Capability Ratio Calculator

Process Capability (Cp & Cpk) Calculator

Cp (Potential) –

Cpk (Actual) –

function calculateCapability() { var usl = parseFloat(document.getElementById('inputUSL').value); var lsl = parseFloat(document.getElementById('inputLSL').value); var mean = parseFloat(document.getElementById('inputMean').value); var sigma = parseFloat(document.getElementById('inputSigma').value); var resultArea = document.getElementById('resultArea'); var interpretation = document.getElementById('interpretation'); if (isNaN(usl) || isNaN(lsl) || isNaN(mean) || isNaN(sigma) || sigma <= 0 || usl = 2.0) { status = "Excellent (Six Sigma Quality): Your process is extremely capable and highly robust against shifts."; color = "#2e7d32"; } else if (cpk >= 1.33) { status = "Capable: The process is meeting requirements comfortably. This is often the industry standard for existing processes."; color = "#1a73e8"; } else if (cpk >= 1.0) { status = "Marginally Capable: The process is barely meeting specifications. Any slight shift in the mean will result in defects."; color = "#f9a825"; } else { status = "Incapable: The process is currently producing parts outside of the specification limits. Immediate intervention is required."; color = "#d32f2f"; } var centering = ""; if (Math.abs(cp – cpk) > 0.1) { centering = "Note: There is a significant difference between Cp and Cpk, suggesting the process is not well-centered within the specification limits."; } interpretation.style.borderLeftColor = color; interpretation.innerHTML = status + centering; }

Understanding Process Capability Ratios

In manufacturing and quality engineering, process capability analysis measures how well a process can produce output within specified limits. It is a fundamental tool in the Six Sigma methodology.

What is Cp?

Cp (Process Capability Ratio) measures the "potential" of your process. it compares the total width of the specification (USL – LSL) to the natural spread of the process (6 sigma). It tells you if the process is physically capable of fitting within the limits, assuming it is perfectly centered.

What is Cpk?

Cpk (Process Capability Index) measures the "actual" performance. It accounts for where the process mean is actually located relative to the specification limits. If a process is perfectly centered, Cp will equal Cpk. If Cpk is lower than Cp, the process is off-center.

Standard Benchmarks

• Cp < 1.0: Inadequate. The process spread is wider than the specification.
• Cp = 1.0: Barely capable. 0.27% defect rate expected.
• Cp = 1.33: Industry standard. Highly capable.
• Cp = 2.0: World-class (Six Sigma level).

Calculation Example

Imagine you are manufacturing metal rods.

• USL: 10.10 mm
• LSL: 9.90 mm
• Mean: 10.02 mm
• Standard Deviation: 0.02 mm

Step 1: Calculate Cp
Cp = (10.10 – 9.90) / (6 * 0.02) = 0.20 / 0.12 = 1.667

Step 2: Calculate Cpk
Cpk_Upper = (10.10 – 10.02) / (3 * 0.02) = 0.08 / 0.06 = 1.333
Cpk_Lower = (10.02 – 9.90) / (3 * 0.02) = 0.12 / 0.06 = 2.000
Cpk = Min(1.333, 2.000) = 1.333

The process is capable, but since Cp (1.667) is higher than Cpk (1.333), the process is slightly shifted toward the Upper Specification Limit.