# Aerospace Key Characteristic Cpk Calculator > Source: https://netray.co/tools/aerospace-key-characteristic-cpk-calculator > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer Enter limits, process mean and within-subgroup standard deviation to get Cp, Cpk, sigma level and expected ppm out of tolerance. ## Category quality ## Industry Aerospace ## Audience - Quality engineer - Manufacturing engineer - Supplier quality ## Tool **Kind:** calculator **Inputs:** #### Upper specification limit **Key:** usl **Type:** number **Default:** 12.018 **Step:** 0.001 **Help:** Upper tolerance limit from the drawing. #### Lower specification limit **Key:** lsl **Type:** number **Default:** 12 **Step:** 0.001 **Help:** Lower tolerance limit from the drawing. #### Process mean **Key:** mean **Type:** number **Default:** 12.0085 **Step:** 0.0005 **Help:** Average of measured values, from at least 30 to 100 consecutive parts. #### Standard deviation (within-subgroup) **Key:** sigma **Type:** number **Default:** 0.0017 **Step:** 0.0001 **Min:** 0 **Help:** Estimated from subgroup ranges or the pooled within-subgroup standard deviation. #### Required Cpk **Key:** target **Type:** select **Default:** 1.33 **Options:** ##### 1.00 **Value:** 1 ##### 1.33 **Value:** 1.33 ##### 1.50 **Value:** 1.5 ##### 1.67 **Value:** 1.67 ##### 2.00 **Value:** 2 **Outputs:** #### Cp (potential capability) **Key:** cp **Expr:** (usl - lsl) / (6 * sigma) **Format:** decimal #### Cpu **Key:** cpu **Expr:** (usl - mean) / (3 * sigma) **Format:** decimal #### Cpl **Key:** cpl **Expr:** (mean - lsl) / (3 * sigma) **Format:** decimal #### Cpk **Key:** cpk **Expr:** min(cpu, cpl) **Format:** decimal **Primary:** true **Description:** The smaller of Cpu and Cpl. Compare it with your required value. #### Gap to required Cpk **Key:** gap **Expr:** cpk - target **Format:** decimal **Description:** Negative means the target is not met. #### Sigma level (Z min) **Key:** zmin **Expr:** 3 * cpk **Format:** decimal #### Expected ppm out of tolerance **Key:** ppm **Expr:** (normsdist(-1 * (usl - mean) / sigma) + normsdist(-1 * (mean - lsl) / sigma)) * 1000000 **Format:** integer **Primary:** true **Description:** Assumes a stable, normally distributed process. #### Expected share within tolerance **Key:** inspec **Expr:** 100 - ppm / 10000 **Format:** percent **Chart:** #### Cpk as the process mean shifts across the tolerance **Type:** line **X:** mean **From:** 12 **To:** 12.018 **Steps:** 36 **Series:** - cpk **Disclaimer:** Assumes a stable process, a normal distribution and a sigma estimated from within-subgroup variation. For non-normal data, short runs or unstable processes, use methods your customer specifies. Required Cpk values vary by customer and by characteristic. ## Content **Intro:** Cpk tells you how well a process fits inside its tolerance, taking both spread and centering into account. Aerospace customers often ask for a minimum Cpk on key characteristics before they will release inspection effort. This calculator gives Cp, Cpk, expected ppm and a chart of how off-center running reduces capability. **Sections:** #### How to use the calculator **Body:** Enter the upper and lower limits from the drawing, the average of your measured values and the within-subgroup standard deviation. Select the Cpk your customer requires. The result shows Cp, Cpk, the gap to the target and the expected ppm out of tolerance. The chart sweeps the mean across the tolerance band to show how fast Cpk falls when the process drifts toward a limit. **Bullets:** - Use at least 30 consecutive parts, ideally 100 or more across normal conditions - Confirm the process is stable on a control chart before calculating capability - Use within-subgroup sigma for Cp and Cpk, overall sigma for Pp and Ppk - Round for reporting only at the end #### The formulas **Body:** Cp equals the tolerance width divided by six sigma. Cpu equals the upper limit minus the mean, divided by three sigma. Cpl equals the mean minus the lower limit, divided by three sigma. Cpk is the smaller of the two. Sigma level equals three times Cpk. Expected ppm adds the normal tail beyond each limit, so a process at 1.33 with perfect centering has roughly 63 ppm outside, and 1.00 has roughly 2,700 ppm. #### Worked example **Body:** A bore with limits 12.000 and 12.018, mean 12.0085 and sigma 0.0017 gives Cp of 1.76. Cpu is 1.86 and Cpl is 1.67, so Cpk is 1.67, which meets a 1.33 requirement and just meets 1.67. The mean sits slightly above center of 12.009, which is why Cpk equals Cpl. If tool wear moved the mean down to 12.004, Cpl falls to 0.78 and the gap to target turns negative. #### Common mistakes **Body:** Frequent errors are using overall standard deviation in place of within-subgroup sigma, calculating capability on an unstable process, applying a normal model to a one-sided characteristic such as flatness or runout, and ignoring measurement error. For one-sided tolerances only Cpu or Cpl applies. Feed the result into your key characteristics worksheet and control plan. **Cta:** If capability studies are built by hand from exported data, we can help calculate them automatically from your ERP or MES inspection results on-prem. **Faq:** #### What is a good Cpk for aerospace? **Answer:** Many customers ask for 1.33 as a minimum and 1.67 for the most critical characteristics, but this is set by contract and AS9103-based procedures rather than by the standard itself. Below the requirement, customers commonly accept interim 100% inspection until capability is demonstrated. #### What is the difference between Cpk and Ppk? **Answer:** Cpk uses within-subgroup variation and describes short-term capability when the process is stable. Ppk uses overall standard deviation across all data and includes shifts and drift. Customers specify which they want. Ppk is often used for initial studies where the process has not yet shown stability. #### How many parts do I need for Cpk? **Answer:** At least 30 is a common minimum, with 100 or more preferred in subgroups collected over time and across tool, material and operator changes. Small samples give wide uncertainty, so a Cpk of 1.4 from 30 parts may be statistically close to 1.2. #### Can I use Cpk for non-normal characteristics? **Answer:** Use caution. Position, flatness and runout are bounded at zero and skewed, so a normal-based Cpk can mislead. Transform the data or use a non-normal capability method, and follow whatever approach your customer accepts. ## Search terms Cpk calculator, process capability calculator, Cp Cpk calculator excel, key characteristic capability, Cpk 1.33 calculator, Cpk to ppm, AS9103 Cpk, Cpk 1.67 aerospace --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json