How To Calculate Cpk And Ppk

Process Capability Formulas:

\[ Cpk = \min\left( \frac{USL - \mu}{3\sigma_{short}}, \frac{\mu - LSL}{3\sigma_{short}} \right) \] \[ Ppk = \min\left( \frac{USL - \mu}{3\sigma_{long}}, \frac{\mu - LSL}{3\sigma_{long}} \right) \]

Upper Specification Limit (USL):

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Lower Specification Limit (LSL):

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Process Mean (μ):

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Short-term Standard Deviation (σ_short):

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Long-term Standard Deviation (σ_long):

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Process Capability Index (Cpk):

Process Performance Index (Ppk):

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1. What Are Cpk And Ppk?

Cpk (Process Capability Index) and Ppk (Process Performance Index) are statistical measures that quantify how well a process meets specification limits. Cpk measures short-term capability while Ppk measures long-term performance of a process.

2. How Does The Calculator Work?

The calculator uses the following formulas:

\[ Cpk = \min\left( \frac{USL - \mu}{3\sigma_{short}}, \frac{\mu - LSL}{3\sigma_{short}} \right) \] \[ Ppk = \min\left( \frac{USL - \mu}{3\sigma_{long}}, \frac{\mu - LSL}{3\sigma_{long}} \right) \]

Where:

\( USL \) — Upper Specification Limit
\( LSL \) — Lower Specification Limit
\( \mu \) — Process Mean
\( \sigma_{short} \) — Short-term Standard Deviation
\( \sigma_{long} \) — Long-term Standard Deviation

Explanation: These indices measure how centered the process is within the specification limits and how much variation exists in the process.

3. Importance Of Process Capability Analysis

Details: Process capability analysis is crucial for quality control, identifying process improvements, reducing variation, and ensuring products meet customer requirements. Higher Cpk/Ppk values indicate better process capability.

4. Using The Calculator

Tips: Enter all specification limits, process mean, and standard deviation values. Ensure standard deviation values are positive and the process mean falls between the specification limits for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between Cpk and Ppk?
A: Cpk measures short-term capability using within-subgroup variation, while Ppk measures long-term performance using overall variation including between-subgroup variation.

Q2: What are acceptable Cpk/Ppk values?
A: Generally, values ≥1.33 indicate capable processes, ≥1.67 indicate good capability, and ≥2.0 indicate excellent capability.

Q3: When should I use Cpk vs Ppk?
A: Use Cpk for stable processes with only common cause variation. Use Ppk for new processes or when both common and special cause variation are present.

Q4: Can Cpk/Ppk be negative?
A: Yes, negative values indicate the process mean is outside the specification limits.

Q5: What if my process has only one specification limit?
A: For one-sided specifications, use the appropriate formula (either upper or lower calculation) instead of taking the minimum.