Process Capability Index (Cpk) Calculator
ANA›Life Services Authority›National Calculator Authority›Process Capability Index (Cpk) Calculator
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Process Capability Index (Cpk) Calculator
Calculate the Process Capability Index (Cpk) to determine how well your process performs relative to specification limits. A Cpk ≥ 1.33 is generally considered capable.
Process Mean (μ)
Process Standard Deviation (σ)
Upper Specification Limit (USL)
Lower Specification Limit (LSL)
Calculate Fill in the fields above and click Calculate.
function proCalc() { const resultEl = document.getElementById('pro-result'); 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);
// --- Validation --- if (isNaN(mean) || isNaN(std) || isNaN(usl) || isNaN(lsl)) { resultEl.innerHTML = '⚠ Please fill in all four fields.'; return; } if (std ⚠ Standard deviation must be greater than zero.'; return; } if (usl ⚠ USL must be strictly greater than LSL.'; return; }
// --- Core Calculations --- const cpu = (usl - mean) / (3 * std); // Upper capability index const cpl = (mean - lsl) / (3 * std); // Lower capability index const cpk = Math.min(cpu, cpl); // Process Capability Index const cp = (usl - lsl) / (6 * std); // Process Capability Ratio (Cp)
// Sigma level approximation const sigmaLevel = cpk * 3;
// Capability rating let rating = '', ratingColor = ''; if (cpk >= 1.67) { rating = 'Excellent (Six Sigma capable)'; ratingColor = '#27ae60'; } else if (cpk >= 1.33) { rating = 'Capable (meets industry standard)'; ratingColor = '#2980b9'; } else if (cpk >= 1.00) { rating = 'Marginally Capable (monitor closely)'; ratingColor = '#f39c12'; } else { rating = 'Not Capable (process improvement needed)'; ratingColor = '#c0392b'; }
// Centering check const centered = Math.abs(cpu - cpl)
Metric Value
Cpk (Process Capability Index) ${cpk.toFixed(4)}
Cp (Process Capability Ratio) ${cp.toFixed(4)}
CPU (Upper Capability Index) ${cpu.toFixed(4)}
CPL (Lower Capability Index) ${cpl.toFixed(4)}
Sigma Level (≈ Cpk × 3) ${sigmaLevel.toFixed(2)}σ
Capability Rating ${rating}
${centered}
`; }
#### Formulas
CPU (Upper Capability Index):
CPU = (USL − μ) / (3σ)
CPL (Lower Capability Index):
CPL = (μ − LSL) / (3σ)
Cpk (Process Capability Index):
Cpk = min(CPU, CPL)
Cp (Process Capability Ratio — assumes centered process):
Cp = (USL − LSL) / (6σ)
Where: μ = process mean, σ = process standard deviation, USL = Upper Specification Limit, LSL = Lower Specification Limit.
#### Assumptions & References
- The process output is assumed to follow a normal (Gaussian) distribution.
- The process is assumed to be in statistical control (stable over time).
- Standard deviation (σ) entered should be the long-term process standard deviation. For short-term capability, use the within-subgroup standard deviation.
- A Cpk ≥ 1.33 (4σ) is the widely accepted minimum for a capable process in most industries.
- A Cpk ≥ 1.67 (5σ) is required in many automotive and aerospace applications.
- References: Montgomery, D.C. (2019). Introduction to Statistical Quality Control, 8th ed. Wiley; AIAG (2010). Statistical Process Control (SPC) Reference Manual, 2nd ed.
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