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Six Sigma Calculator (DPMO and Sigma Level)

Turn defect counts into DPMO, PPM, yield and sigma level, and work out rolled throughput yield across process steps

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  • Indian rules
1

Defects found

Add the 1.5 sigma shift

The usual Six Sigma convention, under which 3.4 DPMO is 6 sigma

2

Yield across steps

· optional

Right first time means no rework, repair or scrap at that step. Reworked units that pass later still count as failures here.

Good to know

  • Fix the list of opportunities before you count. Adding trivial opportunities makes DPMO look better without any real change.
  • DPMO counts defects; PPM counts defective units. One shirt with three faults is three defects but one defective unit.
  • The 1.5 shift assumes your data is long-term and reports a short-term sigma level. Turn it off to see the long-term Z.
  • Rolled throughput yield is always lower than the yield of any single step. The gap shows how much rework the final count hides.

Results

Sigma level (short-term)

3.78

11,250 defects per million opportunities

DPMO

11,250

Yield

98.875%

per opportunity

Defects per unit (DPU)0.09
Defects per opportunity (DPO)0.01125
Defect rate per opportunity1.125%
PPM defective75,000
Units with no defect92.5%
Long-term Z (no shift)2.28

Working

DPO = 180 ÷ (2,000 × 8) = 180 ÷ 16,000 = 0.01125

DPMO = DPO × 10,00,000 = 11,250

Sigma = Φ⁻¹(1 − DPO) + 1.5 = 2.2818 + 1.5 = 3.78

Rolled throughput yield

87.46%

  • First-pass yield, Cutting: 1,960 ÷ 2,00098%
  • First-pass yield, Stitching: 1,840 ÷ 2,00092%
  • First-pass yield, Finishing: 1,940 ÷ 2,00097%

RTY = 98% × 92% × 97% = 87.46%. Only about 87 of every 100 units go through every step without rework.

Reference, with the 1.5 shift

  • 2 sigma3,08,538 DPMO
  • 3 sigma66,807 DPMO
  • 4 sigma6,210 DPMO
  • 5 sigma233 DPMO
  • 6 sigma3.4 DPMO

The sigma level assumes normally distributed data and uses the conventional 1.5 sigma shift unless you turn it off. The shift is a convention from Motorola's early Six Sigma work, not a law, so state which one you used when you report a sigma level.

How it works

What this tool does.

Calculate defects per unit, defects per million opportunities (DPMO), PPM defective, yield and the sigma level, with or without the conventional 1.5 sigma shift. Add your process steps to get the first-pass yield of each and the rolled throughput yield of the whole process.

Enter the number of units checked, the number of opportunities for a defect on each unit and the number of defects found. Add the number of defective units if you want PPM defective as well. The calculator works out DPU, DPO, DPMO, the defect rate and the yield per opportunity, and turns the yield into a sigma level using the inverse of the normal distribution plus the conventional 1.5 sigma shift. Switch the shift off to see the long-term Z. In the steps section, enter how many units went into each step and how many came out right first time. Each step’s first-pass yield is shown, and they are multiplied together for the rolled throughput yield.

Rules and dates last reviewed: October 2026

Official sources

Six Sigma Calculator (DPMO and Sigma Level) formula

DPU = defects ÷ units. DPO = defects ÷ (units × opportunities per unit). DPMO = DPO × 10,00,000. Yield = 1 − DPO. Sigma level = Φ⁻¹(1 − DPO) + 1.5, where Φ⁻¹ is the inverse of the standard normal distribution (NORM.S.INV in Excel) and 1.5 is the conventional shift. PPM defective = defective units ÷ units × 10,00,000. First-pass yield of a step = units right first time ÷ units entering the step. Rolled throughput yield = FPY of step 1 × FPY of step 2 × … × FPY of the last step.

Worked example

A garment exporter in Tiruppur inspects 2,000 shirts. It counts 8 opportunities for a defect on each shirt, such as collar, cuffs, buttons, seams and label. Inspectors find 180 defects on 150 shirts. The three steps had first-pass yields of 98% (cutting), 92% (stitching) and 97% (finishing).

  1. Opportunities = 2,000 × 8 = 16,000
  2. DPO = 180 ÷ 16,000 = 0.01125, so DPMO = 0.01125 × 10,00,000 = 11,250
  3. Yield = 1 − 0.01125 = 98.875%
  4. Long-term Z = NORM.S.INV(0.98875) = 2.28
  5. Sigma level = 2.28 + 1.5 = 3.78
  6. PPM defective = 150 ÷ 2,000 × 10,00,000 = 75,000 (7.5% of shirts)
  7. Rolled throughput yield = 0.98 × 0.92 × 0.97 = 0.8746, or 87.46%

The process runs at about 3.8 sigma, with 11,250 defects per million opportunities. Only about 87 of every 100 shirts get through all three steps without rework, and stitching, at 92%, is where most of it happens.

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Questions

Six Sigma Calculator (DPMO and Sigma Level), answered.

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How do you calculate DPMO?

DPMO = defects ÷ (units × opportunities per unit) × 10,00,000. If 2,000 shirts each have 8 opportunities and you find 180 defects, DPMO = 180 ÷ 16,000 × 10,00,000 = 11,250.

How do you convert DPMO to a sigma level?

Work out the yield per opportunity, 1 − DPMO ÷ 10,00,000, find the Z value for it from the normal distribution (NORM.S.INV in Excel), and add 1.5. For 11,250 DPMO: NORM.S.INV(0.98875) = 2.28, plus 1.5 gives 3.78 sigma. With this convention, 66,807 DPMO is 3 sigma, 6,210 is 4 sigma, 233 is 5 sigma and 3.4 is 6 sigma.

What is the 1.5 sigma shift?

It is a convention from Motorola’s early Six Sigma work, which assumed a process mean drifts by about 1.5 sigma over the long term. Defect data collected over time is taken as long-term, and 1.5 is added to report a short-term sigma level. That is why 3.4 DPMO is called 6 sigma, although on a normal table it is 4.5. The shift is not measured from your data, so say whether you used it.

What is the difference between DPMO and PPM?

DPMO counts defects per million opportunities, and one unit can have several defects. PPM counts defective units per million units, and a unit counts once however many defects it has. A shirt with a loose button and a crooked label is two defects but one defective shirt. When each unit has only one opportunity, the two are the same.

What is rolled throughput yield?

Rolled throughput yield (RTY) is the chance a unit gets through every step of a process without a single defect or rework. Multiply the first-pass yields of all the steps: four steps at 85% each give 0.85 × 0.85 × 0.85 × 0.85 = 52.2%. It is always lower than the yield of any single step.

What is the difference between first-pass yield and final yield?

First-pass yield counts only units that are right the first time at a step. Final yield also counts units that were reworked and then passed. A process can ship 99% good units at the end while its first-pass yield is much lower; the difference is the rework you are paying for.

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