Quality control tools help identify, analyse, and control quality problems. Statistical Process Control (SPC) uses statistical methods to monitor and control process variation.
Seven Basic Quality Tools (Ishikawa)
| Tool | Purpose | When to Use |
| 1. Cause & Effect (Fishbone/Ishikawa) | Identify root causes of a problem (6Ms) | Root cause analysis |
| 2. Pareto Chart | Identify vital few causes; 80/20 rule | Prioritise improvement efforts |
| 3. Control Chart | Monitor process stability over time; UCL/LCL | Ongoing process monitoring |
| 4. Histogram | Show distribution of data | Understand process capability |
| 5. Scatter Diagram | Show correlation between two variables | Test cause-effect hypothesis |
| 6. Flowchart/Process Map | Map process steps and decision points | Understand and improve process |
| 7. Check Sheet | Structured tally of defect data collection | Data collection |
Statistical Process Control (SPC)
- Uses control charts to distinguish special cause variation (assignable) from common cause variation (inherent/random)
- Common cause: natural variation; process is in statistical control
- Special cause: unusual event; indicates process out of control; must be investigated
Control Chart — Key Elements
UCL = μ + 3σ | LCL = μ − 3σ | Centre Line = μ (process mean)
- UCL = Upper Control Limit; LCL = Lower Control Limit; ±3σ limits
- Points outside control limits = out-of-control signal
- X-bar chart: monitors process mean; R chart: monitors process range (variation)
- p-chart: proportion defective (attribute data); c-chart: count of defects per unit
- Control limits ≠ specification limits (spec limits are customer requirements)
Process Capability Indices
Cp = (USL − LSL) / (6σ) — process potential capability
Cpk = min[(USL − μ)/3σ, (μ − LSL)/3σ] — actual capability (centring)
- Cp ≥ 1.33 generally required; Cp ≥ 1.67 for critical processes
- Cpk accounts for process not being centred; Cpk = Cp only when process is centred
- Cpk < 1: process produces defects outside specification
- Six Sigma process: Cp = 2.0 (with 1.5σ mean shift → Cpk = 1.5)
Acceptance Sampling
- Statistical method to accept or reject a batch based on sample inspection
- AQL: Acceptable Quality Level — maximum defective % acceptable as process average
- LTPD: Lot Tolerance Percent Defective — maximum defect rate consumer will accept
- OC Curve: Operating Characteristic Curve — shows probability of acceptance vs. lot quality
- Producer's risk (α): probability of rejecting a good lot; Consumer's risk (β): probability of accepting a bad lot
ESE Tip: Cp measures spread; Cpk measures both spread and centring. Cp = 1.33 is minimum acceptable (4σ process). Control limits (±3σ) ≠ specification limits (customer requirements). p-chart for attribute/proportion data; X-bar chart for variable/measurement data.