Statistical Process Control (SPC) Implementation Guide for Indian Manufacturers

For each subgroup i (i = 1 to k):
  x̄ᵢ = mean of the subgroup
  Rᵢ = range of the subgroup (max - min)

Grand mean: X̄̄ = (Σx̄ᵢ) / k
Average range: R̄ = (ΣRᵢ) / k

Control limits for X-bar chart:
  UCL_x = X̄̄ + A₂ × R̄
  LCL_x = X̄̄ - A₂ × R̄

Control limits for R chart:
  UCL_R = D₄ × R̄
  LCL_R = D₃ × R̄

Process standard deviation: σ = R̄ / d₂
  (d₂ constants: n=2: 1.128, n=3: 1.693, n=4: 2.059, n=5: 2.326)

Cp = (USL - LSL) / (6σ)
  Measures spread relative to tolerance. Does not account for centering.

Cpk = min[(USL - X̄̄) / (3σ), (X̄̄ - LSL) / (3σ)]
  Measures capability accounting for centering. This is the key metric.

For each subgroup i:
  nᵢ = number of items inspected
  dᵢ = number of defective items
  pᵢ = dᵢ / nᵢ (proportion defective)

Average proportion defective: p̄ = Σdᵢ / Σnᵢ

Control limits for each subgroup (variable limits because nᵢ varies):
  UCL_pᵢ = p̄ + 3√(p̄(1-p̄)/nᵢ)
  LCL_pᵢ = p̄ - 3√(p̄(1-p̄)/nᵢ)  [set to 0 if negative]

CREATE TABLE spc_characteristics (
  id              UUID PRIMARY KEY DEFAULT gen_random_uuid(),
  name            VARCHAR(200) NOT NULL,  -- e.g., "Shaft diameter"
  part_number     VARCHAR(100),
  operation       VARCHAR(100),
  usl             DECIMAL(12,4),  -- Upper Specification Limit
  lsl             DECIMAL(12,4),  -- Lower Specification Limit
  target          DECIMAL(12,4),
  unit            VARCHAR(20),
  chart_type      VARCHAR(20) DEFAULT 'xbar_r',
  subgroup_size   INTEGER DEFAULT 5,
  sample_frequency VARCHAR(50),  -- e.g., "Every 30 minutes"
  is_active       BOOLEAN DEFAULT true
);

CREATE TABLE spc_subgroups (
  id              UUID PRIMARY KEY DEFAULT gen_random_uuid(),
  characteristic_id UUID NOT NULL REFERENCES spc_characteristics(id),
  subgroup_number INTEGER NOT NULL,
  collected_at    TIMESTAMPTZ NOT NULL,
  collected_by    UUID,
  machine_id      VARCHAR(100),
  shift           VARCHAR(20),
  notes           TEXT
);

CREATE TABLE spc_measurements (
  id              UUID PRIMARY KEY DEFAULT gen_random_uuid(),
  subgroup_id     UUID NOT NULL REFERENCES spc_subgroups(id),
  sample_number   INTEGER NOT NULL,
  value           DECIMAL(12,4) NOT NULL,
  is_outlier      BOOLEAN DEFAULT false
);

-- Calculated control limits (updated after each Phase 1 analysis)
CREATE TABLE spc_control_limits (
  id              UUID PRIMARY KEY DEFAULT gen_random_uuid(),
  characteristic_id UUID NOT NULL REFERENCES spc_characteristics(id),
  effective_from  TIMESTAMPTZ NOT NULL,
  effective_to    TIMESTAMPTZ,
  x_bar_bar       DECIMAL(12,4),
  r_bar           DECIMAL(12,4),
  ucl_x           DECIMAL(12,4),
  lcl_x           DECIMAL(12,4),
  ucl_r           DECIMAL(12,4),
  lcl_r           DECIMAL(12,4),
  cp              DECIMAL(6,3),
  cpk             DECIMAL(6,3),
  sigma           DECIMAL(12,6)
);

function checkWesternElectricRules(points, ucl, lcl, centerline) {
  const sigma = (ucl - centerline) / 3;
  const violations = [];

  // Rule 1: Point beyond 3σ
  points.forEach((p, i) => {
    if (p > ucl || p < lcl) {
      violations.push({ rule: 1, index: i, value: p, severity: 'CRITICAL' });
    }
  });

  // Rule 2: 9 consecutive points on same side
  for (let i = 8; i < points.length; i++) {
    const window = points.slice(i - 8, i + 1);
    if (window.every(p => p > centerline) || window.every(p => p < centerline)) {
      violations.push({ rule: 2, index: i, severity: 'WARNING' });
    }
  }

  // Rule 3: 6 consecutive points trending
  for (let i = 5; i < points.length; i++) {
    const window = points.slice(i - 5, i + 1);
    const increasing = window.every((p, j) => j === 0 || p > window[j-1]);
    const decreasing = window.every((p, j) => j === 0 || p < window[j-1]);
    if (increasing || decreasing) {
      violations.push({ rule: 3, index: i, severity: 'WARNING' });
    }
  }

  return violations;
}