1. Method Name

Process Capability Analysis

2. Alternative Names

Capability Analysis, Capability Indices (Cp, Cpk, Pp, Ppk)

3. Brief Description

Capability analysis is a set of statistical tools that measure the extent to which a process is capable of producing output within the specification limits defined by the customer. It compares the “voice of the process” (its natural variability) with the “voice of the customer” (the required tolerances).

4. Purpose / When to Use

It is used to quantitatively evaluate process performance after the process has been stabilized (is under statistical control). It helps answer the questions: “Are we able to meet customer requirements?”, “How many defects does our process produce?”, “Do we need to improve our process, or is it good enough?”

5. Procedure / How to Apply It

1. Verify process stability: Before performing a capability analysis, make sure the process is stable (use control charts). It is pointless to analyze the capability of an unstable process.
2. Collect data: Collect a sufficient amount of data from a stable process.
3. Know the specifications: Obtain the upper specification limit (USL) and lower specification limit (LSL) from the customer.
4. Calculate the capability indices:
- Cp (Potential Capability): Measures how many times the process variation “fits” within the tolerance range. It does not take into account whether the process is centered. Cp = (USL - LSL) / 6σ<br> - Cpk (Actual Capability): This is a “weighted” version of Cp. It also takes into account the process’s centering relative to the center of the tolerance band. It is always less than or equal to Cp. Cpk = min[ (USL - μ) / 3σ; (μ - LSL) / 3σ ]<br> (Where μ is the process mean and σ is its standard deviation).<br>5. Interpret the results
:- Cpk > 1.33: The process is considered capable (the standard in many industries).
- 1.0 < Cpk < 1.33: The process is barely capable but requires attention
.- Cpk < 1.0: The process is not capable; it produces defects
.- Cpk ≈ Cp: The process is well-centered
.- Cpk << Cp: The process is significantly off-center from the tolerance field.

6. A Real-World Example

An automotive supplier manufactures pistons with a required diameter of 90 mm and a tolerance of ±0.03 mm (LSL = 89.97, USL = 90.03). After stabilizing the turning process, they collected data and calculated: Process mean (μ) = 90.01 mm, Standard deviation (σ) = 0.005 mm.
- Cp = (90.03 - 89.97) / (6 * 0.005) = 0.06 / 0.03 = 2.0 (Potentially highly capable process).
— Cpk = min[ (90.03 - 90.01) / (3 * 0.005); (90.01 - 89.97) / (3 * 0.005) ] = min[ 0.02/0.015; 0.04/0.015 ] = min[ 1.33; 2.66 ] = 1.33.
Conclusion: The process is capable (Cpk = 1.33), but it is slightly off-center (Cp is significantly higher). Centering the process would further improve its capability.

7. Benefits

- Objective evaluation: Provides a clear, numerical representation of a process’s capability
.- Common language: Enables communication about process performance with customers and suppliers using standardized metrics.
- Performance prediction: Helps estimate the defect rate (PPM—Parts Per Million) without the need for 100% inspection.
- Decision support: Helps determine whether to invest in process improvement or whether the current state is sufficient.

8. Risks / Limits

- Requires process stability: The biggest mistake is to calculate Cpk for an unstable process. The result is then worthless
.- Normal distribution of data: Classical Cp/Cpk indices assume that the data follow a normal (bell-shaped) distribution. If this is not the case, other methods must be used
.- Sufficient amount of data: A sufficient amount of data is required for a reliable calculation
.- Short-term vs. Long-term (Cpk vs. Ppk): Cpk measures short-term capability (within subgroups). Ppk (Performance Index) measures long-term actual performance, which also includes variability between subgroups.

9. Practical Tips

- Supplement the data with a histogram: Always display a histogram of the data along with the specification limits and the process mean. This provides a much better picture than the Cpk number alone
.- The goal is Six Sigma: A Cpk of 2.0 corresponds to the Six Sigma quality level (3.4 defects per million opportunities). A Cpk of 1.33 corresponds approximately to the 4 Sigma level.
- Improving Cpk: If Cpk is low, you have two options: 1) If Cpk << Cp, center the process. 2) If Cpk ≈ Cp, you must reduce the variability (variance) of the process.