Six Sigma Analysis
Statistical Process Control & Anomaly Detection using DMAIC Framework
Cpk: 1.42Process Capable
Data Points
75
Last 30 days
Out of Control
3
>3σ violations
Warnings
5
2σ-3σ range
In Control
67
89.3% stable
Individual-Moving Range (I-MR) Control Charts
Revenue per Machine per Day (RPM)
Daily revenue monitoring with statistical control limits
1 Out of Control2 Warning
Normal
Warning (2σ-3σ)
Out of Control (>3σ)
Mean (X̄)
UCL/LCL (±3σ)
Cash Collection Variance
Weekly variance from expected collections
1 Out of Control1 Warning
Normal
Warning (2σ-3σ)
Out of Control (>3σ)
Mean (X̄)
UCL/LCL (±3σ)
Machine Uptime Percentage
Periodic uptime monitoring
1 Out of Control
Normal
Warning (2σ-3σ)
Out of Control (>3σ)
Mean (X̄)
UCL/LCL (±3σ)
Process Capability (Cpk)
Target: Cpk > 1.33
Variation Sources (Multi-Vari)
% contribution to total variation
FMEA Risk Priority (RPN)
Higher = Higher priority
DMAIC Framework Application
Define
- Revenue variance >±2σ
- CTQ: Cash accuracy, uptime
- Scope: >2σ triggers investigation
Measure
- Baseline Cpk established
- DEX data + GPS timestamps
- MSA validated sensors
Analyze
- I-MR charts by machine
- UCL/LCL at ±3σ
- Multi-vari studies complete
Improve
- Pattern stratification
- Root cause via Fishbone
- FMEA prioritization
Control
- Automated SPC alerts
- SOPs for each anomaly
- Dashboard monitoring
Priority 1 - Immediate (24h)
- Revenue variance >3σ from expected
- Cash shortage >$50 or >5%
- Machine offline >48h (high-traffic)
- Customer complaints >3/day per machine
Priority 2 - Weekly Review
- Revenue variance 2-3σ from expected
- Inventory variance >15% theoretical
- Service call >2x normal frequency
- Product spoilage >5% of load
Priority 3 - Monthly Review
- Trending toward 2σ over 3+ periods
- Cpk degradation 1.33 → 1.0-1.33
- Customer satisfaction declining >10%
- Route efficiency below threshold
Out-of-Control Signal Patterns
Pattern 1critical
Single point beyond 3σ
Action: Immediate investigation
Likely cause: Theft, failure, or data error
Pattern 2warning
2 of 3 consecutive beyond 2σ
Action: Early warning triggered
Likely cause: Process starting to drift
Pattern 3warning
7 consecutive trending
Action: Process shift detected
Likely cause: New competition, demographics
Pattern 4critical
14 alternating up/down
Action: Data quality review
Likely cause: Systematic manipulation
Root Cause Analysis Framework (Fishbone)
Machine
- • Bill validator failure
- • Card reader malfunction
- • Refrigeration issues
Method
- • Incorrect pricing
- • Planogram non-compliance
- • Restocking errors
Materials
- • Product quality
- • Stockouts
- • Expired inventory
Measurement
- • DEX transmission errors
- • Sensor calibration
- • Count accuracy
Environment
- • New competition
- • Construction nearby
- • Weather events
People
- • Route driver issues
- • Service quality
- • Training gaps