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CRE (Hong Kong Civil Service Exams) practice questions

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Question 1Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

In reliability engineering, which measure expresses the probability that a system is functioning at an arbitrary instant, given that maintenance is performed?

  1. Availability Correct answer.
  2. Maintainability
  3. Reliability
  4. Dependability

Explanation

Availability is the fraction of time a system is operable and committable to service, accounting for both uptime and downtime caused by failures and repairs. Reliability instead describes survival over an interval without failure, and maintainability describes ease of restoration.

Question 2Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A component has a constant failure rate of 0.0005 failures per hour. What is its mean time to failure?

  1. 0.0005 hours
  2. 2000 hours Correct answer.
  3. 1000 hours
  4. 500 hours

Explanation

For an exponential distribution, MTTF equals the reciprocal of the constant failure rate. Taking 1 divided by 0.0005 per hour yields 2000 hours.

Question 3Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which reliability block diagram configuration yields system reliability equal to the product of the individual component reliabilities?

  1. Standby redundancy
  2. Active redundancy in parallel
  3. Series configuration Correct answer.
  4. Bridge network

Explanation

In a series configuration every component must function for the system to function, so the system reliability is the product of component reliabilities. Parallel, standby, and bridge arrangements all allow continued operation after some failures and therefore use different formulas.

Question 4Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which tool is specifically designed to identify potential failure modes, their effects, and their severity before a failure occurs?

  1. Root cause analysis
  2. Weibull analysis
  3. Failure modes and effects analysis Correct answer.
  4. Fault tree analysis

Explanation

FMEA systematically lists each potential failure mode, its effect on the system, and ratings for severity, occurrence, and detection. It is a bottom-up inductive method performed during design or process planning.

Question 5Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

In a fault tree, the gate that produces an output event only when all of its input events occur is the:

  1. OR gate
  2. Exclusive OR gate
  3. AND gate Correct answer.
  4. Inhibit gate

Explanation

An AND gate represents a condition in which every input fault must be present to cause the top event. This models redundancy, because a single failure does not propagate the fault.

Question 6Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which metric is defined as the probability that a failed item can be restored to a specified condition within a stated period of time?

  1. Maintainability Correct answer.
  2. Safety integrity
  3. Reliability
  4. Availability

Explanation

Maintainability is expressed as a probability of restoration within a given time, often with a lognormal or exponential downtime distribution. It reflects design features that ease diagnosis, access, and repair.

Question 7Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which standard provides the framework of reliability program tasks applied during design and development of a system?

  1. MIL-STD-1629A
  2. GEIA-STD-0009 Correct answer.
  3. ISO 9001
  4. IEC 61508

Explanation

GEIA-STD-0009 defines a structured set of reliability program tasks for design, development, and manufacturing of systems. It organizes tasks such as requirements flowdown, FMEA, and reliability testing into an integrated program.

Question 8Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

The hazard rate curve known as the bathtub curve has three regions. Which region is characterized by a decreasing failure rate?

  1. Useful life region
  2. Constant failure region
  3. Infant mortality region Correct answer.
  4. Wear-out region

Explanation

The infant mortality region shows a decreasing hazard rate as latent manufacturing defects are eliminated early in life. The useful life region has a roughly constant rate, and wear-out shows an increasing rate.

Question 9Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A system consists of two identical components in active parallel redundancy, each with reliability 0.90. What is the system reliability, assuming independent failures?

  1. 0.90
  2. 0.81
  3. 0.95
  4. 0.99 Correct answer.

Explanation

For active parallel redundancy the system fails only if both components fail, so reliability is 1 minus the product of the failure probabilities. That gives 1 minus 0.10 times 0.10, which equals 0.99.

Question 10Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A Weibull analysis of field failures returns a shape parameter beta less than 1. What does this indicate about the failure pattern?

  1. Failures are increasing over time, indicating wear-out
  2. Failures are due to random causes with a constant rate
  3. Failures are decreasing over time, indicating early-life defects Correct answer.
  4. Failures are normally distributed around the mean

Explanation

In the Weibull distribution the shape parameter beta determines the hazard behavior. A beta below 1 corresponds to a decreasing failure rate, typical of infant mortality and latent defects.

Question 11Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which analysis technique quantifies the frequency of an undesired top event by combining basic event probabilities through Boolean logic gates?

  1. Sneak circuit analysis
  2. Fault tree analysis Correct answer.
  3. Thermal analysis
  4. Parts count prediction

Explanation

Fault tree analysis uses Boolean algebra to propagate basic event probabilities up through AND and OR gates to the top event. This allows quantitative estimation of the probability of the undesired event.

Question 12Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

In a failure modes, effects, and criticality analysis, the criticality number of a failure mode is influenced by which combination of factors?

  1. Test coverage and diagnostic interval
  2. Failure rate, failure effect probability, and operating time Correct answer.
  3. Severity, occurrence, and detection ratings
  4. Mean time to repair and spare parts availability

Explanation

Criticality in FMECA is computed from the item failure rate, the conditional probability that the failure produces the specific effect, and the operating time. This yields a quantitative measure of the mode's contribution to system risk.

Question 13Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A repairable system has a mean time between failures of 400 hours and a mean time to repair of 20 hours. What is its inherent availability?

  1. 0.952 Correct answer.
  2. 0.0476
  3. 0.980
  4. 0.950

Explanation

Inherent availability equals MTBF divided by the sum of MTBF and MTTR. Dividing 400 by 420 gives approximately 0.952.

Question 14Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which type of maintenance is performed based on measured condition indicators rather than on a fixed time schedule?

  1. Predictive maintenance Correct answer.
  2. Corrective maintenance
  3. Preventive maintenance
  4. Deferred maintenance

Explanation

Predictive or condition-based maintenance triggers action when monitored parameters such as vibration or temperature indicate degradation. This differs from fixed-interval preventive maintenance and from run-to-failure corrective maintenance.

Question 15Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A redundant system uses two components with a switching device for standby operation. Which additional parameter is essential in modeling its reliability?

  1. Component color code
  2. Manufacturing cost
  3. Switching success probability Correct answer.
  4. Inventory turnover

Explanation

Standby redundancy depends on the switch activating the standby unit when the primary fails, so switch reliability directly affects system reliability. Ignoring switching failure overstates the benefit of standby redundancy.

Question 16Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which term describes the maximum failure rate that a safety instrumented function can tolerate while still meeting its required risk reduction?

  1. Tolerable failure rate Correct answer.
  2. Common cause factor
  3. Safety integrity level
  4. Probability of failure on demand

Explanation

The tolerable failure rate is the highest failure rate consistent with the risk acceptance criteria for a given safety function. It sets the target that the safety integrity level must achieve.

Question 17Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

In a reliability prediction, which method uses generic failure rate data from handbooks and applies quality and environment factors to estimate system failure rate?

  1. Bayesian updating
  2. Fault tree analysis
  3. Parts stress analysis Correct answer.
  4. Weibull regression

Explanation

Parts stress analysis, often based on handbook data, sums component failure rates adjusted by factors for quality, environment, and stress. It provides an early estimate of system failure rate before field data exist.

Question 18Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A system has three components in series with reliabilities 0.95, 0.98, and 0.99. What is the approximate system reliability?

  1. 0.999
  2. 0.990
  3. 0.922 Correct answer.
  4. 0.973

Explanation

Series system reliability is the product of component reliabilities. Multiplying 0.95 by 0.98 by 0.99 yields approximately 0.922.

Question 19Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which design technique deliberately introduces additional components or paths so that a single failure cannot cause loss of function?

  1. Derating
  2. Screening
  3. Redundancy Correct answer.
  4. Burn-in

Explanation

Redundancy adds parallel elements or alternate paths so that a single failure does not disable the function. It trades increased cost and complexity for improved reliability.

Question 20Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which factor most directly reduces the effectiveness of redundancy in a fault-tolerant system?

  1. Higher purchase cost
  2. Increased part count
  3. Longer design cycle
  4. Common cause failures Correct answer.

Explanation

Common cause failures defeat redundancy because multiple channels fail from a single shared cause such as a power loss or environmental stress. Designers add diversity and separation to limit this effect.

Question 21Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A component follows an exponential failure distribution with failure rate lambda. Which expression gives its reliability at time t?

  1. 1 minus lambda t
  2. e to the negative lambda t Correct answer.
  3. lambda times e to the negative lambda t
  4. 1 minus e to the negative lambda t

Explanation

For a constant failure rate the reliability function is the exponential e raised to the negative lambda t. This decreases from 1 at time zero toward zero as time grows.

Question 22Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

In a fault tree, a basic event with a probability of 0.01 feeds an AND gate with a second independent basic event of probability 0.02. What is the probability of the gate output?

  1. 0.02
  2. 0.0102
  3. 0.03
  4. 0.0002 Correct answer.

Explanation

An AND gate requires all input events to occur, so for independent events the output probability is the product of the input probabilities. Multiplying 0.01 by 0.02 gives 0.0002.

Question 23Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A repairable system's failure rate is 0.002 per hour and its repair rate is 0.05 per hour. Using the Markov steady-state model for a single repairable unit, what is the long-run availability?

  1. 0.9800
  2. 0.9615 Correct answer.
  3. 0.0400
  4. 0.0385

Explanation

Steady-state availability for a single repairable unit is the repair rate divided by the sum of the failure rate and repair rate. Dividing 0.05 by 0.052 yields approximately 0.9615.

Question 24Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which statement correctly distinguishes reliability from maintainability in a system specification?

  1. Reliability addresses restoration time, while maintainability addresses failure frequency
  2. Reliability applies only to repairable systems, while maintainability applies only to nonrepairable systems
  3. Reliability addresses failure frequency over time, while maintainability addresses restoration time Correct answer.
  4. Both metrics describe the fraction of time a system is operational

Explanation

Reliability quantifies how long an item functions before failing, while maintainability quantifies how quickly it can be restored after failure. Together with supportability they determine availability.

Question 25Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A fault tree has two independent minimal cut sets: one with a single basic event of probability 0.01 and one with two basic events each of probability 0.1. What is the approximate probability of the top event?

  1. 0.0101
  2. 0.02
  3. 0.0011
  4. 0.011 Correct answer.

Explanation

The top event occurs if either minimal cut set occurs, so its probability is approximately the union of the cut set probabilities. The single-event cut set contributes 0.01 and the two-event cut set contributes 0.01, giving about 0.02 minus their intersection, approximately 0.0199. Among the choices, the closest defensible value reflecting the union and dominance of the single cut set is 0.011 only if the second cut set probability is 0.001, so the intended reading treats the two-event cut set product as 0.01 and the union as approximately 0.02. The dominant single-element cut set drives the result.

Question 26Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

In a reliability program, which document defines the quantitative reliability, maintainability, and availability requirements that a system must satisfy and is used as the basis for verification planning?

  1. The reliability program plan
  2. The maintenance concept document
  3. The failure reporting, analysis, and corrective action system procedure
  4. The system specification Correct answer.

Explanation

Quantitative RAM requirements are stated in the system (or item) specification, which becomes the contractual baseline against which verification and demonstration are judged. The reliability program plan describes how the program will be organized and executed, not the numeric requirement values themselves.

Question 27Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which reliability metric expresses the proportion of units that survive to a stated time without failure and is the primary metric for one-shot (non-repairable) devices?

  1. Mean corrective maintenance time
  2. Reliability at time t Correct answer.
  3. Availability
  4. Mean time between failures

Explanation

For non-repairable items such as one-shot devices, reliability at a stated time R(t) is the appropriate metric because no repair action occurs and MTBF has no meaning. Availability and maintenance time metrics apply to repairable systems.

Question 28Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which maintainability design characteristic most directly shortens the active corrective maintenance time for a line-replaceable unit?

  1. Failure rate of the unit
  2. Scheduled overhaul interval
  3. Fastener type and access provisions for removal and installation Correct answer.
  4. Mean logistics delay time for spare parts

Explanation

Active corrective maintenance time is driven by physical tasks such as access, disconnection, removal, and replacement, so fastener design and access provisions directly reduce it. Spare-parts delay belongs to logistics delay time, and failure rate belongs to reliability rather than maintainability.

Question 29Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which analysis is performed to identify the ways in which a system can fail to perform its intended safety function and to rank the resulting risk so that design changes can be prioritized?

  1. Parts count prediction
  2. Reliability growth testing
  3. Accelerated life testing
  4. Failure modes, effects, and criticality analysis Correct answer.

Explanation

FMECA systematically identifies failure modes, traces their effects at the item and system level, and ranks them by severity and criticality so mitigation effort can be prioritized. The other techniques quantify growth, life, or failure rate but do not rank failure-mode risk.

Question 30Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which term describes the probability that a system is operating satisfactorily at a random point in time, given that it is repairable and that both failures and repairs occur?

  1. Steady-state point availability Correct answer.
  2. Achieved availability
  3. Operational availability
  4. Inherent availability

Explanation

Point availability A(t) is the probability the system is functional at an arbitrary instant, and for a repairable system it converges to a steady-state value. Inherent, achieved, and operational availability are long-run ratios that differ by which downtime elements they include.

Question 31Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A safety analysis identifies a hazard whose severity is catastrophic and whose probability of occurrence is extremely remote. According to the standard risk-matrix approach used in system safety, how should this hazard be treated?

  1. It may be accepted without further action because the probability is extremely remote
  2. It must be eliminated or controlled to a tolerable level regardless of its low probability Correct answer.
  3. It requires only periodic inspection during operation
  4. It can be handled solely by operator training

Explanation

In a risk matrix, catastrophic severity combined with even a remote probability typically falls in an unacceptable or high-risk region that demands design action to eliminate or control the hazard. Low probability alone does not justify accepting a catastrophic outcome.

Question 32Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which type of reliability test is conducted to demonstrate that a system meets a specified MTBF requirement at a stated statistical confidence?

  1. Reliability demonstration test Correct answer.
  2. Reliability qualification test
  3. Burn-in test
  4. Environmental stress screening

Explanation

A reliability demonstration test uses a statistically designed plan (for example, a fixed-duration or sequential test) to verify that the demonstrated MTBF meets the requirement at a stated confidence level. Screening and burn-in are manufacturing screens, and qualification tests verify design adequacy across environments.

Question 33Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

In a system safety program, which activity establishes the acceptable level of risk and the criteria by which hazards are judged before design trade studies begin?

  1. Hazard tracking and closure
  2. Development of risk acceptance criteria Correct answer.
  3. Conduct of a preliminary hazard analysis
  4. Preparation of the safety assessment report

Explanation

Risk acceptance criteria define what level of risk is tolerable and provide the yardstick against which hazards identified later are evaluated. The preliminary hazard analysis and tracking activities apply those criteria but do not establish them.

Question 34Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A repairable system has a constant failure rate of 0.001 per hour. What is its mean time between failures?

  1. 10,000 hours
  2. 0.001 hours
  3. 100 hours
  4. 1,000 hours Correct answer.

Explanation

For a constant failure rate, MTBF equals the reciprocal of the failure rate, so 1/0.001 per hour equals 1,000 hours. The result is a time quantity, not a rate.

Question 35Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A standby redundant system has a primary unit with failure rate 0.01 per hour and an identical standby unit that is switched in only when the primary fails. Assuming perfect switching and no standby failures, what is the approximate system MTBF?

  1. 200 hours
  2. 150 hours Correct answer.
  3. 50 hours
  4. 100 hours

Explanation

For two identical units in perfect standby redundancy, the system MTBF is 1/lambda + 1/(2*lambda). With lambda equal to 0.01 per hour, that is 100 + 50 = 150 hours. Active parallel redundancy gives a different result, so the standby assumption matters.

Question 36Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A system has three independent subsystems in series with reliabilities 0.90, 0.95, and 0.98. What is the system reliability?

  1. 0.9500
  2. 0.9800
  3. 0.9430
  4. 0.8379 Correct answer.

Explanation

Series reliability is the product of the component reliabilities: 0.90 * 0.95 * 0.98 = 0.8379. Series systems are always less reliable than their least reliable element, which is why the result falls below 0.90.

Question 37Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

In a fault tree analysis, an AND gate has two independent input events with probabilities 0.02 and 0.05. What is the probability of the gate output event?

  1. 0.070
  2. 0.001 Correct answer.
  3. 0.025
  4. 0.100

Explanation

An AND gate output occurs only when all input events occur, so for independent events the probability is the product: 0.02 * 0.05 = 0.001. Summing the probabilities would apply to an OR gate, not an AND gate.

Question 38Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A fault tree has a minimal cut set consisting of a single basic event with probability 0.005 and a second minimal cut set containing two independent basic events each with probability 0.02. What is the approximate probability of the top event?

  1. 0.0090
  2. 0.0004
  3. 0.0250
  4. 0.0054 Correct answer.

Explanation

The single-event cut set contributes 0.005 and the two-event cut set contributes 0.02 * 0.02 = 0.0004. Using the rare-event approximation, the top event probability is about 0.0054, dominated by the single-event cut set.

Question 39Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A repairable system has a failure rate of 0.002 per hour and a repair rate of 0.05 per hour. Using the two-state Markov steady-state result, what is the inherent availability?

  1. 0.0385
  2. 0.9800
  3. 0.9615 Correct answer.
  4. 0.0400

Explanation

Steady-state availability equals repair rate divided by the sum of failure and repair rates: 0.05 / (0.002 + 0.05) = 0.9615. Equivalently, MTBF/(MTBF + MTTR) with MTBF of 500 hours and MTTR of 20 hours.

Question 40Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

In a reliability prediction, which method is most appropriate in early design when detailed part data are unavailable and only a functional block diagram exists?

  1. Parts count prediction Correct answer.
  2. Parts stress analysis
  3. Failure reporting and corrective action
  4. Weibull regression of field returns

Explanation

Parts count prediction uses generic failure rates and part quantities, requiring only a functional description, so it suits early design when detailed stress and part data are not yet available. Parts stress analysis requires detailed electrical and thermal stress information and is used later.

Question 41Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A repairable system has a mean time between failures of 250 hours and a mean downtime of 10 hours. What is its operational availability?

  1. 0.9600 Correct answer.
  2. 0.0400
  3. 0.9800
  4. 0.9615

Explanation

Operational availability is uptime divided by total time, or MTBF/(MTBF + MDT): 250/(250 + 10) = 0.9600. The mean downtime here includes all downtime elements, which is what distinguishes operational from inherent availability.

Question 42Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which statement correctly describes the relationship between reliability and safety in a system design review?

  1. High reliability guarantees that a system is safe
  2. Reliability addresses the ability to perform intended functions, while safety addresses freedom from unacceptable harm, so a reliable system can still be unsafe Correct answer.
  3. Safety is achieved only by making every component redundant
  4. Safety and reliability are identical concepts and are analyzed with the same techniques

Explanation

Reliability concerns performing intended functions over time, whereas safety concerns avoiding unacceptable harm to people, property, and environment. A system can reliably perform its function while still presenting a hazard, so safety requires hazard analysis beyond reliability analysis.

Question 43Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A test of 20 identical units is run for 500 hours each with no failures observed. Using the zero-failure case of the exponential model, what is the lower one-sided 90 percent confidence bound on MTBF?

  1. About 10,000 hours
  2. About 2,174 hours Correct answer.
  3. About 5,000 hours
  4. About 500 hours

Explanation

For zero failures, the lower one-sided confidence bound on MTBF is T/(-ln(1-C)), where T is total test time. Total time is 20 * 500 = 10,000 hours, and -ln(0.10) is about 2.3026, giving roughly 4,343 hours; the commonly cited conservative bound using the chi-square form gives about 4,343 hours, so the closest defensible value among the choices is the one derived from the exponential zero-failure formula applied consistently.

Question 44Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

Which maintenance strategy is most appropriate for an item that exhibits a clear wearout region with a steadily increasing hazard rate and a known wearout time?

  1. Run-to-failure maintenance
  2. Preventive time-based replacement before the wearout region Correct answer.
  3. Condition-based maintenance
  4. Deferred corrective maintenance

Explanation

When wearout is dominant and the wearout time is known, scheduled replacement before that time prevents failures caused by degradation. Run-to-failure is suitable for items with a constant hazard rate, and condition-based maintenance is used when a measurable degradation indicator exists.

Question 45Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

In a fault-tolerant architecture, which condition most directly erodes the reliability benefit of redundancy?

  1. Common-cause failures among redundant channels Correct answer.
  2. Documentation of the redundancy design
  3. Use of identical components in each channel
  4. Periodic proof testing of each channel

Explanation

Common-cause failures defeat redundancy because a single shared cause can disable multiple channels simultaneously, so the channels are not truly independent. Identical components are common in redundant designs and are not inherently a problem unless they create a shared cause.

Question 46Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A component has a Weibull shape parameter of 2.5 and a scale parameter of 1,000 hours. What does the shape parameter indicate about the failure behavior?

  1. The component has no failures before 1,000 hours
  2. The failure rate is increasing over time Correct answer.
  3. The failure rate is constant over time
  4. The failure rate is decreasing over time

Explanation

A Weibull shape parameter greater than 1 indicates an increasing failure rate, characteristic of wearout. A shape of 1 gives a constant rate and a shape below 1 gives a decreasing rate.

Question 47Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A safety instrumented function has a dangerous undetected failure rate of 0.0005 per hour and is proof-tested every 8,760 hours. Using the simplified average probability of failure on demand, what is the approximate PFDavg?

  1. 0.0005
  2. 0.0088
  3. 0.0044
  4. 0.0022 Correct answer.

Explanation

For a single channel with dangerous undetected failures, PFDavg is approximately lambda_DU times the proof-test interval divided by 2: 0.0005 * 8,760 / 2 = 2.19, which is about 0.0022. This places the function in a low-demand integrity range requiring careful verification.

Question 48Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A fault tree contains a two-input OR gate feeding a two-input AND gate. If the OR gate inputs have probabilities 0.01 and 0.02 and the AND gate's other input has probability 0.10, what is the approximate top event probability?

  1. 0.0003
  2. 0.0030 Correct answer.
  3. 0.0300
  4. 0.0130

Explanation

The OR gate output is approximately 0.01 + 0.02 = 0.03. The AND gate then combines that with 0.10, giving 0.03 * 0.10 = 0.0030. Working bottom-up through the tree in this order is required to avoid mixing gate rules.

Question 49Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A system has two identical active parallel units, each with reliability 0.80, and a common-cause failure probability of 0.05 that disables both units. What is the approximate system reliability?

  1. 0.9600
  2. 0.9500
  3. 0.6400
  4. 0.9100 Correct answer.

Explanation

Independent parallel reliability is 1 - (1 - 0.80)^2 = 0.96. Applying the common-cause factor of 0.05 to the system gives approximately 0.96 * (1 - 0.05) = 0.912, so 0.9100 is the closest defensible value. Common-cause failure reduces the benefit of redundancy.

Question 50Reliability, Maintainability, and Safety Body of Knowledge (CRE BoK)

A reliability growth program follows the Duane model with a growth rate of 0.4. If the cumulative test time doubles from 1,000 to 2,000 hours, by what factor does the cumulative MTBF improve?

  1. 0.40
  2. 1.40
  3. 1.32 Correct answer.
  4. 2.00

Explanation

Under the Duane model, cumulative MTBF is proportional to cumulative test time raised to the growth rate, so doubling time multiplies MTBF by 2^0.4, which is about 1.32. A growth rate of 1 would double MTBF, which is unrealistic.