Process Capability (Cpk) Calculator
ANA›Life Services Authority›National Calculator Authority›Process Capability (Cpk) Calculator
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Process Capability (Cpk) Calculator
Calculate process capability indices (Cp and Cpk) to determine how well your process fits within specification limits.
Process Mean (μ)
Process Standard Deviation (σ)
Upper Specification Limit (USL)
Lower Specification Limit (LSL)
Calculate Results will appear here.
function proCalc() { const mean = parseFloat(document.getElementById('pro-mean').value); const std = parseFloat(document.getElementById('pro-std').value); const usl = parseFloat(document.getElementById('pro-usl').value); const lsl = parseFloat(document.getElementById('pro-lsl').value); const res = document.getElementById('pro-result');
// --- Validation --- if (isNaN(mean) || isNaN(std) || isNaN(usl) || isNaN(lsl)) { res.innerHTML = '⚠ Please fill in all four fields.'; return; } if (std ⚠ Standard deviation must be greater than zero.'; return; } if (usl ⚠ USL must be greater than LSL.'; return; }
// --- Core Formulas --- // Cp = (USL - LSL) / (6σ) const cp = (usl - lsl) / (6 * std);
// Cpu = (USL - μ) / (3σ) const cpu = (usl - mean) / (3 * std);
// Cpl = (μ - LSL) / (3σ) const cpl = (mean - lsl) / (3 * std);
// Cpk = min(Cpu, Cpl) const cpk = Math.min(cpu, cpl);
// Process centering offset k = |μ - midpoint| / ((USL - LSL) / 2) const midpoint = (usl + lsl) / 2; const k = Math.abs(mean - midpoint) / ((usl - lsl) / 2);
// Estimated % out-of-spec (approximation via normal CDF) function normCDF(z) { const t = 1 / (1 + 0.2316419 * Math.abs(z)); const d = 0.3989423 * Math.exp(-z * z / 2); const p = d * t * (0.3193815 + t * (-0.3565638 + t * (1.7814779 + t * (-1.8212560 + t * 1.3302744)))); return z >= 0 ? 1 - p : p; } const zUpper = (usl - mean) / std; const zLower = (mean - lsl) / std; const pctOut = (normCDF(-zLower) + (1 - normCDF(zUpper))) * 100; const ppm = pctOut * 10000; // parts per million
// --- Capability Rating --- function rating(val) { if (val >= 1.67) return { label: 'Excellent', color: '#27ae60' }; if (val >= 1.33) return { label: 'Capable', color: '#2980b9' }; if (val >= 1.00) return { label: 'Marginal', color: '#f39c12' }; return { label: 'Incapable', color: '#c0392b' }; } const cpkRating = rating(cpk); const cpRating = rating(cp);
res.innerHTML = `
Index Value Rating
Cp (Potential Capability) ${cp.toFixed(4)}
${cpRating.label}
Cpk (Actual Capability) ${cpk.toFixed(4)}
${cpkRating.label}
Cpu (Upper) ${cpu.toFixed(4)} —
Cpl (Lower) ${cpl.toFixed(4)} —
Centering Factor (k) ${k.toFixed(4)} —
Est. % Out-of-Spec ${pctOut.toFixed(4)}% —
Est. PPM Defective ${ppm.toFixed(1)} —
Midpoint of spec: ${midpoint.toFixed(4)} | Spec width (USL−LSL): ${(usl - lsl).toFixed(4)} | 6σ spread: ${(6 * std).toFixed(4)}
`; }
#### Formulas Used
Cp (Potential / Process Spread Capability):
Cp = (USL − LSL) / (6σ)
Measures whether the process spread fits within the specification width, ignoring centering.
Cpu (Upper Capability Index):
Cpu = (USL − μ) / (3σ)
Cpl (Lower Capability Index):
Cpl = (μ − LSL) / (3σ)
Cpk (Actual / Centered Capability):
Cpk = min(Cpu, Cpl)
Accounts for both spread and centering. Always ≤ Cp.
Centering Factor k:
k = |μ − midpoint| / ((USL − LSL) / 2)
Relationship: Cpk = Cp × (1 − k)
Capability Benchmarks:
Cpk Value Rating Sigma Level
≥ 1.67Excellent (Six Sigma)5σ+ ≥ 1.33Capable4σ ≥ 1.00Marginal3σ < 1.00Incapable<3σ
#### Assumptions & References
- The process output is assumed to follow a normal (Gaussian) distribution.
- The process must be in statistical control (stable over time) for Cpk to be meaningful.
- σ should be the within-subgroup standard deviation (short-term) for true capability; using overall σ gives a performance index (Ppk).
- Industry standard: Cpk ≥ 1.33 is the minimum acceptable for most manufacturing processes; Cpk ≥ 1.67 for safety-critical parts.
- References: Montgomery, D.C. Introduction to Statistical Quality Control, 7th ed.; AIAG SPC Manual, 2nd ed.
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