Statistical Process Control (SPC) for Manufacturing
Statistical Process Control (SPC) uses statistical methods to monitor and control production processes. By detecting variation early, SPC prevents defects, reduces scrap, and ensures consistent product quality.
Two Types of Variation
- Common cause variation: Inherent to the process. Stable, predictable, within control limits. Requires process redesign to eliminate.
- Special cause variation: External, unexpected events. Unstable, unpredictable. Requires immediate investigation and correction. Examples: tool breakage, material lot change, operator error.
Key SPC Charts
| Chart | Data Type | Sample Size | Application |
|---|---|---|---|
| X-bar & R | Variable (continuous) | 2-10 | Process mean and range monitoring |
| X-bar & S | Variable (continuous) | >10 | Process mean and std dev monitoring |
| Individual & MR | Variable (continuous) | 1 | Slow processes, batch operations |
| p chart | Attribute (defect rate) | 50-200 | Fraction non-conforming |
| np chart | Attribute (defect count) | 50-200 | Number non-conforming, constant sample |
| c chart | Attribute (defects per unit) | Unit area | Count of defects on a surface |
Control Limits vs. Specification Limits
Control limits (UCL/LCL) are calculated from process data ±3σ. They define expected process variation. Specification limits (USL/LSL) are engineering requirements for part function. A process can be in control but not capable (producing outside spec). Both metrics matter.
Process Capability Indices
- Cp = (USL - LSL) / 6σ: Measures potential capability assuming centered process. Cp > 1.33 is minimum for production. Cp > 1.67 preferred.
- Cpk = min(USL - mean, mean - LSL) / 3σ: Measures actual capability accounting for centering. Cpk > 1.33 required for most applications.
- Pp/Ppk: Same formulas, but using overall standard deviation instead of within-subgroup. Pp/Ppk measures total process performance including between-subgroup variation.
Implementing SPC
- Identify critical-to-quality (CTQ) characteristics on the product
- Establish measurement system with GR&R analysis (GR&R < 20% of tolerance)
- Collect 25+ subgroups to establish baseline control limits
- Calculate trial control limits and check for out-of-control points
- Remove special causes, recalculate limits
- Deploy chart at workstation with clear reaction plan for out-of-control conditions
- Review and update limits after 100+ subgroups or after major process changes