algo-mfg-cpk

# Cpk Process Capability Index ## Overview Cpk measures how well a process fits within specification limits, accounting for both variation (spread) and centering. Cpk = min((USL - μ) / 3σ, (μ - LSL) / 3σ). Cpk ≥ 1.33 is typically required; Cpk ≥ 1.67 for critical characteristics. Unlike Cp, Cpk penalizes off-center processes. ## When to Use **Trigger conditions:** - Assessing whether a manufacturing process can meet customer specifications - Comparing capability across processes, machines, or time periods - Qualifying a process for production readiness **When NOT to use:** - When the process is not in statistical control (stabilize first with SPC) - For non-normal distributions without transformation ## Algorithm ``` IRON LAW: Cpk Is Only Valid for a STABLE, IN-CONTROL Process Computing Cpk on an unstable process gives a meaningless number. The process MUST be in statistical control (per SPC charts) before capability analysis. An unstable process with Cpk=2.0 today may produce defects tomorrow when it shifts. ``` ### Phase 1: Input Validation Collect: 100+ measurements from a stable process. Determine: USL, LSL (customer specifications). Verify process is in control (SPC charts show stability). **Gate:** Process in control, specifications defined, 100+ data points. ### Phase 2: Core Algorithm 1. Compute process mean: μ = Σxᵢ / n 2. Compute process standard deviation: σ = estimated from R-bar/d₂ or S-bar/c₄ (within-subgroup) — NOT overall std dev 3. Cp = (USL - LSL) /...