Home / Lean Six Sigma / SPC & process capability
Type what you have — counted defects, DPMO, PPM, yield, sigma level or Cpk — and see all the others at once. Use it to answer a customer asking for "4 sigma", to compare different processes on one ruler or to understand what a quality figure means in bad parts per million. Pick the convention: short term with the classic Six Sigma 1.5σ shift, or long term with no shift (Z.Bench).
Pre-sizing and estimating tool: results do not replace design, calculations or reports signed by a licensed professional, nor verification against the applicable codes and standards.
Normal distribution of the process in σ units; the red area beyond the limit is the share of opportunities with a defect.
How to read: the horizontal axis is the distance from target in standard deviations (σ). The dashed curve is the short-term process, centered on target; the solid curve is the long-term process, with its mean shifted toward the limit. The vertical "limit" line is the specification limit; everything to its right, shaded red, is a defect. The farther the limit, the smaller the tail and the higher the sigma level.
DPMO on a log scale for each sigma level, with your process marked.
How to read: each gridline on the vertical axis is 10 times the one below (log scale). The curve drops fast: each 1σ step cuts defects by 10 to 40 times. The dot is your process; the distance to the next whole level shows the size of the improvement needed.
How to read: each row is a whole sigma level; the highlighted row is your process, placed in its position. DPMO = defects per million opportunities; yield = % of opportunities with no defect; long-term Z = sigma level minus the shift; Cpk = sigma level ÷ 3.
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Divide defects by total opportunities (units × opportunities per unit) and multiply by 1 million to get DPMO. In the example, 150 ÷ (5,000 × 12) × 10⁶ = 2,500 DPMO. The long-term Z is the standard normal value with a 0.25% tail, 2.81; adding the 1.5 shift, the sigma level is 4.31.
DPMO counts defects per million opportunities; PPM counts defective parts per million parts. A part with several checked points can have more than one defect but is only one defective. In the example, 2,500 DPMO with 12 opportunities per harness gives about 29,591 PPM: almost 3% of harnesses have some defect.
Because the usual tables apply the 1.5σ shift: a 6σ process is treated as having its mean 1.5σ closer to the limit in the long run, leaving it 4.5σ away. The normal tail beyond 4.5σ is 3.4 per million. Without the shift, 6σ would be about 0.001 DPMO.
No. It is a convention created at Motorola to represent mean drift over time. Many practitioners use it because the tables do; others criticize it as a fixed value applied to any process. Use the field to change the value or choose the long-term scale (Z.Bench), with no shift, and state in your report which one you used.
Multiply by 3: Cpk measures the distance from the mean to the limit in blocks of 3σ. Cpk 1.33 corresponds to 4σ (about 6,210 DPMO with the shift); Cpk 1.67 to 5σ; Cpk 2.0 to 6σ. The conversion only considers the side nearest the limit.
Only the characteristics that are actually inspected and matter to the customer, always counted the same way. Counting too many opportunities lowers DPMO and inflates the sigma level with no real improvement. When in doubt, use 1 opportunity per part: then DPMO = PPM and the comparison stays honest.
It depends on the industry and the cost of a defect. Many plants run between 3σ and 4σ; automotive contracts often ask for Cpk 1.33 (4σ) or 1.67 (5σ) on key characteristics; 6σ is the benchmark for serious failures. More important than the number are the trend and the cost: look at PPM and the cost of poor quality.
Important notice: Indus Metrics tools produce estimates and pre-sizing results from the data you enter and from published engineering methods. They do not replace design, calculations or reports signed by a licensed professional engineer (PE), nor verification against the applicable codes, standards and regulations, such as OSHA rules and the ASME codes. Material and fuel properties vary: check manufacturer data or your own process analyses before deciding. By using this site you agree to the Terms of Use.
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