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Sigma Level to DPMO, Yield and Cpk Conversion Table

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.

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Basis	Sigma level or index	Defects per million	Yield	Note
Long-term, 1.5 shift	1.0 sigma	691,462	30.85%	Typical of very poor, uncontrolled processes
Long-term, 1.5 shift	1.5 sigma	500,000	50.00%	Half the output is defective
Long-term, 1.5 shift	2.0 sigma	308,538	69.15%	Common in unmanaged administrative processes
Long-term, 1.5 shift	2.5 sigma	158,655	84.13%	Roughly one defect in six
Long-term, 1.5 shift	3.0 sigma	66,807	93.32%	Short-term Cp equivalent about 1.0
Long-term, 1.5 shift	3.5 sigma	22,750	97.72%	Roughly one defect in 44
Long-term, 1.5 shift	4.0 sigma	6,210	99.379%	Short-term Cp equivalent about 1.33
Long-term, 1.5 shift	4.5 sigma	1,350	99.865%	Typical goal for a mature manufacturing line
Long-term, 1.5 shift	5.0 sigma	233	99.9767%	Short-term Cp equivalent about 1.67
Long-term, 1.5 shift	5.5 sigma	32	99.9968%	Approx. 32 defects per million opportunities
Long-term, 1.5 shift	6.0 sigma	3.4	99.99966%	Six Sigma target; short-term Cp equivalent 2.0
Centered, two-sided	Cp = Cpk = 1.00	2,700	99.73%	3 sigma to each spec limit, no shift
Centered, two-sided	Cp = Cpk = 1.33	63	99.9937%	4 sigma to each spec limit; common minimum for existing processes
Centered, two-sided	Cp = Cpk = 1.50	6.8	99.99932%	4.5 sigma to each spec limit
Centered, two-sided	Cp = Cpk = 1.67	0.57	99.999943%	5 sigma to each spec limit; common target for new processes and safety characteristics
Centered, two-sided	Cp = Cpk = 2.00	0.002	99.9999998%	6 sigma to each spec limit
One-sided spec	Cpk = 1.00	1,350	99.865%	Only one spec limit, 3 sigma away
One-sided spec	Cpk = 1.33	31.7	99.9968%	Only one spec limit, 4 sigma away
One-sided spec	Cpk = 1.67	0.29	99.99997%	Only one spec limit, 5 sigma away
Formula	Sigma level (Z)	Z = NORMSINV(1 - DPMO/1,000,000) + 1.5	n/a	Spreadsheet formula for the long-term sigma level with the 1.5 shift
Formula	DPMO	defects / (units x opportunities) x 1,000,000	n/a	Count every opportunity, not only defective units
Formula	Cpk from Z	Cpk = Z(min) / 3	n/a	Z(min) is the distance in sigma from the mean to the nearest spec limit

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.

Track DPMO from your ERP quality data

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How to use the table

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.

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

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

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

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.

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

Frequently Asked Questions

Why is 6 sigma only 3.4 DPMO?

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?

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?

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?

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.

If DPMO and yield numbers are scattered across inspection records and ERP quality tables, Netray can help build a single read-only view.

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