CRE (ASQ) cheat sheet

Reliability R(t) is the probability a unit performs its required function without failure for a stated time under stated conditions; it is a probability, so 0 <= R(t) <= 1.

Failure rate lambda(t) = f(t)/R(t); hazard function relates density and survival, and F(t) = 1 - R(t).

Exponential model: R(t) = exp(-lambda*t), constant failure rate, MTBF = 1/lambda, and memoryless property.

Weibull reliability: R(t) = exp(-(t/eta)^beta); beta < 1 infant mortality, beta = 1 random, beta > 1 wear-out.

Bathtub curve phases: decreasing failure rate (infant mortality), constant (useful life), increasing (wear-out).

Mean life for exponential equals MTBF; median life = MTBF * ln(2) = 0.693 * MTBF.

Series system reliability R_s = product of component reliabilities; system is only as strong as its weakest link.

Parallel (active redundancy) with n identical units: R_s = 1 - (1 - R)^n.

Availability A = MTBF / (MTBF + MTTR) for steady-state repairable systems.

Reliability program plan defines tasks, responsibilities, schedules, and deliverables tied to program phases and milestones.

Design reviews (preliminary, critical) are formal gates where reliability analyses and test results are evaluated against requirements.

FRACAS: closed-loop Failure Reporting, Analysis, and Corrective Action System tracks failures to verified corrective action.

Reliability growth tracking uses Duane model: cumulative MTBF = A * T^alpha, where alpha is growth slope.

Cost of poor reliability rises sharply later in the life cycle; failures found in design are cheapest to correct.

Reliability requirements must be quantitative, measurable, and traceable to customer and mission needs.

Supplier reliability management includes specifications, qualification testing, and data requirements in contracts.

Reliability metrics include MTBF, failure rate, mission reliability, and probability of success.

Derating applies components below rated stress (power, voltage, temperature) to reduce failure rate and extend life.

Redundancy types: active (parallel, all powered) vs standby (switched); standby needs a reliable switch and monitor.

FMEA ranks severity, occurrence, detection; RPN = S * O * D; high severity items require action regardless of RPN.

Fault tree analysis is top-down deductive logic using AND/OR gates to model causes of an undesired top event.

Robust design (Taguchi) reduces sensitivity to noise factors using parameter design and orthogonal arrays.

Thermal management and stress-strength interference: failure occurs when stress exceeds strength distribution.

Design for reliability includes parts selection, derating, redundancy, and environmental protection.

Reliability allocation distributes system reliability targets to subsystems by complexity or criticality weighting.

Parts count prediction: system failure rate = sum of part failure rates times quality and environment factors.

Parts stress prediction applies stress factors to base failure rates for each component category.

Series RBD: R_s = product of R_i; parallel RBD: R_s = 1 - product of (1 - R_i).

k-out-of-n system reliability uses the binomial sum of terms C(n,i) R^i (1-R)^(n-i) for i = k to n.

Markov models use state transition rates (lambda, mu) to compute state probabilities and availability.

Reliability block diagram is success-oriented; fault tree is failure-oriented.

MTBF predictions from MIL-HDBK-217 style models use base failure rate times pi factors for stress, temperature, quality.

Monte Carlo simulation estimates system reliability when closed-form solutions are intractable.

Type I (producer's risk alpha) rejects good lot; Type II (consumer's risk beta) accepts bad lot.

OC curve plots probability of acceptance vs lot fraction defective; steeper curve means better discrimination.

Weibull probability plot: straight line indicates Weibull fit; slope estimates beta, intercept estimates eta.

Maximum likelihood estimation gives point estimates of parameters; confidence intervals quantify uncertainty.

Accelerated life testing uses Arrhenius (temperature) or inverse power law (voltage) models to extrapolate life.

Reliability demonstration test sample size depends on required MTBF, discrimination ratio, and risk levels.

Censored data (suspended items) must be included in life data analysis to avoid bias.

Goodness-of-fit (Anderson-Darling, chi-square) tests whether a distribution adequately models the data.

Maintainability M(t) = probability a failed unit is restored within time t; MTTR is its mean.

Inherent availability A_i = MTBF / (MTBF + MTTR); operational availability includes logistics and admin delay.

Preventive maintenance intervals balance failure cost against maintenance cost; too frequent PM can increase failures.

Maintenance strategies: corrective, preventive, predictive (condition-based), and reliability-centered maintenance.

RCM selects maintenance tasks by failure consequence and mode: condition-based, scheduled, redesign, or run-to-failure.

Repairable system metrics include MTBF, MTTR, and mean downtime; availability is a function of both.

Spare parts provisioning affects operational availability through logistics delay time.

Maintainability design features: accessibility, modularity, diagnostics, and standardized fasteners.

Risk = probability of occurrence * severity of consequence; risk ranking prioritizes mitigation.

Hazard analysis identifies energy sources and unsafe conditions before failures occur.

FMEA severity scale is 1-10; detection and occurrence also 1-10; RPN ranges 1-1000.

Fault tree minimal cut sets identify single points of failure; a cut set of order one is a critical single point.

Safety integrity levels (SIL) map to target probability of failure on demand ranges.

Common cause failure defeats redundancy; design diversity and physical separation reduce it.

Risk matrix plots likelihood vs consequence to classify risk as acceptable, tolerable, or unacceptable.

Pareto analysis prioritizes the vital few failure modes that account for most failures or cost.