CRPE Engineer Registration flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Reliability definition

Probability that an item performs its required function under stated conditions for a stated time interval. It is a probability between 0 and 1, with R(0) = 1.

Exponential reliability formula

R(t) = e^(−λt) for constant failure rate λ. MTBF equals 1/λ, and the distribution is memoryless: survival to time t does not change future failure probability.

Bathtub curve phases

Three regions of failure rate over life: infant mortality with decreasing rate, useful life with constant rate, and wear-out with increasing rate. Each phase calls for a different mitigation.

Series system reliability

R_s = product of all component reliabilities. For constant rates, system failure rate is the sum of component rates. Any single component failure causes system failure.

Active parallel redundancy

For n identical independent units, system reliability R = 1 − (1 − R_unit)^n. All units operate simultaneously; system fails only when all fail.

Inherent availability formula

A_i = MTBF/(MTBF + MTTR). It excludes preventive maintenance and logistics delay; operational availability includes those delays and is therefore lower.

Weibull reliability function

R(t) = exp[−(t/η)^β], where η is characteristic life and β is shape. β<1 means decreasing failure rate, β=1 exponential, β>1 wear-out.

Weibull characteristic life

η is the time at which reliability equals e^(−1), about 0.368, regardless of β. It is not the mean life unless β equals 1.

B10 life calculation

Time at which 10 percent of units fail: B10 = η·[−ln(0.9)]^(1/β), approximately 0.10536^(1/β) times η.

Binomial distribution use

P(k) = C(n,k)·p^k·(1−p)^(n−k). Used for attribute tests with fixed trials, such as success-run demonstrations and pass/fail acceptance sampling.

Poisson failure count model

P(k failures in time t) = (λt)^k·e^(−λt)/k!. Applies when failures occur randomly at constant rate, equivalent to exponential interarrival times.

Chi-square failure rate interval

For time-terminated testing with r failures and total time T, confidence bounds on MTBF use 2T/χ² with 2r and 2r+2 degrees of freedom.

Parts stress derating

Operating parts below rated electrical, thermal, or mechanical stress to lower failure rate. Derating guidelines specify maximum stress ratios by part type.

Stress-strength interference

Failure occurs when applied stress exceeds inherent strength. Increasing the margin or reducing the variability of either distribution lowers failure probability.

k-out-of-n reliability

System succeeds if at least k of n identical units succeed: R = sum from i=k to n of C(n,i)·R^i·(1−R)^(n−i).

Arrhenius acceleration factor

AF = exp[(Ea/k)·(1/T_use − 1/T_stress)], with Ea activation energy and k Boltzmann constant. Temperatures must be in kelvin.

Common-cause failure beta factor

Fraction of failures that defeat redundancy simultaneously. System failure rate is approximately β·λ plus the independent term; separation and diversity reduce β.

Success-run demonstration formula

For zero failures allowed, n = ln(1−C)/ln(R), where C is confidence and R is reliability. All n units must survive the stated test time.

Environmental stress screening

Manufacturing screen using thermal cycling, vibration, or burn-in to precipitate latent defects. It removes defects but is not a reliability demonstration.

HALT versus HASS

HALT finds operating and destruct limits during design. HASS applies those limits in production to screen units without damaging good product.

Accelerated life test models

Arrhenius for temperature, inverse power law for voltage, Coffin-Manson for thermal cycling. The model extrapolates accelerated results to use conditions.

FMECA criticality number

Mode criticality = β·α·λ·t, where β is conditional probability of the effect, α the mode ratio, λ the item failure rate, t operating time.

Risk priority number

RPN = Severity × Occurrence × Detection, each scored 1 to 10. Higher RPN ranks higher priority, but high severity should also trigger action independently.

Minimal cut set

Smallest combination of basic events that causes the top event. A single-element cut set is a single point of failure requiring design correction.

Fault tree AND gate

Output occurs only if all inputs occur. In the success path this corresponds to parallel redundancy, so the gate reduces top-event probability.

Rare-event approximation

Top-event probability approximately equals the sum of cut-set probabilities when basic events are rare and cut sets do not overlap strongly.

P-F interval

Time between detection of a potential failure and functional failure. Inspection frequency should be a fraction of this interval for predictive maintenance.

Duane growth model

Cumulative MTBF = A·T^α, with T cumulative test time. Instantaneous MTBF = A·T^α/(1−α); α is the growth rate.

AMSAA Crow model

Cumulative failures N(t) = λ·t^β. Growth occurs when β<1; instantaneous failure intensity is λ·β·t^(β−1).

Right-censored data

Units still operating at test end contribute time without failure. They must be included in life data analysis; omitting them biases MTBF downward.

ALARP principle

Risk must be reduced as low as reasonably practicable. Further reduction is required unless its cost is grossly disproportionate to the benefit.

FRACAS purpose

Failure reporting, analysis, and corrective action system. It traces each failure to root cause, assigns corrective action, and verifies effectiveness before closure.