design-for-reliability

name	design-for-reliability
description	Design for reliability (DFR) — FMEA, fault tree analysis, MTBF, Weibull analysis, reliability block diagram, derating, reliability growth (Duane), ALT, MIL-HDBK-217, IEC 61709 prediction standards.
metadata	{"priority":7,"promptSignals":{"phrases":["design for reliability","DFR","FMEA","reliability analysis","MTBF","fault tree analysis"],"minScore":3}}

Design for Reliability (DFR) — Complete Skill

Reliability Fundamentals

Reliability R(t): probability of failure-free operation from t=0 to time t R(t) = 1 - F(t) = 1 - CDF [Cumulative Distribution Function] Hazard rate (failure rate): h(t) = f(t) / R(t) [instantaneous failure rate; f = PDF]

Bathtub curve:

1. Infant mortality: high h(t) decreasing; defects, poor workmanship; burn-in to eliminate
2. Useful life: constant h(t) = λ; random failures; exponential distribution
3. Wearout: increasing h(t); fatigue, wear, degradation; Weibull β > 1

Mean Time Between Failures (MTBF): MTBF = ∫₀^∞ R(t) dt [hours] Exponential: MTBF = 1/λ; R(t) = exp(-λt)

Weibull Analysis

Two-parameter Weibull: R(t) = exp(-(t/η)^β) η = characteristic life (63.2% fail at t = η); β = shape parameter

β interpretation: β < 1: infant mortality (decreasing failure rate) β = 1: random failures (constant; exponential distribution) β = 2: linear wear-out β > 2: wear-out mode (rapid near end-of-life) β = 3.5: approximately normal distribution

Characteristic life from test data (MLE or regression): Plot ln(-ln(R)) vs. ln(t) on Weibull probability paper → straight line → slope = β, intercept = ln(η) Median rank: F_i = (i - 0.3) / (N + 0.4) [Bernard approximation; i = failure rank; N = total sample size]

B10 life (10% failure probability): t_B10 = η × (ln(1/0.9))^(1/β) = η × 0.1054^(1/β)

B50 life (median life): t_B50 = η × (ln 2)^(1/β) = η × 0.6931^(1/β)

Reliability Prediction (Parts Count Method)

MIL-HDBK-217F (electronic parts): λ_system = Σ λ_bi × π_Q × π_E × π_other [failures per 10⁶ hours] λ_bi = base failure rate (component, from tables); π_Q = quality factor; π_E = environment factor

IEC 61709 (equivalent European): Reference conditions: 40°C, ground fixed; π factors for temperature, stress, environment

Electronic reliability rule of thumb: 10°C decrease in junction temperature → 2× increase in MTBF (Arrhenius) Derating to 50% of rated current → 2–5× reliability improvement

Mechanical reliability prediction: No direct equivalent to 217F; use NPRD (Nonelectronic Parts Reliability Data) database Or: Weibull analysis of test data; design calculations (fatigue life, wear life)

FMEA (Failure Mode and Effects Analysis)

Process:

1. List all failure modes for each part/function
2. Assess Severity (S), Occurrence (O), Detection (D) on 1–10 scale
3. RPN = S × O × D; prioritize RPN > 100–150

FMEA rating scales:

Rating	Severity	Occurrence	Detection
10	Hazardous (no warning)	> 1 in 2	No detection possible
7	Major (loss of function)	1 in 100	Only detect post-failure
4	Minor (some effect)	1 in 10,000	Likely detect
1	No effect	< 1 in 10⁶	Always detected

Action priority (AP, per AIAG-VDA 2019): High AP: S=9–10 or S=9–10 and O≥4; action required regardless of RPN Medium AP: S=8 and O≥4; should be addressed Low AP: remaining; address if feasible

Fault Tree Analysis (FTA)

Top event: undesired system failure (defined at highest level) Decompose via AND/OR gates: AND gate (series): P(top) = P(A) × P(B) [both required for failure] OR gate (parallel): P(top) = 1 - (1-P(A)) × (1-P(B)) ≈ P(A) + P(B) if small

Minimal cut sets: smallest combination of basic events that cause top event Importance measures: Birnbaum importance: I_i = ∂P_top/∂P_i [sensitivity of system failure to component i] Criticality importance: CR_i = I_i × P_i / P_top

Common cause failure (CCF): β factor: λ_CCF = β × λ_independent [common cause fraction; β = 0.01–0.10] Two-out-of-two (2oo2) system: P_CCF = β × P_single (dominant for redundant systems)

Reliability Block Diagram (RBD)

Series system (all must work): R_system = R₁ × R₂ × ... × R_n = Π R_i MTBF_series = 1 / (Σ λ_i) [for exponential distributions]

Parallel (redundant) system (any one sufficient): R_system = 1 - Π (1 - R_i) [for n identical units: R_sys = 1 - (1-R)^n] MTBF_parallel = MTBF_single × (1 + 1/2 + ... + 1/n) [for identical exponential units] Two identical: MTBF_2 = 1.5 × MTBF_1

M-of-N (voting) system: R_MofN = Σ_{k=M}^{N} C(N,k) × R^k × (1-R)^(N-k) [binomial; R each unit; M required]

Derating

Derating: operate components below rated limits to reduce failure rate Capacitors: derate to 50–70% of rated voltage (at 50%: MTBF ≈ 3–5× vs. 100%) Semiconductors: derate to 70–80% of rated current; 80% of rated power Springs: derate to 80% of yield shear stress (creep/fatigue life extension) Bearings: derate to 50–70% of rated load (L10 life ∝ (C/P)³ → 30% derating = 2.9× L10)

Reliability Growth (Duane Model)

As development testing proceeds, failures are found and fixed → MTBF grows: MTBF_cum = K × T^α [T = cumulative test time; α = growth slope; K = constant] α = 0.3–0.6 (good program); 0 = no growth

Crow-AMSAA (AMSAA reliability growth): λ(T) = λ × β × T^(β-1) [intensifying power law; β < 1 → improvement] Plot cumulative failures vs. test time on log-log: slope = β

Standards

Standard	Scope
MIL-HDBK-217F	Electronic parts reliability prediction
IEC 61709	Electronic components — reference conditions
IEC 60812	FMEA technique
IEC 61025	Fault tree analysis
SAE J1739	FMEA for automotive
MIL-HDBK-189C	Reliability growth management
AIAG-VDA FMEA	Automotive FMEA (2019 edition)

Output

Provide: reliability target (R(t) [%] at t [hours]), distribution model (Weibull: β, η; or exponential: λ), MTBF [hours], B10 life [hours], system configuration (series/parallel), system reliability R_sys [%], top FMEA failure modes (top 3 RPN or AP, with S, O, D), fault tree top event probability, redundancy improvement (MTBF_parallel / MTBF_single), derating factors applied (voltage/current/load [%]), reliability growth target (Crow-AMSAA α), applicable standard (MIL-HDBK-217F, IEC 60812, AIAG-VDA FMEA).