Defects Per Million Opportunities (DPMO)

Percent defective stops being a useful scale once processes get good. DPMO rescales it and, crucially, divides by the number of ways a unit can be wrong rather than by units alone. Twelve defects found in 500 units with eight opportunities each is $12/(500 \times 8) = 0.003$, which is 3,000 DPMO. The famous 3.4 DPMO of six sigma is 3.4 defects in a million chances to make one.

Counting opportunities is where this goes wrong, and it goes wrong in a predictable direction. Nothing in the definition stops you from deciding a circuit board has 500 opportunities instead of 50, and the defect rate divides by ten with no change on the floor. Opportunity counts inflate quietly over the life of a programme. Compare DPMO across departments only when the opportunity definition is written down and audited, and never compare it across companies.

The 3.4 figure itself hides a convention worth knowing. A process centred at six sigma from the nearest limit produces about two defects per billion, not 3.4 per million. The 3.4 comes from Motorola's decision to allow the mean to drift 1.5 sigma over the long run, which is an empirical fudge for real processes rather than a result from the normal distribution. Almost nobody who quotes the number knows it is in there.