Statistical Process Control (SPC) Control Limits Calculator
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.calc-container { max-width: 640px; margin: 2rem 0; padding: 1.5rem; background: #fff; border: 1px solid #ddd; border-radius: 8px; box-shadow: 0 1px 3px rgba(0,0,0,0.06); font-family: system-ui, -apple-system, sans-serif; } .calc-container h3 { font-family: Georgia, serif; font-size: 1.15rem; color: #1a1a1a; margin-bottom: 1rem; padding-bottom: 0.5rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-row { display: flex; align-items: center; gap: 0.75rem; margin-bottom: 0.75rem; flex-wrap: wrap; } .calc-row label { min-width: 160px; font-size: 0.9rem; color: #333; font-weight: 500; } .calc-row input[type="number"], .calc-row select { flex: 1; min-width: 120px; max-width: 200px; padding: 0.5rem 0.6rem; border: 1px solid #ccc; border-radius: 4px; font-size: 0.9rem; font-family: system-ui, sans-serif; color: #1a1a1a; background: #fafaf8; } .calc-row input:focus, .calc-row select:focus { outline: none; border-color: var(--ac, #3d5a80); box-shadow: 0 0 0 2px rgba(26,74,138,0.12); } .calc-row .unit { font-size: 0.82rem; color: #888; min-width: 30px; } .calc-btn { display: inline-block; margin-top: 0.5rem; padding: 0.55rem 1.5rem; background: var(--ac, #3d5a80); color: #fff; border: none; border-radius: 4px; font-size: 0.9rem; font-weight: 600; cursor: pointer; font-family: system-ui, sans-serif; } .calc-btn:hover { opacity: 0.9; } .calc-result { margin-top: 1.25rem; padding: 1rem 1.25rem; background: #f0f6fc; border-left: 3px solid var(--ac, #3d5a80); border-radius: 0 6px 6px 0; display: none; } .calc-result.visible { display: block; } .calc-result-label { font-size: 0.78rem; text-transform: uppercase; letter-spacing: 0.06em; color: #666; margin-bottom: 0.25rem; } .calc-result-value { font-size: 1.6rem; font-weight: 700; color: var(--ac, #3d5a80); } .calc-result-detail { font-size: 0.85rem; color: #555; margin-top: 0.5rem; line-height: 1.5; } .calc-note { margin-top: 1rem; font-size: 0.8rem; color: #888; font-style: italic; } .calc-grid { display: grid; grid-template-columns: 1fr 1fr; gap: 0.75rem; margin-top: 0.75rem; } .calc-grid-item { padding: 0.6rem 0.8rem; background: #f8f9fa; border-radius: 4px; border: 1px solid #eee; } .calc-grid-item .label { font-size: 0.75rem; color: #888; text-transform: uppercase; letter-spacing: 0.04em; } .calc-grid-item .value { font-size: 1.1rem; font-weight: 600; color: #1a1a1a; } @media (max-width: 720px) { .calc-row { flex-direction: column; align-items: flex-start; gap: 0.3rem; } .calc-row label { min-width: auto; } .calc-row input[type="number"], .calc-row select { max-width: 100%; width: 100%; } .calc-grid { grid-template-columns: 1fr; } } .calc-chart { margin: 1rem 0; text-align: center; } .calc-chart svg { max-width: 100%; height: auto; } .calc-chart-legend { display: flex; flex-wrap: wrap; justify-content: center; gap: 0.6rem 1.2rem; margin-top: 0.6rem; font-size: 0.8rem; color: #555; } .calc-chart-legend span { display: inline-flex; align-items: center; gap: 0.3rem; } .calc-chart-legend i { display: inline-block; width: 10px; height: 10px; border-radius: 2px; font-style: normal; } .calc-related { max-width: 640px; margin: 2rem 0 1rem; padding: 1.25rem 1.5rem; background: #f8f9fa; border: 1px solid #e8e8e8; border-radius: 8px; } .calc-related h3 { font-family: Georgia, serif; font-size: 1rem; color: #1a1a1a; margin: 0 0 0.75rem; padding-bottom: 0.4rem; border-bottom: 2px solid var(--ac, #3d5a80); } .calc-related-list { list-style: none; padding: 0; margin: 0 0 0.75rem; display: grid; grid-template-columns: 1fr 1fr; gap: 0.4rem 1.5rem; } .calc-related-list li a { font-size: 0.88rem; color: var(--ac, #3d5a80); text-decoration: none; } .calc-related-list li a:hover { text-decoration: underline; } .calc-browse-all { margin: 0.5rem 0 0; font-size: 0.9rem; font-weight: 600; } .calc-browse-all a { color: var(--ac, #3d5a80); text-decoration: none; } .calc-browse-all a:hover { text-decoration: underline; } @media (max-width: 720px) { .calc-related-list { grid-template-columns: 1fr; } }
Statistical Process Control (SPC) Control Limits Calculator
Calculate Upper Control Limit (UCL) and Lower Control Limit (LCL) for X-bar, R-chart, and S-chart using standard SPC control chart constants.
Chart Type
X-bar & R Chart (subgroup size 2–10) X-bar & S Chart (subgroup size > 10)
Grand Mean (X̄̄) — average of subgroup means
Average Range (R̄) — average of subgroup ranges
Average Std Dev (S̄) — average of subgroup std deviations
Subgroup Size (n)
Calculate ...
// SPC Control Chart Constants (A2, D3, D4 for R-chart; A3, B3, B4 for S-chart) // Source: AIAG SPC Manual, 2nd Edition; Montgomery "Introduction to Statistical Quality Control" const STA_CONSTANTS = { // n: [A2, D3, D4, A3, B3, B4, d2, c4 ] 2: [1.880, 0.000, 3.267, 2.659, 0.000, 3.267, 1.128, 0.7979], 3: [1.023, 0.000, 2.574, 1.954, 0.000, 2.568, 1.693, 0.8862], 4: [0.729, 0.000, 2.282, 1.628, 0.000, 2.266, 2.059, 0.9213], 5: [0.577, 0.000, 2.114, 1.427, 0.000, 2.089, 2.326, 0.9400], 6: [0.483, 0.000, 2.004, 1.287, 0.030, 1.970, 2.534, 0.9515], 7: [0.419, 0.076, 1.924, 1.182, 0.118, 1.882, 2.704, 0.9594], 8: [0.373, 0.136, 1.864, 1.099, 0.185, 1.815, 2.847, 0.9650], 9: [0.337, 0.184, 1.816, 1.032, 0.239, 1.761, 2.970, 0.9693], 10: [0.308, 0.223, 1.777, 0.975, 0.284, 1.716, 3.078, 0.9727], 11: [0.285, 0.256, 1.744, 0.927, 0.321, 1.679, 3.173, 0.9754], 12: [0.266, 0.283, 1.717, 0.886, 0.354, 1.646, 3.258, 0.9776], 13: [0.249, 0.307, 1.693, 0.850, 0.382, 1.618, 3.336, 0.9794], 14: [0.235, 0.328, 1.672, 0.817, 0.406, 1.594, 3.407, 0.9810], 15: [0.223, 0.347, 1.653, 0.789, 0.428, 1.572, 3.472, 0.9823], 16: [0.212, 0.363, 1.637, 0.763, 0.448, 1.552, 3.532, 0.9835], 17: [0.203, 0.378, 1.622, 0.739, 0.466, 1.534, 3.588, 0.9845], 18: [0.194, 0.391, 1.608, 0.718, 0.482, 1.518, 3.640, 0.9854], 19: [0.187, 0.403, 1.597, 0.698, 0.497, 1.503, 3.689, 0.9862], 20: [0.180, 0.415, 1.585, 0.680, 0.510, 1.490, 3.735, 0.9869], 21: [0.173, 0.425, 1.575, 0.663, 0.523, 1.477, 3.778, 0.9876], 22: [0.167, 0.434, 1.566, 0.647, 0.534, 1.466, 3.819, 0.9882], 23: [0.162, 0.443, 1.557, 0.633, 0.545, 1.455, 3.858, 0.9887], 24: [0.157, 0.451, 1.548, 0.619, 0.555, 1.445, 3.895, 0.9892], 25: [0.153, 0.459, 1.541, 0.606, 0.565, 1.435, 3.931, 0.9896] };
function staToggleInputs() { const type = document.getElementById('sta-chart-type').value; document.getElementById('sta-rbar-group').style.display = (type === 'xbar-r') ? '' : 'none'; document.getElementById('sta-sbar-group').style.display = (type === 'xbar-s') ? '' : 'none'; document.getElementById('sta-result').innerHTML = '...'; }
function staFmt(v, d=4) { return (Math.abs(v) Please fill in all required fields.'; return; } const xbar = parseFloat(xbarVal); const n = parseInt(nVal, 10);
if (isNaN(xbar)) { res.innerHTML = 'Grand Mean must be a valid number.'; return; } if (isNaN(n) || n 25) { res.innerHTML = 'Subgroup size (n) must be an integer between 2 and 25.'; return; }
const C = STA_CONSTANTS[n]; if (!C) { res.innerHTML = 'No constants available for n = ' + n + '.'; return; }
let html = '';
if (type === 'xbar-r') { if (n > 10) { res.innerHTML = 'X-bar & R chart is recommended for n ≤ 10. Use X-bar & S chart for larger subgroups.'; return; } const rbarVal = document.getElementById('sta-rbar').value.trim(); if (rbarVal === '') { res.innerHTML = 'Please enter the Average Range (R̄).'; return; } const rbar = parseFloat(rbarVal); if (isNaN(rbar) || rbar Average Range (R̄) must be a non-negative number.'; return; }
const [A2, D3, D4] = [C[0], C[1], C[2]];
// X-bar chart limits const xbar_UCL = xbar + A2 * rbar; const xbar_LCL = xbar - A2 * rbar;
// R chart limits const R_UCL = D4 * rbar; const R_LCL = D3 * rbar;
// Process std dev estimate const d2 = C[6]; const sigma_est = rbar / d2;
html = ` ### X-bar & R Chart Results (n = ${n})
ChartStatisticValue
X-bar ChartUCL (X̄ + A₂R̄)${staFmt(xbar_UCL)} Center Line (X̄̄)${staFmt(xbar)} LCL (X̄ − A₂R̄)${staFmt(xbar_LCL)} R ChartUCL (D₄R̄)${staFmt(R_UCL)} Center Line (R̄)${staFmt(rbar)} LCL (D₃R̄)${staFmt(R_LCL)} Process Std Dev Estimate (σ̂ = R̄/d₂)${staFmt(sigma_est)} Constants used: A₂=${A2}, D₃=${D3}, D₄=${D4}, d₂=${C[6]}
Note: LCL for R chart is 0 when D₃ = 0 (n < 7), meaning the range cannot be negative.
`;
} else { // X-bar & S chart const sbarVal = document.getElementById('sta-sbar').value.trim(); if (sbarVal === '') { res.innerHTML = 'Please enter the Average Std Dev (S̄).'; return; } const sbar = parseFloat(sbarVal); if (isNaN(sbar) || sbar Average Std Dev (S̄) must be a non-negative number.'; return; }
const [A3, B3, B4] = [C[4], C[5], C[6]]; // Note: index mapping for S-chart constants const A3v = C[4]; const B3v = C[5]; const B4v = C[6]; // Correct index: [A2,D3,D4,A3,B3,B4,d2,c4] => indices 3,4,5 const A3c = C[3]; const B3c = C[4]; const B4c = C[5]; const c4 = C[7];
// X-bar chart limits const xbar_UCL = xbar + A3c * sbar; const xbar_LCL = xbar - A3c * sbar;
// S chart limits const S_UCL = B4c * sbar; const S_LCL = B3c * sbar;
// Process std dev estimate const sigma_est = sbar / c4;
html = ` ### X-bar & S Chart Results (n = ${n})
ChartStatisticValue
X-bar ChartUCL (X̄ + A₃S̄)${staFmt(xbar_UCL)} Center Line (X̄̄)${staFmt(xbar)} LCL (X̄ − A₃S̄)${staFmt(xbar_LCL)} S ChartUCL (B₄S̄)${staFmt(S_UCL)} Center Line (S̄)${staFmt(sbar)} LCL (B₃S̄)${staFmt(S_LCL)} Process Std Dev Estimate (σ̂ = S̄/c₄)${staFmt(sigma_est)} Constants used: A₃=${A3c}, B₃=${B3c}, B₄=${B4c}, c₄=${c4}
Note: LCL for S chart is 0 when B₃ = 0 (n ≤ 5).
`; }
res.innerHTML = html; }
.calc-table { width:100%; border-collapse:collapse; margin-top:1rem; } .calc-table th, .calc-table td { border:1px solid #ddd; padding:8px 12px; text-align:left; } .calc-table thead { background:#f0f4f8; } .calc-table tbody tr:nth-child(even) { background:#fafafa; }
#### Formulas
X-bar & R Chart:
X-bar & S Chart:
Where A₂, D₃, D₄, d₂ (R-chart) and A₃, B₃, B₄, c₄ (S-chart) are standard unbiasing constants that depend solely on subgroup size n, derived from the distribution of the range and standard deviation of normal samples.
#### Assumptions & References
- References: Montgomery, D.C. (2020). Introduction to Statistical Quality Control, 8th Ed. Wiley. | AIAG (2005). Statistical Process Control Reference Manual, 2nd Ed.
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