ReliabilityCalc

Reliability Engineering & Quality Management Examples

Practical examples and real-world scenarios for reliability engineering calculations and quality management tools to help you understand and apply these metrics effectively

Reliability Engineering Examples

MTTR Examples

Example 1: Manufacturing Equipment

Scenario

A production line had 5 breakdowns in the past month:

  • • Breakdown 1: 2.5 hours
  • • Breakdown 2: 1.8 hours
  • • Breakdown 3: 4.2 hours
  • • Breakdown 4: 3.1 hours
  • • Breakdown 5: 2.4 hours
Calculation

Total Repair Time = 2.5 + 1.8 + 4.2 + 3.1 + 2.4 = 14.0 hours

Number of Repairs = 5

MTTR = 14.0 ÷ 5 = 2.8 hours

Example 2: IT Server Maintenance

Scenario

Server incidents over 6 months:

  • • 8 incidents requiring 45 minutes each
  • • 3 incidents requiring 2 hours each
  • • 1 major incident requiring 8 hours
Calculation

Total Time = (8 × 0.75) + (3 × 2) + (1 × 8) = 20 hours

Number of Repairs = 8 + 3 + 1 = 12

MTTR = 20 ÷ 12 = 1.67 hours

MTBF Examples

Example 1: Fleet of Delivery Trucks

Scenario

Fleet performance over 1 year:

  • • 10 trucks in operation
  • • Each truck operates 8 hours/day, 250 days/year
  • • Total failures across fleet: 25
Calculation

Total Operating Time = 10 × 8 × 250 = 20,000 hours

Number of Failures = 25

MTBF = 20,000 ÷ 25 = 800 hours

Example 2: Manufacturing Pump System

Scenario

Pump system data:

  • • Operates 24/7 for 6 months
  • • 3 major failures occurred
  • • Total downtime: 48 hours
Calculation

Total Operating Time = (6 × 30 × 24) - 48 = 4,272 hours

Number of Failures = 3

MTBF = 4,272 ÷ 3 = 1,424 hours

Availability Examples

Example 1: Web Server Availability

Scenario

Web server performance in one month:

  • • Total time in month: 744 hours (31 days)
  • • Planned maintenance: 4 hours
  • • Unplanned downtime: 6 hours
Calculation

Total Downtime = 4 + 6 = 10 hours

Uptime = 744 - 10 = 734 hours

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

Example 2: Using MTBF and MTTR

Scenario

Equipment reliability data:

  • • MTBF = 500 hours
  • • MTTR = 5 hours
Calculation

Availability = MTBF ÷ (MTBF + MTTR)

Availability = 500 ÷ (500 + 5)

Availability = 500 ÷ 505 = 99.0%

OEE Examples

Example 1: Packaging Line

Availability Data
  • • Planned: 8 hours
  • • Actual: 7.5 hours
  • • Availability: 93.8%
Performance Data
  • • Ideal cycle: 0.5 min/unit
  • • Actual count: 800 units
  • • Performance: 88.9%
Quality Data
  • • Total count: 800 units
  • • Good count: 760 units
  • • Quality: 95.0%
OEE Calculation

OEE = Availability × Performance × Quality

OEE = 93.8% × 88.9% × 95.0%

OEE = 79.2%

Example 2: Injection Molding Machine

Shift Data
  • • Shift duration: 8 hours (480 minutes)
  • • Breakdowns: 30 minutes
  • • Changeovers: 20 minutes
  • • Ideal cycle time: 2 minutes
  • • Parts produced: 200
  • • Defective parts: 10
Detailed Calculation

Availability:

(480 - 30 - 20) ÷ 480 = 89.6%

Performance:

(2 × 200) ÷ 430 = 93.0%

Quality:

(200 - 10) ÷ 200 = 95.0%

OEE = 89.6% × 93.0% × 95.0% = 79.2%

Quality Management Tool Examples

Pareto Analysis Examples

Example 1: Customer Complaint Analysis

Complaint Data (6 months)
  • • Late delivery: 245 complaints (42%)
  • • Product defects: 156 complaints (27%)
  • • Poor service: 89 complaints (15%)
  • • Wrong product: 58 complaints (10%)
  • • Billing errors: 23 complaints (4%)
  • • Others: 12 complaints (2%)
Pareto Analysis Results

Top 2 issues: 69% of complaints

Top 3 issues: 84% of complaints

Action: Focus on delivery process and quality control

Example 2: Manufacturing Defect Analysis

Defect Types (Monthly)
  • • Dimensional errors: 187 units (35%)
  • • Surface finish: 134 units (25%)
  • • Material flaws: 98 units (18%)
  • • Assembly errors: 67 units (12%)
  • • Contamination: 34 units (6%)
  • • Others: 21 units (4%)
Cost Impact Analysis

Total defects: 541 units

Cost per defect: $45 average

Monthly cost: $24,345

Fixing top 3 issues could save 78% of costs

Fishbone Diagram Examples

Example: High Scrap Rate Problem

Root Cause Categories
Man (People)
  • • Insufficient training
  • • Operator fatigue
  • • New employees
Machine
  • • Worn cutting tools
  • • Machine vibration
  • • Calibration drift
Material
  • • Supplier quality issues
  • • Material hardness variation
  • • Storage conditions
Analysis Results

Problem: Scrap rate increased from 2% to 8%

Primary cause: Worn cutting tools (40% contribution)

Secondary cause: New operator training (30%)

Actions: Implement preventive tool maintenance + enhanced training program

Control Chart Examples

Example: Automotive Parts Diameter Control

Process Data
  • • Target diameter: 50.0 mm
  • • Tolerance: ±0.1 mm
  • • Sample size: 5 parts/hour
  • • Process average: 49.98 mm
  • • Average range: 0.06 mm
Control Limits
  • • UCL (X-bar): 50.01 mm
  • • LCL (X-bar): 49.95 mm
  • • UCL (R): 0.13 mm
Process Analysis

Process Status: In statistical control

Capability: Cpk = 1.67 (Very capable)

Defect Rate: < 0.1%

Result: Process meets all quality requirements

Process Capability Examples

Example: Chemical Process Temperature Control

Process Parameters
  • • Specification: 200°C ± 5°C
  • • USL: 205°C
  • • LSL: 195°C
  • • Process mean: 201°C
  • • Process std dev: 1.2°C
Capability Calculations

Cp: (205-195)/(6×1.2) = 1.39

Cpk: min[(205-201)/(3×1.2), (201-195)/(3×1.2)]

= min[1.11, 1.67] = 1.11

Result: Process is capable but slightly off-center

Industry Benchmarks

Typical Values by Industry

Manufacturing

MTBF: 200-2000 hours | MTTR: 1-8 hours | OEE: 60-85%

IT Systems

MTBF: 8000+ hours | MTTR: 0.5-4 hours | Availability: 99.9%+

Automotive

MTBF: 500-5000 hours | MTTR: 0.5-2 hours | OEE: 70-90%

Improvement Targets

World Class MTTR

< 1 hour for critical equipment

World Class Availability

99.9% (8.77 hours downtime/year)

World Class OEE

≥ 85% overall effectiveness