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Process sigma converts defects per million opportunities into a z-score and adds the conventional 1.5 sigma long-term shift. Six sigma corresponds to 3.4 DPMO, four sigma to about 6210 and three sigma to roughly 66,800 — the scale is steeply non-linear, so each sigma level is a large real improvement.
DPMO
DPO = defects / (units x opportunities per unit); DPMO = DPO x 1,000,000
Sigma level
Sigma = z(1 - DPO) + 1.5 shift
It is a convention accounting for long-term process drift that a short-term capability study does not see. It is an assumption, not a measurement, and should be stated whenever sigma levels are quoted.
Consistently and defensibly — each independent way the unit can fail to meet requirements. Inflating the opportunity count is the easiest way to manufacture a flattering sigma level.