ReliabilityCalc

Reliability Engineering & Quality Management Formulas

Complete reference guide for reliability engineering calculations and quality management tools with detailed explanations and practical examples

Reliability Engineering Formulas

MTTR - Mean Time To Repair

Basic Formula

MTTR = Total Repair Time / Number of Repairs

Where repair time is measured from when the failure is detected until the system is fully operational again

Example Calculation

System repairs: 4 failures

Repair times: 2h, 3h, 1.5h, 2.5h

Total time: 9 hours

MTTR = 9h ÷ 4 = 2.25 hours

Industry Benchmarks

  • • IT Systems: 1-4 hours
  • • Manufacturing: 2-8 hours
  • • Power Plants: 8-24 hours
  • • Automotive: 0.5-2 hours

MTBF - Mean Time Between Failures

Basic Formula

MTBF = Total Operating Time / Number of Failures

Where operating time is the total time the system is functioning before a failure occurs

Example Calculation

Total operating time: 500 hours

Number of failures: 10

MTBF = 500h ÷ 10 = 50 hours

Industry Benchmarks

  • • IT Systems: 8000+ hours
  • • Manufacturing: 200-2000 hours
  • • Power Plants: 500-1500 hours
  • • Automotive: 500-5000 hours

Availability

Primary Formula

Availability = (Uptime / Total Time) × 100%

Uptime: Total Time - Downtime

Total Time: Complete time period being measured

Alternative Formula

Availability = MTBF / (MTBF + MTTR)

Units: Percentage (0-100%)

High Availability: 99.9% or higher (8.77 hours downtime/year)

Example Calculation

Total time: 744 hours (31 days)

Downtime: 10 hours

Uptime: 734 hours

Availability = (734 ÷ 744) × 100% = 98.7%

Availability Levels

  • • 99.9%: 8.77 hours/year downtime
  • • 99.99%: 52.6 minutes/year downtime
  • • 99.999%: 5.26 minutes/year downtime
  • • Basic: 95-99% availability

OEE - Overall Equipment Effectiveness

Main Formula

OEE = Availability × Performance × Quality

Availability

Operating Time / Planned Production Time

Accounts for all events that stop planned production

Performance

(Ideal Cycle Time × Total Count) / Operating Time

Accounts for all factors that reduce speed

Quality

Good Count / Total Count

Accounts for all defective units produced

OEE Benchmarks

≥85%
World Class
70-85%
Good
60-70%
Fair
<60%
Poor

Quality Management & Statistical Formulas

Pareto Analysis (80/20 Rule)

Key Formulas

Percentage = (Category Value / Total Value) × 100
Cumulative Percentage = Sum of all previous percentages + Current percentage

Example Analysis

Defect A: 120 (40%)

Defect B: 90 (30%)

Defect C: 60 (20%)

Others: 30 (10%)

Focus on A & B (70% of problems)

Applications

  • • Quality problem prioritization
  • • Cost reduction opportunities
  • • Customer complaint analysis
  • • Resource allocation decisions

Control Chart Formulas

X-bar and R Chart

X-bar Chart (Sample Average)
X̄ = Σx / nUCL = X̄̄ + A₂R̄LCL = X̄̄ - A₂R̄
R Chart (Range)
R = Xmax - XminUCL = D₄R̄LCL = D₃R̄

Control Chart Constants (n=5)

A₂ = 0.577, D₃ = 0, D₄ = 2.114

Interpretation: Points outside control limits indicate special cause variation

Process Capability

Capability Indices

Cp = (USL - LSL) / (6σ)

Process potential capability

Cpk = min[(USL - μ)/3σ, (μ - LSL)/3σ]

Process actual capability

Capability Interpretation

  • • Cpk ≥ 1.33: Process very capable
  • • Cpk = 1.0-1.33: Process adequate
  • • Cpk < 1.0: Process not capable

Correlation Analysis

Correlation Coefficient

r = Σ[(xi - x̄)(yi - ȳ)] / √[Σ(xi - x̄)² × Σ(yi - ȳ)²]

Measures linear relationship strength between two variables (-1 to +1)

Correlation Strength

  • • 0.9 to 1.0: Very strong positive
  • • 0.7 to 0.9: Strong positive
  • • 0.3 to 0.7: Moderate positive
  • • 0.0 to 0.3: Weak positive
  • • Negative values: Inverse relationship

Applications

  • • Temperature vs. defect rate
  • • Training hours vs. productivity
  • • Machine speed vs. quality
  • • Experience vs. error rate

Histogram & Descriptive Statistics

Statistical Measures

Central Tendency
Mean (x̄) = Σx / nMedian = Middle value when sortedMode = Most frequent value
Variability
σ = √[Σ(x - x̄)² / n]Range = Max - MinCV = (σ / x̄) × 100%

Check Sheet Analysis

Frequency Analysis

Frequency = Count of occurrences
Relative Frequency = (Category Frequency / Total Count) × 100%

Process Flow Analysis

Process Metrics

Cycle Time = Total process time from start to finish
Process Efficiency = Value-added time / Total cycle time
Throughput = Units processed / Time period