Capability Index Calculator

Calculate short-term (Cp, Cpk, Cpm) and long-term (Pp, Ppk) capability indices. Includes normality tests, histograms, and control charts.

How to Use This Tool

  1. Enter Process Data and Specifications: Fill in the measurements from your process, along with the Lower (LSL), Upper (USL), and Target values.
  2. Calculate Short-Term Results: Press the Calculate button. The tool will compute short-term indices (Cp, Cpk, Cpm), perform normality tests, and display a process histogram and an Individuals Control Chart.
  3. Review and Aggregate: Analyze the short-term results. If you wish to include this data in a long-term study, click Add to List. The result will be saved in the "Aggregated Results" table.
  4. Add More Data (Optional): To analyze another dataset, click the New Data button. This will scroll you back to the top and clear the form for the next entry. Repeat steps 1-3.
  5. Calculate Long-Term Performance: Once you have added at least two datasets to the list, the Calculate Overall Performance button will appear. Click it to compute long-term indices (Pp, Ppk) based on all aggregated data and generate the corresponding long-term graphs.
  6. Export Your Analysis: Click Export to Excel at any time to download a spreadsheet containing all individual calculations and the overall performance summary.
Data Input
Aggregated Results for Long-Term Analysis

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).

Mathematical Formulas

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)

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

Ppk (Centering)

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

Capability Legend

  • Cp, Pp: Process Capability/Performance. Measures spread relative to tolerance.
  • Cpk, Ppk: Process Capability/Performance Index. Measures spread and centering.
  • Cpm: Third-generation capability index. Accounts for deviation from the target.
  • USL, LSL: Upper and Lower Specification Limits (the "voice of the customer").
  • T: Target value of the process.
  • µ: Process Mean (Average).
  • σ_within: Short-term ("within-subgroup") standard deviation.
  • σ_overall: Long-term ("overall") standard deviation.

Normality Test Formulas

Shapiro-Wilk

$$ W = \frac{\left( \sum_{i=1}^{n} a_i x_{(i)} \right)^2}{\sum_{i=1}^{n} (x_i - \mu)^2} $$

Kolmogorov-Smirnov

$$ D = \sup_x |F_n(x) - F(x)| $$

Anderson-Darling

$$ A^2 = -n - \frac{S}{n} $$

Normality Legend

  • W, D, A²: Test statistics for Shapiro-Wilk, Kolmogorov-Smirnov, and Anderson-Darling.
  • x(i): The i-th ordered data point.
  • a_i: Coefficients for the Shapiro-Wilk test.
  • n: Sample size.
  • sup |...|: The supremum of the set of distances (greatest difference).
  • Fn(x): The empirical distribution function.
  • F(x): The cumulative distribution function of the standard normal distribution.
  • S: Summation term specific to the Anderson-Darling test.
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