Process Capability Ratio Calculator

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Process Capability Ratio (Cp & Cpk) Calculator

Analyze how well your process meets specification limits.

Cp (Process Capability): –
Cpk (Capability Index): –
CPL (Lower Capability): –
CPU (Upper Capability): –

Understanding Process Capability Indices

Process capability analysis is a statistical tool used to evaluate the ability of a manufacturing process to produce parts within specified limits. It bridges the gap between statistical process control and engineering specifications.

What is Cp?

Cp is the Potential Process Capability. It measures the width of your process spread (6 standard deviations) against the width of the specification limits (USL – LSL). It does not take into account how well the process is centered; it only tells you if the process is "thin" enough to fit within the specifications.

Formula: Cp = (USL – LSL) / (6 * σ)

What is Cpk?

Cpk is the Actual Process Capability Index. It accounts for the centering of the process mean within the specification limits. If the process is perfectly centered, Cp will equal Cpk. If the process drifts toward one of the limits, Cpk will be lower than Cp.

Formula: Cpk = min[(USL – μ) / (3 * σ), (μ – LSL) / (3 * σ)]

Interpreting the Results

  • Cp/Cpk < 1.0: The process is not capable. It is producing defects.
  • 1.0 ≤ Cp/Cpk < 1.33: The process is marginally capable but requires close monitoring.
  • 1.33 ≤ Cp/Cpk < 1.67: The process is capable and meets most industrial standards.
  • Cp/Cpk ≥ 1.67: The process is highly capable (Six Sigma quality level begins around 2.0).

A Practical Example

Imagine you are manufacturing steel rods that must be between 9.95mm (LSL) and 10.05mm (USL). Your measurement data shows a mean of 10.01mm and a standard deviation of 0.01mm.

  • Cp: (10.05 – 9.95) / (6 * 0.01) = 0.1 / 0.06 = 1.67
  • Cpk: min[(10.05 – 10.01)/0.03, (10.01 – 9.95)/0.03] = min[1.33, 2.0] = 1.33

In this case, while the process spread is narrow enough for a high Cp, the slight offset of the mean (10.01 vs 10.00) reduces the Cpk, indicating the process is capable but could be improved by centering the mean.

function calculateProcessCapability() { var usl = parseFloat(document.getElementById('cp_usl').value); var lsl = parseFloat(document.getElementById('cp_lsl').value); var mean = parseFloat(document.getElementById('cp_mean').value); var std = parseFloat(document.getElementById('cp_std').value); if (isNaN(usl) || isNaN(lsl) || isNaN(mean) || isNaN(std)) { alert("Please enter valid numeric values for all fields."); return; } if (usl <= lsl) { alert("Upper Specification Limit must be greater than Lower Specification Limit."); return; } if (std = 1.33) { interpretation = "Status: Process is CAPABLE. The Cpk value meets or exceeds the industry standard benchmark of 1.33."; } else if (cpk >= 1.0) { interpretation = "Status: Process is MARGINALLY CAPABLE. The process is meeting specs but has very little room for error (Cpk between 1.0 and 1.33)."; } else { interpretation = "Status: Process is NOT CAPABLE. The process is likely producing out-of-spec parts or is significantly off-center."; } if (cp > cpk + 0.1) { interpretation += " Note: Your Cp is significantly higher than your Cpk, suggesting the process centering could be improved to increase capability."; } document.getElementById('cp_interpretation_text').innerText = interpretation; document.getElementById('cp_results_box').style.display = 'block'; }

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