algo-mfg-spclisted

# Statistical Process Control ## Overview SPC uses control charts to monitor process stability over time. Upper and Lower Control Limits (UCL/LCL) are set at ±3σ from the process mean. Points within limits = common cause variation (stable). Points outside or showing patterns = special cause variation (investigate). Primary charts: X-bar/R, X-bar/S, I-MR, p-chart, c-chart. ## When to Use **Trigger conditions:** - Monitoring production process for stability and detecting shifts - Setting statistically-based control limits for quality metrics - Distinguishing normal variation from assignable causes **When NOT to use:** - For process capability assessment (use Cpk) - For root cause analysis of known problems (use fishbone/5-why) ## Algorithm ``` IRON LAW: Control Limits Are NOT Specification Limits Control limits (±3σ) describe what the process IS doing. Specification limits describe what the process SHOULD do. A process can be in statistical control (stable) but still produce out-of-spec products (incapable). Conversely, a capable process may be out of control (drifting). Monitor control FIRST, then assess capability. ``` ### Phase 1: Input Validation Collect: 25+ subgroups of measurements (5 per subgroup typical for X-bar/R). Verify: measurement system is adequate (gauge R&R < 10%), data collected in time order. **Gate:** Sufficient subgroups, time-ordered data, measurement system verified. ### Phase 2: Core Algorithm **X-bar/R Chart (subgroup data):** 1. Compute subgr