An Introduction to Reliability and Maintainability
Engineering, 3rd Edition (2019) – Ebeling – Solutions
Manual PDF
Section 1: Core Concepts & Definitions (Questions 1–20)
1. Reliability is defined as the probability that an item will perform its intended function for a
specified period of time under stated operating conditions.
Answer: True
Explanation: This is the standard engineering definition of reliability as presented in Chapter 1 of
Ebeling. It emphasizes the four key elements: probability, intended function, specified time, and
stated conditions.
2. Maintainability is defined as the probability that a failed item will be restored to operational
status within a given active repair time.
Answer: True
Explanation: Maintainability is a measure of how easily and quickly a system can be repaired.
Ebeling defines it as the probability that repair, when performed under stated conditions, will be
completed within a specified time.
3. Availability is a function of reliability and maintainability only and does not depend on logistics
support.
Answer: False
Explanation: Availability depends on reliability (MTTF), maintainability (MTTR), and logistics
factors such as spare parts availability, administrative delays, and transportation. Ebeling discusses
operational availability as including all these factors.
4. The bathtub curve describes the failure rate of a product over its lifetime and consists of three
distinct periods: infant mortality, constant failure rate, and wear‑out.
Answer: True
,Explanation: The bathtub curve is a fundamental concept in reliability engineering. The early
period (decreasing failure rate) is dominated by manufacturing defects; the middle period (constant
failure rate) is characterized by random failures; the final period (increasing failure rate) results
from aging and wear.
5. The hazard rate function h(t) is also known as the instantaneous failure rate.
Answer: True
Explanation: The hazard rate is the limit of the conditional probability of failure in a small interval
divided by the length of the interval as the interval approaches zero. It represents the instantaneous
potential for failure per unit time.
6. The reliability function R(t) and the cumulative distribution function F(t) are related by R(t) =
1 – F(t).
Answer: True
Explanation: The reliability function is the probability of survival beyond time t, while F(t) is the
probability of failure by time t. Since an item either fails or survives, these probabilities sum to 1.
7. The mean time to failure (MTTF) is defined as the expected value of the failure time distribution
for a non‑repairable item.
Answer: True
Explanation: For non‑repairable items, MTTF is the average time until first failure. For repairable
systems, the analogous measure is mean time between failures (MTBF).
8. The mean time to repair (MTTR) is defined as the expected value of the repair time distribution.
Answer: True
Explanation: MTTR is a key maintainability parameter. It includes only active repair time
(diagnosis, repair, checkout), not administrative or logistics delays.
9. The failure rate of a system with redundancy is always higher than that of a single component.
Answer: False
,Explanation: Redundancy (parallel configuration) typically increases reliability and reduces the
overall failure rate compared to a single component, because the system can survive individual
component failures.
10. Preventive maintenance is performed after a failure has occurred.
Answer: False
Explanation: Preventive maintenance is performed on a scheduled basis to reduce the probability
of failure. Corrective maintenance is performed after a failure has occurred.
11. Reliability is a design parameter that can be predicted, measured, and improved.
Answer: True
Explanation: Reliability engineering involves prediction during design, measurement during
testing, and improvement through design changes, part selection, and manufacturing process
controls.
12. The conditional probability of failure in the interval (t, t+Δt) given survival to time t, divided
by Δt, approaches the hazard rate as Δt → 0.
Answer: True
Explanation: This is the formal definition of the hazard rate: h(t) = lim Δt→0 P(t < T ≤ t+Δt | T >
t)/Δt.
13. The exponential distribution is the only continuous distribution with a constant failure rate.
Answer: True
Explanation: A constant failure rate implies that the hazard function is independent of time. The
exponential distribution is uniquely characterized by this property (memoryless property).
14. The Weibull distribution can model increasing, constant, or decreasing failure rates depending
on its shape parameter β.
Answer: True
Explanation: When β = 1, the Weibull reduces to the exponential (constant failure rate); β < 1 gives
a decreasing failure rate; β > 1 gives an increasing failure rate.
, 15. A system is defined as a collection of components organized to accomplish a specific function.
Answer: True
Explanation: This is the basic definition of a system in reliability engineering. Systems can be
simple (few components) or complex (many components).
16. Redundancy always improves system reliability regardless of how it is implemented.
Answer: False
Explanation: While active parallel redundancy generally improves reliability, certain types of
redundancy (e.g., standby with imperfect switching) may provide less benefit, and redundancy can
actually reduce reliability if not properly designed (e.g., common‑cause failures).
17. Maintainability is a characteristic of design and installation that affects the ease, accuracy,
safety, and economy of maintenance actions.
Answer: True
Explanation: Maintainability is determined during the design phase. It influences repair time,
maintenance cost, and overall system availability.
18. The reliability function R(t) is a monotonically decreasing function of time.
Answer: True
Explanation: As time increases, the probability of survival cannot increase. R(t) is non‑increasing,
starting at R(0) = 1 and approaching 0 as t → ∞.
19. The cumulative hazard function H(t) is defined as the integral of the hazard rate from 0 to t.
Answer: True
Explanation: H(t) = ∫₀ᵗ h(u) du. The reliability function can be expressed as R(t) = exp(‑H(t)).
20. The concept of "design for reliability" includes the selection of high‑quality components,
derating, and redundancy.
Answer: True
Explanation: Design for reliability (DfR) involves many strategies, including component selection,
thermal management, derating (operating below rated limits), and fault tolerance.
Engineering, 3rd Edition (2019) – Ebeling – Solutions
Manual PDF
Section 1: Core Concepts & Definitions (Questions 1–20)
1. Reliability is defined as the probability that an item will perform its intended function for a
specified period of time under stated operating conditions.
Answer: True
Explanation: This is the standard engineering definition of reliability as presented in Chapter 1 of
Ebeling. It emphasizes the four key elements: probability, intended function, specified time, and
stated conditions.
2. Maintainability is defined as the probability that a failed item will be restored to operational
status within a given active repair time.
Answer: True
Explanation: Maintainability is a measure of how easily and quickly a system can be repaired.
Ebeling defines it as the probability that repair, when performed under stated conditions, will be
completed within a specified time.
3. Availability is a function of reliability and maintainability only and does not depend on logistics
support.
Answer: False
Explanation: Availability depends on reliability (MTTF), maintainability (MTTR), and logistics
factors such as spare parts availability, administrative delays, and transportation. Ebeling discusses
operational availability as including all these factors.
4. The bathtub curve describes the failure rate of a product over its lifetime and consists of three
distinct periods: infant mortality, constant failure rate, and wear‑out.
Answer: True
,Explanation: The bathtub curve is a fundamental concept in reliability engineering. The early
period (decreasing failure rate) is dominated by manufacturing defects; the middle period (constant
failure rate) is characterized by random failures; the final period (increasing failure rate) results
from aging and wear.
5. The hazard rate function h(t) is also known as the instantaneous failure rate.
Answer: True
Explanation: The hazard rate is the limit of the conditional probability of failure in a small interval
divided by the length of the interval as the interval approaches zero. It represents the instantaneous
potential for failure per unit time.
6. The reliability function R(t) and the cumulative distribution function F(t) are related by R(t) =
1 – F(t).
Answer: True
Explanation: The reliability function is the probability of survival beyond time t, while F(t) is the
probability of failure by time t. Since an item either fails or survives, these probabilities sum to 1.
7. The mean time to failure (MTTF) is defined as the expected value of the failure time distribution
for a non‑repairable item.
Answer: True
Explanation: For non‑repairable items, MTTF is the average time until first failure. For repairable
systems, the analogous measure is mean time between failures (MTBF).
8. The mean time to repair (MTTR) is defined as the expected value of the repair time distribution.
Answer: True
Explanation: MTTR is a key maintainability parameter. It includes only active repair time
(diagnosis, repair, checkout), not administrative or logistics delays.
9. The failure rate of a system with redundancy is always higher than that of a single component.
Answer: False
,Explanation: Redundancy (parallel configuration) typically increases reliability and reduces the
overall failure rate compared to a single component, because the system can survive individual
component failures.
10. Preventive maintenance is performed after a failure has occurred.
Answer: False
Explanation: Preventive maintenance is performed on a scheduled basis to reduce the probability
of failure. Corrective maintenance is performed after a failure has occurred.
11. Reliability is a design parameter that can be predicted, measured, and improved.
Answer: True
Explanation: Reliability engineering involves prediction during design, measurement during
testing, and improvement through design changes, part selection, and manufacturing process
controls.
12. The conditional probability of failure in the interval (t, t+Δt) given survival to time t, divided
by Δt, approaches the hazard rate as Δt → 0.
Answer: True
Explanation: This is the formal definition of the hazard rate: h(t) = lim Δt→0 P(t < T ≤ t+Δt | T >
t)/Δt.
13. The exponential distribution is the only continuous distribution with a constant failure rate.
Answer: True
Explanation: A constant failure rate implies that the hazard function is independent of time. The
exponential distribution is uniquely characterized by this property (memoryless property).
14. The Weibull distribution can model increasing, constant, or decreasing failure rates depending
on its shape parameter β.
Answer: True
Explanation: When β = 1, the Weibull reduces to the exponential (constant failure rate); β < 1 gives
a decreasing failure rate; β > 1 gives an increasing failure rate.
, 15. A system is defined as a collection of components organized to accomplish a specific function.
Answer: True
Explanation: This is the basic definition of a system in reliability engineering. Systems can be
simple (few components) or complex (many components).
16. Redundancy always improves system reliability regardless of how it is implemented.
Answer: False
Explanation: While active parallel redundancy generally improves reliability, certain types of
redundancy (e.g., standby with imperfect switching) may provide less benefit, and redundancy can
actually reduce reliability if not properly designed (e.g., common‑cause failures).
17. Maintainability is a characteristic of design and installation that affects the ease, accuracy,
safety, and economy of maintenance actions.
Answer: True
Explanation: Maintainability is determined during the design phase. It influences repair time,
maintenance cost, and overall system availability.
18. The reliability function R(t) is a monotonically decreasing function of time.
Answer: True
Explanation: As time increases, the probability of survival cannot increase. R(t) is non‑increasing,
starting at R(0) = 1 and approaching 0 as t → ∞.
19. The cumulative hazard function H(t) is defined as the integral of the hazard rate from 0 to t.
Answer: True
Explanation: H(t) = ∫₀ᵗ h(u) du. The reliability function can be expressed as R(t) = exp(‑H(t)).
20. The concept of "design for reliability" includes the selection of high‑quality components,
derating, and redundancy.
Answer: True
Explanation: Design for reliability (DfR) involves many strategies, including component selection,
thermal management, derating (operating below rated limits), and fault tolerance.
