Capability Index Calculator

Process Capability Index (Cp & Cpk) Calculator

Analyze process performance and statistical quality control

Cp (Potential)

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Cpk (Performance)

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function calculateCapability() { var usl = parseFloat(document.getElementById('usl').value); var lsl = parseFloat(document.getElementById('lsl').value); var mean = parseFloat(document.getElementById('mean').value); var sigma = parseFloat(document.getElementById('sigma').value); if (isNaN(usl) || isNaN(lsl) || isNaN(mean) || isNaN(sigma)) { alert("Please enter valid numerical values for all fields."); return; } if (usl <= lsl) { alert("Upper Specification Limit must be greater than Lower Specification Limit."); return; } if (sigma = 1.67) { interpretationBox.innerHTML = "Excellent: Six Sigma Process (World Class)"; container.style.borderLeftColor = "#27ae60"; } else if (cpk >= 1.33) { interpretationBox.innerHTML = "Capable: Good process performance"; container.style.borderLeftColor = "#2980b9"; } else if (cpk >= 1.0) { interpretationBox.innerHTML = "Marginal: Barely capable, requires close monitoring"; container.style.borderLeftColor = "#f39c12"; } else { interpretationBox.innerHTML = "Incapable: Process is producing defects"; container.style.borderLeftColor = "#c0392b"; } }

Understanding Process Capability Index (Cp & Cpk)

The Process Capability Index is a statistical tool used in quality management and Six Sigma to measure how well a manufacturing or business process can produce output within specific limits. It quantifies the relationship between the "Voice of the Customer" (Specification Limits) and the "Voice of the Process" (Standard Deviation and Mean).

Key Definitions

• Cp (Process Capability): This index measures the potential capability of a process. It assumes the process mean is perfectly centered between the specification limits. It only considers the spread (variability) of the process.
• Cpk (Process Capability Index): This is a more realistic measure because it accounts for both the process spread and how well the process mean is centered relative to the specification limits.
• USL & LSL: The Upper and Lower Specification Limits defined by design requirements or customer expectations.
• Sigma (σ): The standard deviation representing the process variability.

The Formulas

The calculations for these indices are as follows:

Cp = (USL – LSL) / (6 × σ)
Cpk = min[ (USL – μ) / (3 × σ) , (μ – LSL) / (3 × σ) ]

Interpretation of Results

Index Value	Interpretation
Cpk < 1.0	Incapable; the process spread is wider than the spec limits or off-center.
1.0 ≤ Cpk < 1.33	Marginally capable; requires constant control and improvement.
1.33 ≤ Cpk < 1.67	Satisfactory; common for most industrial processes.
Cpk ≥ 1.67	Excellent; signifies a highly stable and precise process (Six Sigma level).

Realistic Example

Imagine a factory producing metal rods that must be 100mm long. The customer allows a tolerance of ±2mm, meaning the USL is 102mm and the LSL is 98mm.

If the production line has a Mean of 100.5mm and a Standard Deviation of 0.4mm:

• Cp calculation: (102 – 98) / (6 * 0.4) = 4 / 2.4 = 1.667
• Cpk calculation: Min[(102 – 100.5)/(3*0.4), (100.5 – 98)/(3*0.4)] = Min[1.25, 2.08] = 1.25

In this case, the process has the potential to be excellent (Cp = 1.667), but because the mean is slightly shifted toward the upper limit, the actual performance (Cpk = 1.25) is only "Marginally Capable."