Capability Index Calculator – Cp, Cpk, Cpm, Pp & Ppk

Free online process capability tool for Six Sigma and SPC. Compute short‑term (Cp, Cpk, Cpm) and long‑term (Pp, Ppk) indices, run normality tests, generate histograms, I‑charts, and Q‑Q plots. Instant results with confidence intervals and export to JSON or PDF.

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Select a .json file saved from this tool to restore your data and results.

What is Process Capability? Understanding Cp, Cpk, and SPC

Process Capability analysis is a fundamental tool in Statistical Process Control (SPC) used to measure the ability of a process to produce output within specification limits (LSL and USL). It helps determine if a process is capable of consistently meeting customer requirements.

This analysis uses key indices:

  • Cp (Process Capability): Measures the potential capability of the process. It compares the total specification width (USL - LSL) to the natural process variation (6-sigma), but it does not account for centering. It answers: "Is the process spread narrow enough?"
  • Cpk (Process Capability Index): Measures the actual capability of the process. It accounts for both spread and centering by comparing the process mean to the nearest specification limit. It answers: "Is the process spread narrow enough AND is it running near the target?"

Generally, a Cpk value of 1.33 or higher is considered capable for many industries, though this requirement can vary.

Brief History of Statistical Process Control (SPC)

The concept of process control is rooted in the work of Walter A. Shewhart at Bell Labs in the 1920s. He developed control charts to distinguish between "common cause" variation (the natural, inherent variability of a process) and "special cause" variation (external, unpredictable events). This was the birth of Statistical Process Control (SPC).

How to Use the Capability Index Calculator

  1. Enter Process Data and Specifications: Add one or more datasets using the "Add Dataset" button. Fill in measurements for each dataset, along with the common Lower (LSL), Upper (USL), and Target values.
  2. Select Calculation Method: Choose the method for calculating σ within (short-term standard deviation). For multiple datasets (subgroups), use R-bar (recommended) or S-bar to align with JASP and other statistical software.
  3. Calculate Results: Press the Analyze button. The tool will compute short-term indices (Cp, Cpk, Cpm) for each dataset, overall long-term indices (Pp, Ppk) combining all datasets, perform normality tests, and display process distribution plots and Individuals Control Charts.
  4. Review Results: Analyze both the individual dataset results and the overall performance. Switch between datasets using the tabs to see detailed results for each one.
  5. Add or Remove Datasets (Optional): Use the "Add Dataset" button to include more data or the "Remove" button next to each dataset to delete it.
  6. Save or Export Your Analysis: Click Save to download a JSON file with your data, or Export PDF to generate a formatted visual report of all datasets.

Data Input

Measurements (Dataset #1)

Short‑Term Capability Results

Mean: -

Std Dev (short-term): -

Cp: -

95% CI: -

Cpk: -

95% CI: -

Cpm: -

95% CI: -

Expected Failures: - ppm

Defective Parts: -%

Normality Tests

Shapiro-Wilk: -

Kolmogorov-Smirnov: -

Anderson-Darling: -

Overall Performance

Total Points: 1

Overall Mean: -

Process Performance (Total - Long Term)

σ total (long-term): -

Pp: -

95% CI: -

Ppk: -

95% CI: -

Short-Term Variation

σ within (short-term): -

Method: -

Expected Failures: - ppm

Defective Parts: -%

Overall Normality Tests

Shapiro-Wilk: -

Kolmogorov-Smirnov: -

Anderson-Darling: -

Capability Index Formulas: Cp, Cpk, Pp, Ppk & Sigma Calculations

Sigma Within (R-bar method)

$$ \sigma_{\text{within}} = \frac{\overline{R}}{d_2} $$

Where $d_2$ depends on subgroup size $n$

Sigma Within (Moving Range)

$$ \sigma_{\text{within}} = \frac{\overline{MR}}{d_2} $$

Where $d_2 = 1.128$ for $n=2$

Cp (Capability)

$$ C_p = \frac{USL - LSL}{6\sigma_{\text{within}}} $$

Cpk (Centering)

$$ C_{pk} = \min\left( \frac{USL - \mu}{3\sigma_{\text{within}}}, \frac{\mu - LSL}{3\sigma_{\text{within}}} \right) $$

Cpm (Targeting)

$$ C_{pm} = \frac{USL - LSL}{6\sqrt{\sigma_{\text{within}}^2 + (\mu - T)^2}} $$

Pp (Performance)

$$ P_p = \frac{USL - LSL}{6\sigma_{\text{total}}} $$

Ppk (Centering)

$$ P_{pk} = \min\left( \frac{USL - \mu}{3\sigma_{\text{total}}}, \frac{\mu - LSL}{3\sigma_{\text{total}}} \right) $$

Confidence Interval for Cp (Chi-square)

$$ CI_{Cp} = C_p \sqrt{\frac{\chi^2_{\alpha/2, n-1}}{n-1}}, C_p \sqrt{\frac{\chi^2_{1-\alpha/2, n-1}}{n-1}} $$

Confidence Interval for Cpk (Improved)

$$ CI_{Cpk} = C_{pk} \pm Z_{\alpha/2} \sqrt{\frac{1}{9n} + \frac{C_{pk}^2}{2(n-1)}} $$

Capability Legend

  • Cp, Cpk, Cpm: Process Capability indices (short-term, within-subgroup variation)
  • Pp, Ppk: Process Performance indices (long-term, total variation)
  • LSL, USL: Lower and Upper Specification Limits
  • T: Target value
  • μ: Process mean
  • σwithin: Short-term standard deviation (within-subgroup variation)
  • σtotal: Long-term standard deviation (overall/total variation)
  • CI: Confidence Interval (95% by default)

Automatic Method Selection

  • For individual datasets: Uses Moving Range (MR/d₂) with length 2
  • For multiple datasets (subgroups): Automatically selects:
       - R-bar (R̄/d₂) if all subgroups have equal size ≤ 10
       - Pooled SD with c₄ correction otherwise