# Sigma Level to DPMO, Yield and Cpk Conversion Table > Source: https://netray.co/tools/sigma-level-dpmo-ppm-cpk-conversion-table > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer Convert between sigma level, defects per million, process yield and Cpk equivalents using the standard 1.5 sigma shift convention and the centered case. ## Category quality ## Audience - Quality engineer - Six Sigma Black Belt - Supplier quality ## Tool **Kind:** worksheet **Mode:** reference **Columns:** #### Basis **Key:** basis **Type:** text #### Sigma level or index **Key:** level **Type:** text #### Defects per million **Key:** ppm **Type:** text #### Yield **Key:** yield **Type:** text #### Note **Key:** note **Type:** text **Rows:** **Basis:** Long-term, 1.5 shift **Level:** 1.0 sigma **Ppm:** 691,462 **Yield:** 30.85% **Note:** Typical of very poor, uncontrolled processes **Basis:** Long-term, 1.5 shift **Level:** 1.5 sigma **Ppm:** 500,000 **Yield:** 50.00% **Note:** Half the output is defective **Basis:** Long-term, 1.5 shift **Level:** 2.0 sigma **Ppm:** 308,538 **Yield:** 69.15% **Note:** Common in unmanaged administrative processes **Basis:** Long-term, 1.5 shift **Level:** 2.5 sigma **Ppm:** 158,655 **Yield:** 84.13% **Note:** Roughly one defect in six **Basis:** Long-term, 1.5 shift **Level:** 3.0 sigma **Ppm:** 66,807 **Yield:** 93.32% **Note:** Short-term Cp equivalent about 1.0 **Basis:** Long-term, 1.5 shift **Level:** 3.5 sigma **Ppm:** 22,750 **Yield:** 97.72% **Note:** Roughly one defect in 44 **Basis:** Long-term, 1.5 shift **Level:** 4.0 sigma **Ppm:** 6,210 **Yield:** 99.379% **Note:** Short-term Cp equivalent about 1.33 **Basis:** Long-term, 1.5 shift **Level:** 4.5 sigma **Ppm:** 1,350 **Yield:** 99.865% **Note:** Typical goal for a mature manufacturing line **Basis:** Long-term, 1.5 shift **Level:** 5.0 sigma **Ppm:** 233 **Yield:** 99.9767% **Note:** Short-term Cp equivalent about 1.67 **Basis:** Long-term, 1.5 shift **Level:** 5.5 sigma **Ppm:** 32 **Yield:** 99.9968% **Note:** Approx. 32 defects per million opportunities **Basis:** Long-term, 1.5 shift **Level:** 6.0 sigma **Ppm:** 3.4 **Yield:** 99.99966% **Note:** Six Sigma target; short-term Cp equivalent 2.0 **Basis:** Centered, two-sided **Level:** Cp = Cpk = 1.00 **Ppm:** 2,700 **Yield:** 99.73% **Note:** 3 sigma to each spec limit, no shift **Basis:** Centered, two-sided **Level:** Cp = Cpk = 1.33 **Ppm:** 63 **Yield:** 99.9937% **Note:** 4 sigma to each spec limit; common minimum for existing processes **Basis:** Centered, two-sided **Level:** Cp = Cpk = 1.50 **Ppm:** 6.8 **Yield:** 99.99932% **Note:** 4.5 sigma to each spec limit **Basis:** Centered, two-sided **Level:** Cp = Cpk = 1.67 **Ppm:** 0.57 **Yield:** 99.999943% **Note:** 5 sigma to each spec limit; common target for new processes and safety characteristics **Basis:** Centered, two-sided **Level:** Cp = Cpk = 2.00 **Ppm:** 0.002 **Yield:** 99.9999998% **Note:** 6 sigma to each spec limit **Basis:** One-sided spec **Level:** Cpk = 1.00 **Ppm:** 1,350 **Yield:** 99.865% **Note:** Only one spec limit, 3 sigma away **Basis:** One-sided spec **Level:** Cpk = 1.33 **Ppm:** 31.7 **Yield:** 99.9968% **Note:** Only one spec limit, 4 sigma away **Basis:** One-sided spec **Level:** Cpk = 1.67 **Ppm:** 0.29 **Yield:** 99.99997% **Note:** Only one spec limit, 5 sigma away **Basis:** Formula **Level:** Sigma level (Z) **Ppm:** Z = NORMSINV(1 - DPMO/1,000,000) + 1.5 **Yield:** n/a **Note:** Spreadsheet formula for the long-term sigma level with the 1.5 shift **Basis:** Formula **Level:** DPMO **Ppm:** defects / (units x opportunities) x 1,000,000 **Yield:** n/a **Note:** Count every opportunity, not only defective units **Basis:** Formula **Level:** Cpk from Z **Ppm:** Cpk = Z(min) / 3 **Yield:** n/a **Note:** Z(min) is the distance in sigma from the mean to the nearest spec limit **Notes:** The 1.5 sigma shift is a Six Sigma convention, not a law. If you have long-term data, compute Ppk and use the real defect rate instead of assuming a shift. ## Content **Intro:** People mix up sigma level, DPMO, yield and Cpk constantly because each one describes the same capability on a different scale. This table puts the conventional values side by side, with and without the 1.5 sigma shift, so you can translate a customer requirement into the number your team measures. **Sections:** #### How to use the table **Body:** Find the row that matches the number you already have, then read across. If a customer asks for a 1.33 Cpk, the table shows that a centered two-sided process then produces roughly 63 defects per million. If your DPMO is 6,210, the long-term sigma level is 4.0. Use the Basis column carefully: the 1.5 shift rows give the familiar 3.4 DPMO at 6 sigma, while the centered rows give the raw normal distribution tails. **Bullets:** - Search for a sigma level, a Cpk value, or a word such as yield - Check the Basis column before comparing two numbers - Export to Excel to use as a lookup in a scorecard #### The math behind the numbers **Body:** DPMO is defects divided by units times opportunities per unit, scaled by one million. Sigma level is the normal quantile of the yield, plus 1.5 when the shift convention is used. Cpk is the distance from the mean to the nearest specification limit divided by three standard deviations, so a Cpk of 1.33 means that limit sits four standard deviations away. For a centered two-sided process the defect rate is twice the single tail area. #### Worked example **Body:** A line builds 20,000 boards a month with 12 opportunities for a solder defect on each board. The month produces 840 defects. DPMO is 840 divided by 240,000 times one million, which is 3,500. On the shift convention that falls between 4.0 sigma (6,210) and 4.5 sigma (1,350), roughly 4.2. Without the shift the same defect rate corresponds to a Z near 2.7, so be explicit about which one a report uses. #### Common mistakes **Body:** The biggest error is counting units instead of opportunities, which understates the DPMO denominator and hides real defect density. A second is quoting a sigma level from short-term data as if it were long-term. A third is assuming normality: heavy-tailed data can produce far more defects than the table predicts, so check the histogram and a normality test, or use the observed PPM. **Bullets:** - Define opportunities before collecting data and keep them fixed - State whether the sigma level includes the 1.5 shift - Use observed PPM when the data are not normal **Cta:** If DPMO and yield numbers are scattered across inspection records and ERP quality tables, Netray can help build a single read-only view. **Faq:** #### Why is 6 sigma only 3.4 DPMO? **Answer:** Because the convention assumes the process mean drifts by 1.5 sigma over the long term. A centered 6 sigma process would give about 0.002 defects per million, but the shift moves the nearest limit to 4.5 sigma, whose tail is 3.4 per million. #### Is the 1.5 sigma shift always correct? **Answer:** No. It is an empirical rule of thumb from Motorola practice. If you have long-term data, compute actual Ppk and the observed PPM instead. Many quality standards and customers specify Cpk or PPM directly and never mention the shift. #### What Cpk do customers usually ask for? **Answer:** Automotive customers commonly ask for 1.33 on existing processes and 1.67 on new processes, and sometimes higher on safety characteristics. Always use the value in your customer-specific requirements or control plan. #### How do I convert my yield to a sigma level? **Answer:** Take one minus the yield as the defect fraction, then use the normal quantile of the yield and add 1.5 if you follow the shift convention. In Excel that is NORM.S.INV(yield) + 1.5. ## Search terms sigma level chart, six sigma conversion table, dpmo to sigma table, sigma level to cpk, ppm to sigma level, 6 sigma 3.4 dpmo, yield to sigma conversion, 1.5 sigma shift table --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json