Capability Index Calculator

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

How to Use This Tool

  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. Calculate Results: Press the Calculate 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.
  3. 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.
  4. 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.
  5. Export Your Analysis: Click Export to Excel to download a spreadsheet containing all individual calculations and the overall performance summary.
Data Input
Measurements (Dataset #1)
Overall Performance (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.