Process Capability (Cp & Cpk) Calculator

Central Tendency and Dispersion Measures

Enter your process parameters and specification limits below to calculate the key process capability indices, Cp and Cpk.

Practical Examples

Click on an example to load its data into the calculator.

Example 1: Capable & Centered Process

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A well-controlled process where the mean is perfectly centered between the specification limits and variation is low. Cpk is high and equal to Cp.

USL: 110, LSL: 90

Mean: 100, StdDev: 2

Example 2: Capable but Off-Center Process

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The process variation is acceptable (high Cp), but the mean has shifted towards one of the limits, reducing the Cpk.

USL: 110, LSL: 90

Mean: 105, StdDev: 2

Example 3: Incapable Process (High Variation)

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The process is centered, but the variation is too high, causing it to produce parts outside both specification limits. Both Cp and Cpk are low.

USL: 110, LSL: 90

Mean: 100, StdDev: 5

Example 4: One-Sided Specification

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A scenario where only an upper specification limit is relevant. Cpk calculation will only consider the relevant limit.

USL: 5.0, LSL:

Mean: 3.8, StdDev: 0.3

Other Titles
Understanding the Process Capability Index (Cp & Cpk): A Comprehensive Guide
An in-depth look into how Cp and Cpk are used to measure and improve process quality in statistical process control (SPC).

What is the Process Capability Index?

  • Defining Process Capability
  • The Difference Between Cp and Cpk
  • Why These Indices Matter
Process Capability is a statistical measure of a process's ability to produce output within specified limits. It quantifies how well a process can meet customer requirements. The main indices used are Cp (Process Capability) and Cpk (Process Capability Index), which provide a simple, standardized way to assess performance.
Cp: The Potential Capability
The Cp index measures the potential capability of a process, assuming it is perfectly centered between the specification limits. It compares the tolerance width (the distance between the Upper and Lower Specification Limits) to the process's natural variation (typically 6 standard deviations). A Cp greater than 1.0 indicates the process variation is smaller than the specification width.
Cpk: The Actual Capability
The Cpk index measures the actual capability of a process by accounting for its centering. It considers the distance from the process mean to the nearest specification limit. Therefore, Cpk gives a more realistic picture of performance. If a process is not centered, Cpk will be lower than Cp.
Key Takeaway
Use Cp to understand what your process could do if perfectly centered. Use Cpk to understand what your process is currently doing, including any shifts in the average.

Common Benchmarks

  • Cpk < 1.0: Process is not capable.
  • 1.0 ≤ Cpk < 1.33: Process is marginally capable.
  • Cpk ≥ 1.33: Process is capable (common target).
  • Cpk ≥ 1.67: Process has Six Sigma level capability (excellent).

Step-by-Step Guide to Using the Calculator

  • Gathering Your Data
  • Entering Values into the Tool
  • Interpreting the Results
This calculator simplifies the Cp and Cpk calculation. Follow these steps to get your results.
Step 1: Define Specification Limits
Identify your Upper Specification Limit (USL) and Lower Specification Limit (LSL). These are the engineering requirements or customer expectations for the process output.
Step 2: Determine Process Parameters
You need the process mean (μ) and process standard deviation (σ). These should be calculated from a stable process using data collected over time. The mean represents the average, and the standard deviation represents the consistency of the process.
Step 3: Input the Values
Enter the USL, LSL, Process Mean, and Process Standard Deviation into the designated fields in the calculator. Ensure that USL is greater than LSL and the standard deviation is a positive number.
Step 4: Analyze the Output
Click 'Calculate' to see the Cp, Cpk, and other metrics. The interpretation will tell you if the process is considered capable and how centered it is.

Input Tips

  • Ensure your process is in a state of statistical control before using this analysis.
  • Use a sufficient amount of data to get a reliable estimate of the mean and standard deviation.
  • If you only have one specification limit (e.g., strength must be *above* a minimum value), you can leave the other field blank.

Real-World Applications of Process Capability

  • Manufacturing and Production
  • Healthcare Services
  • Software Development
Process capability analysis is a cornerstone of quality improvement across many industries.
Manufacturing
The most common application. A car manufacturer might use Cpk to ensure the diameter of a piston is consistently within engineering tolerances. This reduces engine failures and warranty claims.
Healthcare
Hospitals can use capability analysis to monitor and improve processes like patient wait times. The LSL could be zero minutes, and the USL could be a target like 15 minutes. A high Cpk would mean patients are consistently seen quickly.
Finance and Banking
In a bank, the time it takes to approve a loan can be analyzed. Specification limits can be set by service level agreements (SLAs), and Cpk can track how consistently the bank meets these targets.

Common Misconceptions and Correct Methods

  • Cp vs. Pp and Cpk vs. Ppk
  • The Assumption of Normality
  • Capability of a Single Measurement
Misconception 1: Cp is always the best measure.
Reality: Cpk is often more useful for day-to-day management because it reflects the current state of the process, including its centering. A high Cp is meaningless if the process mean is about to drift outside a specification limit.
Misconception 2: Cp/Cpk can be calculated from any data.
Reality: The process must be stable and in statistical control. If the process is unpredictable (e.g., has special causes of variation), the capability indices are not meaningful. Furthermore, the data is assumed to be normally distributed. If the data is heavily skewed, transformations or different indices may be needed.
Cp vs. Pp (Process Performance)
Cp and Cpk use the 'within-subgroup' standard deviation, which reflects the short-term, potential variation. Pp and Ppk use the overall standard deviation, which includes both short-term and long-term variation (like shifts between subgroups). This calculator focuses on Cp/Cpk, which measures capability, not overall performance.

Mathematical Derivation and Formulas

  • The Formula for Cp
  • The Formula for Cpk
  • Z-Score and PPM Calculation
Here are the formulas used by the calculator to determine the process capability indices.
Process Capability (Cp)
The formula for Cp is the ratio of the specification width to the process width.
Formula: Cp = (USL - LSL) / (6 * σ)
Where USL is the Upper Specification Limit, LSL is the Lower Specification Limit, and σ is the process standard deviation.
Process Capability Index (Cpk)
Cpk is calculated as the lesser of two values: Cpu (capability relative to the upper limit) and Cpl (capability relative to the lower limit).
Formula: Cpk = min( (USL - μ) / (3 σ), (μ - LSL) / (3 σ) )
Where μ is the process mean.
Z-Score and Parts Per Million (PPM)
The Z-score represents how many standard deviations a point is from the mean. From the Z-score, we can estimate the proportion of the process that falls outside the specification limits, often expressed as PPM (defective Parts Per Million).
Formula: Z_USL = (USL - μ) / σ
Formula: Z_LSL = (LSL - μ) / σ