DPMO / sigma level

DPU — defects per unit. Simple, but not comparable from one product to another: a unit may carry three opportunities for a defect or three hundred.

DPO — defects per opportunity. You divide by the number of chances to get it wrong, which neutralises complexity.

DPMO — the DPO scaled to one million, to handle whole numbers rather than decimals with six zeros.

The notion of opportunity is the sensitive point of the whole. It is the number of places, in a unit, where a defect can appear. It is defined once, written down, and never moves again: increasing it improves the DPMO without anything changing in the process, which makes it the most tempting lever on a dashboard.

The usual conversion table gives about 66,800 DPMO for 3σ, 6,210 for 4σ, 233 for 5σ and 3.4 for 6σ.

These values are not derived directly from the normal distribution. They include a conventional 1.5σ shift of the mean, meant to represent the drift of a process over the long term. It is a working assumption specific to Six Sigma, not a mathematical result — without it, 6σ would correspond to about two defects per billion.

Stating this is not an expert’s refinement. It is what explains why two serious sources give different figures for the same level, and what avoids a painful discussion in an audit or in front of a customer who has redone the calculation.

DPMO exists to make comparable things that are not spontaneously so. A scrap rate of 2 % on a plastic gasket and a rate of 2 % on an on-board controller with six hundred components do not describe the same control: the second process is incomparably better, and the percentage does not say so.

Three uses follow. Arbitrating between projects: at equal scrap rate, the DPMO designates the most fragile process. Setting a target in design: from the DPMO targeted on the finished product and the number of steps, one works back to the level required of each step — a chain of twenty operations at 99.5 % does not give 99.5 % at the output, but about 90 %. Speaking to the customer in their vocabulary, when the customer reasons in ppm or in sigma level.

Elsewhere, the indicator muddies the reading. A process that turns out one part a day is not measured per million, nor is a process with a single possible defect: the scrap rate is enough. DPMO is useful only when the complexity of the product makes the percentage misleading.

Batch of 2,500 boards assembled, each carrying 420 components and 1,340 solder joints. Inspection records 187 defects on the batch: cold joints, bridges, missing or shifted components.

DPU = 187 / 2,500 = 0.075 defect per board. An exact and incomparable figure: it says nothing about the difficulty of the board. At equal DPU, a board with thirty solder joints would describe a far inferior process.

DPO = 187 / (2,500 × 1,340) = 0.0000558, since the batch represents 3,350,000 chances to get it wrong. Multiplied by one million: DPMO ≈ 56. That is the number that compares with that of another line or another year.

Placed on the sigma scale, 56 DPMO puts the line between 5 and 5.5 sigma — around 5.3 depending on the table used. The range is not coyness: published tables do not agree to the tenth, and announcing "5.3 sigma" without saying where the value comes from invites challenge.

Then comes the demonstration that counts. Same batch, same 187 defects, but the opportunity defined per component rather than per solder joint: you divide by 2,500 × 420 = 1,050,000, which gives DPMO ≈ 178, barely more than 5 sigma. Three times worse, without a single board having changed. Both counts are defensible; not writing it down is not.

The DPU, for its part, has not moved: 0.075 in both cases. It is the denominator that changed, not the process.

One last reading, the one that speaks to planning: under the usual assumption of a Poisson distribution of defects, a DPU of 0.075 corresponds to a first-pass yield of about 93 %, i.e. one board in fourteen going back to rework. That sentence triggers decisions that "56 DPMO" never triggers.