability function for a system with multiple components, where λ is the failure rate of each component.

Question 49

What does MTTF stand for?

Answer 49

Mean Time To Failure ## Footnote MTTF is a measure of the average time until a system or component fails.

Question 50

In a k-out-of-n configuration, what does 'k' represent?

Answer 50

'k' represents the minimum number of components that must function for the system to be considered operational. ## Footnote This concept is used in reliability engineering to design systems with redundancy.

Question 51

True or False: In a series configuration, the failure of any single component leads to the failure of the entire system.

Answer 51

True ## Footnote This is a characteristic of series configurations; they do not provide redundancy.

Question 52

Fill in the blank: The formula for system reliability in a parallel configuration is R = 1 - (1 - R_A)(1 - R_B). This indicates that ___ reliability increases with redundancy.

Answer 52

component ## Footnote This formula shows how redundancy in components improves overall system reliability.

Question 53

What does TMR stand for?

Answer 53

Triple Modular Redundancy ## Footnote TMR is a fault-tolerant system design that uses three identical components to ensure reliability.

Question 54

What is the effect of a single point of failure in a system?

Answer 54

It can significantly impact the system's reliability. ## Footnote Systems designed with redundancy can mitigate this risk.

Question 55

What is the residual reliability of a system?

Answer 55

The probability that a system will perform its intended function for a specified period after a certain time. ## Footnote It is often calculated in reliability assessments.

Question 56

What is the formula for calculating the reliability of a series-parallel configuration?

Answer 56

R(t) = R_S(t) = R_A(t) * R_B(t) ## Footnote This combines the reliability of series and parallel components.

Question 57

What is the significance of the term 'high-level redundancy'?

Answer 57

It refers to redundancy designed at the system level, such as dual central processors. ## Footnote High-level redundancy can enhance system reliability by providing alternative paths for functionality.

Question 58

What does the notation R(t) represent?

Answer 58

The reliability function at time t ## Footnote It quantifies the likelihood that a system or component will function without failure for a given time.

Question 59

Fill in the blank: In a mixed configuration, the reliability function R(t) can be expressed as R(t) = e^{-λ_1 t} + e^{-λ_2 t} - e^{-(λ_1 + λ_2)t}. This shows the ___ of various configurations.

Answer 59

interaction ## Footnote Interaction between different components influences overall system reliability.

Question 60

What is the function of a Reliability Block Diagram (RBD)?

Answer 60

To visually represent the reliability of a system and its components. ## Footnote RBDs help in understanding the dependencies and configurations of system components.

Question 61

What does the term 'single element reliability' refer to?

Answer 61

The reliability of an individual component within a system. ## Footnote This is the basic building block for calculating system reliability.

Question 62

True or False: In a parallel-series configuration, the reliability of the system is always greater than that of single elements when R_A > 0.382.

Answer 62

True ## Footnote This indicates that redundancy enhances reliability beyond a certain threshold.

Question 63

What is the role of component-level redundancy in reliability?

Answer 63

It increases system reliability by providing backups at the component level. ## Footnote Examples include dual kidneys and lungs in the human body.