SPC Statistical Process Control
Process Capability
IATF 16949
About This Article
Cpk (Process Capability Index) and Ppk (Process Performance Index) are core statistical indicators that measure whether process output conforms to specification. This article explains in plain language the definitions, calculation formulas, comparison of differences, and acceptance criteria of the two, and describes the conversion relationship between Cpk and Six Sigma (6 Sigma). To learn more about SPC process control applications, please refer to the MiDFUN SPC Statistical Process Control system.
What Are Cpk and Ppk?
In quality management, simply looking at whether a product is "conforming or not" is not enough; we even more need to know how much capability the process itself has to stably produce conforming products. This is the meaning of the Process Capability Index.
Cpk (Process Capability Index) is the "short-term process capability index." It measures whether, in a stable state, the process output is concentrated within the specification range. It uses within-subgroup variation (Within-subgroup variation), that is, the degree of data spread within the same batch.
Ppk (Process Performance Index) is the "long-term process performance index." It reflects the true performance of the process in the actual production environment. It uses overall variation (Overall variation), covering all sources of variation between batches such as personnel changes, raw material differences, and environmental changes.
Put simply: Cpk looks at "the best state the process is capable of achieving," while Ppk looks at "the level the process actually achieves". Only by using the two together can you fully grasp the quality capability of the process. For the basic concepts of variation and the standard deviation (Sigma), you can refer to the glossary definition page to learn more.
Calculation Formulas for Cpk and Ppk
The calculation logic of Cpk and Ppk is the same; the only difference lies in the standard deviation used.
Cpk Calculation Formula (Short-Term Process Capability)
Cpk = min [ (USL − X̄) ⁄ 3σwithin , (X̄ − LSL) ⁄ 3σwithin ]
σwithin = within-subgroup standard deviation (estimated from R-bar/d2 or S-bar/c4)
Ppk Calculation Formula (Long-Term Process Performance)
Ppk = min [ (USL − X̄) ⁄ 3σoverall , (X̄ − LSL) ⁄ 3σoverall ]
σoverall = overall standard deviation (the sample standard deviation s calculated directly from all data points)
Here, USL (Upper Specification Limit) is the upper specification limit, LSL (Lower Specification Limit) is the lower specification limit, and X̄ is the process mean. The formula takes the smaller of the capabilities on the two sides, reflecting whether the "weakest side" of the process is sufficient.
In the practice of SPC Statistical Process Control, σwithin is usually estimated from the R̄/d2 or S̄/c4 in the control chart, whereas σoverall is the sample standard deviation calculated directly from all measurement data.
Cpk vs Ppk: A Comparison of the Differences
The table below summarizes the key differences between Cpk and Ppk in terms of definition, source of variation, and timing of use:
| Comparison Item | Cpk | Ppk |
|---|---|---|
| Full Name | Process Capability Index | Process Performance Index |
| Time Frame | Short-term | Long-term |
| Source of Variation | Within-subgroup variation (Within) | Overall variation (Overall) |
| Standard Deviation Estimate | σwithin (R̄/d2) | σoverall (sample standard deviation s) |
| Primary Use | Mass-production monitoring, continuous improvement | PPAP sample submission, initial capability assessment |
| IATF 16949 Requirement | Cpk ≥ 1.33 | Ppk ≥ 1.67 |
| Numerical Relationship | Usually Cpk ≥ Ppk (because within-subgroup variation ≤ overall variation) | |
If there is a large gap between the values of Cpk and Ppk, it indicates that there is significant batch-to-batch variation in the process (such as material changes, mold changes, temperature changes, etc.), and the source of variation needs to be analyzed further.
How to Interpret Cpk Values
The higher the Cpk value, the more capable the process is of stably producing products that conform to specification. Below are the acceptance criteria commonly used in the industry:
| Cpk Range | Grade Determination | Description |
|---|---|---|
| < 1.00 | Insufficient Capability | The process spread exceeds the specification range, the nonconformance rate is high, and improvement measures must be initiated immediately. |
| 1.00 ~ 1.33 | Marginally Acceptable | Process capability is on the low side with insufficient margin; a slight variation may produce nonconforming products. Continuous monitoring and improvement are recommended. |
| 1.33 ~ 1.67 | Acceptable | Meets the IATF 16949 mass-production requirement (Cpk ≥ 1.33), with a nonconformance rate of approximately 63 PPM or below. The baseline threshold for most automotive-industry customers. |
| > 1.67 | Excellent | Process capability is sufficient and stable. The PPAP stage requires Ppk ≥ 1.67, indicating that the initial process has ample margin. |
In practice, different industries and customers may have stricter requirements. For example, the aerospace, medical, or semiconductor industries may require Cpk ≥ 1.67 or even 2.0. To understand the latest AIAG-VDA standard requirements for process capability, please refer to An Analysis of SPC in the New VDA Yellow Book.
The Relationship Between Cpk and Six Sigma
There is a direct mathematical conversion relationship between Cpk and Six Sigma (6 Sigma):
Sigma Level = 3 × Cpk
Therefore, Cpk = 2.0 is equivalent to a 6 Sigma level, meaning that the process mean is 6 standard deviations away from the nearest specification limit. Below is a common conversion reference:
| Cpk | Sigma Level | Estimated Nonconformance Rate (PPM) | Process Yield |
|---|---|---|---|
| 1.00 | 3σ | 2,700 | 99.73% |
| 1.33 | 4σ | 63 | 99.9937% |
| 1.67 | 5σ | 0.57 | 99.999943% |
| 2.00 | 6σ | 0.002 | 99.9999998% |
The PPM values above are theoretical values under a two-sided specification. In practice, if the long-term 1.5σ shift (Sigma Shift) is taken into account, the actual nonconformance rate of 6 Sigma is approximately 3.4 PPM. This figure has become the benchmark for global quality excellence.
Frequently Asked Questions (FAQ)
Want to track process Cpk/Ppk in real time?
The MiDFUN SPC system automatically calculates process capability indices and, combined with AIAG-VDA anomaly determination rules, lets quality issues be intercepted before they occur.
Copyright © 2026 MiDFUN Co., Ltd. Some rights reserved
Author: Pei-Chi Chiu. First published: 2026-03-31. Type: Quality Management Column
Original link: https://www.midfun.com.tw/qc/glossary-cpk-ppk-process-capability/
This work is released under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). You are welcome to share it freely, provided that you credit the original author, include the original link, do not use it commercially, and do not modify the content.
Suggested citation format: Chiu, P.-C. (2026). "What Are Cpk and Ppk? Definitions, Formulas, and Acceptance Criteria of Process Capability Indices." MiDFUN Quality Management Column.
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