CRE (Hong Kong Civil Service Exams) cheat sheet

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

• 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 and R(0) = 1.

• Exponential model: R(t) = e^(−λt), constant failure rate λ, MTBF = 1/λ, and F(t) = 1 − e^(−λt); memoryless property means used units retain the same residual MTBF.

• Weibull reliability: R(t) = e^(−(t/η)^β), where β < 1 is infant mortality, β = 1 is constant rate (exponential), β > 1 is wear-out; η is the scale (characteristic life) at which R = 0.368.

• Bathtub curve phases: decreasing-hazard infant mortality (burn-in, screening), constant-hazard useful life (random failures), increasing-hazard wear-out (preventive replacement).

• Series system: R_s = Π R_i and λ_s = Σ λ_i; adding components always lowers reliability, so series MTBF is dominated by the least reliable element.

• Parallel (active redundancy) system with n identical units: R_s = 1 − (1 − R)^n; two-unit case R_s = 2R − R^2.

• k-out-of-n identical units: R_s = Σ from i=k to n of C(n,i) R^i (1−R)^(n−i); a 1-out-of-n is parallel, an n-out-of-n is series.

• Hazard rate h(t) = f(t)/R(t); average failure rate over an interval = [ln R(t1) − ln R(t2)] / (t2 − t1).

• Maintainability M(t) = 1 − e^(−μt) for exponential repair times; MTTR = 1/μ, and availability A = MTBF / (MTBF + MTTR) = μ / (λ + μ).

• Safety hierarchy and risk metrics: risk = probability × severity; ALARP requires risk reduced as low as reasonably practicable; SIL levels derive from PFDavg targets (SIL 1: 10^−1 to 10^−2, SIL 2: 10^−2 to 10^−3, SIL 3: 10^−3 to 10^−4, SIL 4: 10^−4 to 10^−5).