Reliability & Availability Calculators
MTBF, Weibull, series/parallel systems, and availability arithmetic.
- Serial/Parallel System MTBFRoll up component failure rates into a system MTBF for series or active-parallel redundancy.Series: λ_sys = Σλᵢ, MTBF = 1/λ_sys , Parallel(n identical): MTBF = (1/λ)·Σ_{k=1}^{n} 1/k , R_series = ∏Rᵢ, R_parallel = 1 − ∏(1−Rᵢ)
- Sigma Level ⇄ DPMOConvert between process sigma level, DPMO, and yield — with the standard 1.5σ long-term shift baked in.DPMO = (1 − Φ(σ − shift)) · 10⁶ , σ = Φ⁻¹(yield) + shift , yield = 1 − DPMO/10⁶
- MTBF from Runtime + Failure CountTurn logged operating hours and failure counts into MTBF, failure rate, and availability.MTBF = (operating hours × units) / failures , λ = 1 / MTBF , Aᵢ = MTBF / (MTBF + MTTR)
- Weibull B10 Life (β, η)Turn a Weibull shape and characteristic life into B10 (or any B-life), median life, and MTTF — the numbers a warranty or bearing spec actually asks for.t_B = η · [−ln(1 − B/100)]^(1/β) B50 = η · (ln 2)^(1/β) MTTF = η · Γ(1 + 1/β)
- Availability (MTBF / MTTR)Steady-state availability of a repairable system from its mean time between failures and mean time to repair.A = MTBF / (MTBF + MTTR)
- Series/Parallel System ReliabilityCombine identical block reliabilities into a series chain, a parallel (redundant) bank, or a k-out-of-n voting group.Series: R = Rⁿ , Parallel: R = 1 − (1−R)ⁿ , k-of-n: R = Σ_{i=k}^{n} C(n,i)·Rⁱ·(1−R)^{n−i}
- Weibull Reliability R(t)Survival probability, failure fraction, and hazard rate at a given time for a two-parameter Weibull life model.R(t) = exp[ −(t/η)^β ] , F(t) = 1 − R(t) , h(t) = (β/η)·(t/η)^(β−1)
- Normal Distribution Tail ProbabilityTurn a z-score into CDF, tail area, and two-sided probability — the guts of a Z-table without the table.z = (x − μ)/σ , Φ(z) = ½[1 + erf(z/√2)] , upper = 1 − Φ(z)
- Combined Uncertainty (GUM)Root-sum-square of up to five uncertainty components, with coverage factor for an expanded uncertainty.uₙ = √(u₁² + u₂² + … + uₙ²) , U = k · uₙ
- ISO 17025 CMC (Calibration & Measurement Capability)Roll reference-standard, repeatability, resolution, and other contributors into an ILAC P14-style CMC claim for your scope of accreditation.u_ref = U_ref/2 u_rep = s/√n u_res = r/(2√3) , u_c = √(u_ref² + u_rep² + u_res² + u_other²) CMC = k · u_c