Core reliability metrics
MTTR — Mean Time To Repair
Open calculator →MTTR = Total Repair Time / Number of RepairsKey notes
- Repair time = detection to full restoration. Lower is better.
Example
(2h + 3h + 1.5h + 2.5h) ÷ 4 repairs = 2.25 hours
Typical ranges (orientation only)
- IT Systems
- 1–4 h
- Manufacturing
- 2–8 h
- Automotive
- 0.5–2 h
MTBF — Mean Time Between Failures
Open calculator →MTBF = Total Operating Time / Number of FailuresKey notes
- Operating time = time the system is running, excluding downtime.
Example
500 hours ÷ 10 failures = 50 hours
Typical ranges (orientation only)
- IT Systems
- 8,000+ h
- Manufacturing
- 200–2,000 h
- Automotive
- 500–5,000 h
MTTF — Mean Time To Failure
Open calculator →MTTF = Total Operating Time / Number of Units FailedKey notes
- Used for non-repairable items. MTTF ≠ MTBF.
Example
10 bulbs × 1,000 h, 5 fail → MTTF = 10,000 ÷ 5 = 2,000 h
Typical ranges (orientation only)
- LED Bulbs
- 25,000+ h
- Hard Drives
- 1.5M h
- Industrial Motors
- 20,000–50,000 h
Availability
Open calculator →A = Uptime / (Uptime + Downtime) ≡ MTBF / (MTBF + MTTR)Key notes
- Expressed as % or decimal. High availability ≥ 99.9% (≤ 8.77 h downtime/year).
Example
MTBF=500h, MTTR=5h → A = 500 ÷ 505 = 99.01%
Typical ranges (orientation only)
- 5 Nines
- 99.999%
- 4 Nines
- 99.99%
- 3 Nines
- 99.9%
Uptime & SLA — Allowed Downtime
Open calculator →Allowed downtime = (1 − SLA) × periodNines = −log₁₀(1 − uptime)Key notes
- 365-day year (8,760 h); average month = 730 h. Error budget used = measured downtime ÷ allowed downtime.
Example
99.9% over 730 h → (1 − 0.999) × 730 h = 0.73 h = 43 m 48 s per month
OEE — Overall Equipment Effectiveness
Open calculator →OEE = Availability × Performance × QualityKey notes
- Availability = Run Time / Planned Production Time
- Performance = (Ideal Cycle Time × Total Count) / Run Time
- Quality = Good Count / Total Count
Example
93.8% × 88.9% × 95.0% = 79.2%
Typical ranges (orientation only)
- World Class
- ≥ 85%
- Good
- 70–85%
- Poor
- < 60%
Takt Time
Open calculator →Takt = Available Production Time / Customer DemandStations = ⌈ Total Work Content / Takt ⌉Key notes
- Available time excludes planned breaks and stops only. Every station’s cycle time must be ≤ takt.
Example
2 shifts × (480 − 40) min = 52,800 s ÷ 880 units = 60 s per unit
Downtime Cost
Open calculator →Cost = (Lost Revenue + Labor Cost + Overhead + Penalty + Repair) × Downtime HoursKey notes
- Includes direct and indirect costs. Used for business case for maintenance investments.
Example
$5,000/h rate × 4 hours downtime = $20,000 total cost
Spare Parts Optimization
Open calculator →P(X ≤ k) = Σ [e⁻λ × λˣ / x!] (Poisson CDF)Key notes
- λ = expected demand per period. k = stock quantity. Targets service level (e.g., 95%).
Example
λ = 3 parts/yr, target 95% SL → stock 6 parts (P = 96.6%; 5 parts gives 91.6%)
Typical ranges (orientation only)
- High Criticality
- 99% SL
- Medium
- 95% SL
- Low
- 90% SL
Advanced reliability analysis
Reliability R(t)
Open calculator →R(t) = e^(−λt) = e^(−t / MTBF)Key notes
- λ = failure rate. t = mission time. Assumes constant failure rate (exponential distribution).
Example
MTBF=1000h, t=100h → R(100) = e^(−0.1) = 90.48%
System Reliability
Open calculator →Series: Rs = R₁ × R₂ × … × RnParallel: Rs = 1 − (1−R₁)(1−R₂)…(1−Rn)k-of-n: Rs = Σ C(n,i) × Rⁱ × (1−R)^(n−i) for i ≥ kKey notes
- Parallel configurations improve availability through redundancy.
Example
2 components at 90% in parallel → Rs = 1−(0.1×0.1) = 99%
Failure Rate (λ)
Open calculator →λ = Number of Failures / Total Operating TimeKey notes
- Units: failures per hour, or FIT (failures per 10⁹ hours = λ × 10⁹). λ = 1 / MTBF.
Example
5 failures ÷ 10,000 hours = 0.0005 per hour = 500,000 FIT
Weibull Analysis
Open calculator →R(t) = e^−(t/η)^βKey notes
- η = characteristic life (scale parameter)
- β = shape parameter: β<1 early failures, β=1 random, β>1 wear-out
- MTTF = η × Γ(1 + 1/β)
Example
β=2, η=1000h → R(500) = e^−(0.5)² = e^−0.25 = 77.9%
Typical ranges (orientation only)
- β < 1
- Infant mortality
- β = 1
- Random failures
- β > 1
- Wear-out
FMEA — Risk Priority Number
Open calculator →RPN = Severity × Occurrence × DetectionKey notes
- Each factor rated 1–10. High RPN → prioritize corrective action.
Example
S=8, O=4, D=5 → RPN = 160 (High priority)
Typical ranges (orientation only)
- Critical
- RPN > 200
- High
- RPN 100–200
- Low
- RPN < 100
Gage R&R
Open calculator →%GRR = (σ_GRR / σ_Total) × 100%Where: σ²_Total = σ²_Part + σ²_GRRσ²_GRR = σ²_Repeatability + σ²_ReproducibilityKey notes
- %GRR < 10% → acceptable. 10–30% → marginal. > 30% → unacceptable.
Example
σ_GRR=0.05, σ_Total=0.20 → %GRR = 25% (marginal)
Typical ranges (orientation only)
- Acceptable
- < 10%
- Marginal
- 10–30%
- Unacceptable
- > 30%
Quality & statistical tools
Process Capability (Cp / Cpk)
Open calculator →Cp = (USL − LSL) / (6σ)Cpk = min[ (USL − μ) / 3σ, (μ − LSL) / 3σ ]Key notes
- Cp measures potential; Cpk measures actual (accounts for centering).
Example
USL=205, LSL=195, μ=201, σ=1.2 → Cp=1.39, Cpk=1.11
Typical ranges (orientation only)
- Excellent
- Cpk ≥ 1.67
- Capable
- Cpk ≥ 1.33
- Marginal
- Cpk 1.0–1.33
DPMO & Sigma Level
Open calculator →DPMO = (Defects / (Units × Opportunities)) × 1,000,0006σ process: DPMO = 3.4Key notes
- DPU = Defects / Units; DPO = Defects / (Units × Opportunities). Yield = (1 − DPO) × 100%.
Example
12 defects, 1000 units, 3 opportunities → DPMO = 4,000 → ~4.1σ
Typical ranges (orientation only)
- 6 Sigma
- 3.4 DPMO
- 5 Sigma
- 233 DPMO
- 4 Sigma
- 6,210 DPMO
Sample Size
Open calculator →n = (Z × σ / E)² or n = Z² × p(1−p) / E²Key notes
- Z = confidence z-score (95%→1.96). E = margin of error. σ = std dev.
Example
95% CI, σ=10, E=2 → n = (1.96×10/2)² = 96.04 → 97 samples
AQL Sampling Plan
Open calculator →Lot size + inspection level → code letter → n, Ac, ReAccept if nonconforming ≤ Ac; reject if ≥ ReKey notes
- Single sampling, MIL-STD-105E / ANSI Z1.4 tables. Pa = Σ C(n,x) pˣ (1−p)ⁿ⁻ˣ for x = 0…Ac.
Example
Lot 1,000, level II → J, n = 80; AQL 2.5 normal → Ac 5, Re 6
Control Chart (X̄-R)
Open calculator →UCLₓ = X̄̄ + A₂R̄ LCLₓ = X̄̄ − A₂R̄UCL_R = D₄R̄ LCL_R = D₃R̄Key notes
- Constants for n=5: A₂=0.577, D₃=0, D₄=2.114. Points outside limits = special cause.
Example
X̄̄=50, R̄=0.06, n=5 → UCL = 50+0.577×0.06 = 50.035
Pareto Analysis
Open calculator →Category % = (Category Value / Total) × 100Cumulative % = Σ previous % + Current %Key notes
- 80/20 Rule: ~20% of causes account for ~80% of problems.
Example
A=42%, B=27%, C=15% → Top 2 = 69% of issues
Correlation (Pearson r)
Open calculator →r = Σ[(xᵢ−x̄)(yᵢ−ȳ)] / √[Σ(xᵢ−x̄)² × Σ(yᵢ−ȳ)²]Key notes
- r ranges −1 to +1. |r| > 0.7 = strong. |r| < 0.3 = weak.
Example
Temperature vs defect rate: r = −0.82 (strong negative correlation)
Typical ranges (orientation only)
- Very Strong
- |r| ≥ 0.9
- Strong
- |r| 0.7–0.9
- Weak
- |r| < 0.3
Descriptive Statistics
Open calculator →Mean (x̄) = Σx / nStd Dev (s) = √[Σ(x−x̄)² / (n − 1)]CV = (s / x̄) × 100%Key notes
- CV = coefficient of variation. Describes spread relative to mean.
Example
Data: 10,12,11,13,14 → x̄=12, s=1.58, CV=13.2%