Process Sigma Calculator

Work out process sigma instantly with clear inputs, formula shown and shareable results.

About Process Sigma Calculator

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.

Formulas

DPMO

DPO = defects / (units x opportunities per unit); DPMO = DPO x 1,000,000

Sigma level

Sigma = z(1 - DPO) + 1.5 shift

Worked example

With the default values below, Process Sigma Calculator returns Process Sigma Level of 3.930. Change any input above and every figure here is recalculated in your browser.

Inputs used

Defects Observedminimum 0: 45
Units Inspectedminimum 1: 1,500
Defect Opportunities Per Unitminimum 1: 4
Long-Term Shift Allowanceaccepts 0–3 sigma: 1.5 sigma

Results

Process Sigma Level: 3.930
Defects Per Million Opportunities: 7,500.0
Defects Per Opportunity: 0.0075000
Process Yield: 99.25000%

Step by step

1Values used
2DPMO
3Sigma level
4Process Sigma Level= 3.930
5Defects Per Million Opportunities= 7,500.0
6Defects Per Opportunity= 0.0075000
7Process Yield= 99.25000

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 7 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why add 1.5 sigma?

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.

How should opportunities be counted?

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.