Statistical Process Control

SPC is built on the distinction between common cause and special cause variation:

Common Cause Variation:
Inherent process variability from many small, random sources:
- Machine vibration, material inconsistency, environmental factors
- Always present, predictable in aggregate
- Reduced only by fundamental process changes
- Process is "in control" when only common causes present

Special Cause Variation:
Exceptional events that stand out from normal variation:
- Tool wear, operator error, material defect, equipment malfunction
- Identifiable and correctable
- Process is "out of control" when special causes present
- Must be eliminated to achieve stability

Control Charts:
Visual tools for monitoring process stability:

Variables Charts (Continuous Data):
- X-bar and R Chart: Average and range for subgroups
- X-bar and S Chart: Average and standard deviation
- Individual and Moving Range (I-MR): Single measurements
- Used for dimensions, weight, temperature, pressure

Attributes Charts (Count Data):
- p-Chart: Proportion defective
- np-Chart: Number of defectives
- c-Chart: Count of defects per unit
- u-Chart: Defects per unit (variable sample size)

Control Limits:
- Upper Control Limit (UCL): typically +3 sigma
- Center Line (CL): process mean
- Lower Control Limit (LCL): typically -3 sigma
- NOT specification limits - based on actual process performance

Process capability compares process variation to specification requirements:

Capability Indices:

Cp (Potential Capability):
Cp = (USL - LSL) / (6 x sigma)
- Measures spread relative to tolerance
- Does not account for centering
- Cp >= 1.33 typically required
- Higher values indicate more capable process

Cpk (Demonstrated Capability):
Cpk = min[(USL - mean) / (3 x sigma), (mean - LSL) / (3 x sigma)]
- Accounts for process centering
- Always <= Cp
- Cpk = Cp when perfectly centered
- Cpk >= 1.33 typically required

Ppk (Performance Index):
Similar to Cpk but uses overall standard deviation:
- Includes all variation sources
- Often lower than Cpk
- Better represents actual performance
- Used for initial process qualification

Interpreting Capability:
| Cpk Value | PPM Defective | Process Status |
|-----------|---------------|----------------|
| 0.67 | 45,500 | Poor |
| 1.00 | 2,700 | Minimum |
| 1.33 | 63 | Good |
| 1.67 | 0.57 | Excellent |
| 2.00 | 0.002 | Six Sigma |

Assumptions for Capability:
- Process is in statistical control
- Data follows normal distribution
- Measurement system is adequate
- Sample represents production range

Successful SPC implementation requires systematic approach:

Implementation Steps:

1. Select Critical Characteristics:
- Customer-critical dimensions
- Safety-related features
- Process-sensitive parameters
- Cost of failure considerations

2. Establish Measurement System:
- Gage R&R studies
- Calibration procedures
- Operator training
- Data collection methods

3. Collect Baseline Data:
- Sufficient samples (typically 100+)
- Normal operating conditions
- Document process settings
- Calculate initial statistics

4. Set Control Limits:
- Based on actual process data
- NOT specification limits
- Recalculate after process changes
- Document and communicate

5. Monitor and React:
- Real-time charting
- Out-of-control reaction plans
- Root cause investigation
- Continuous improvement

Advanced Techniques:

Western Electric Rules:
Beyond simple limit violations:
- 8 consecutive points on one side of center
- 6 points trending up or down
- 2 of 3 points beyond 2 sigma
- 4 of 5 points beyond 1 sigma

Pre-Control:
Simple alternative for operators:
- Green (target) zone: run freely
- Yellow (warning) zone: adjust if two consecutive
- Red (out of spec): stop and fix

Multivariate SPC:
For related characteristics:
- Hotelling's T-squared
- Principal Component Analysis
- Detect subtle pattern shifts

SPC expertise opens diverse career paths:

Quality Engineer:
Design and implement SPC systems:
- Select characteristics and methods
- Train operators on charting
- Analyze data for improvement
- $65,000-$95,000

Process Engineer:
Use SPC for process optimization:
- Identify variation sources
- Implement improvements
- Validate process changes
- $70,000-$100,000

Quality Manager:
Lead quality organizations:
- Develop SPC programs
- Set capability requirements
- Drive improvement culture
- $90,000-$130,000

Six Sigma Black Belt:
Advanced statistical problem-solving:
- Teach SPC methods
- Lead improvement projects
- Reduce variation systematically
- $100,000-$140,000

SPC Software Systems:

Minitab:
- Industry standard statistical software
- Comprehensive SPC capabilities
- Training widely available

InfinityQS:
- Enterprise quality management
- Real-time SPC across plants
- Cloud and on-premise options

Wonderware (AVEVA):
- Integrated with historians/MES
- Real-time control charting
- Shop floor focus

Custom/In-House:
- Excel with add-ins (basic)
- Python/R for analysis
- Database-driven solutions

Industries:
- Automotive (IATF 16949 requirements)
- Aerospace (AS9100)
- Medical devices (FDA expectations)
- Electronics manufacturing
- Food and beverage
- Pharmaceutical

SPC fundamentals apply across all manufacturing sectors.