Process Capability Formulas Reference
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Target Z, Zupper, and Zlower formulas
Target Z
Zupper
Zlower
Where:
= the mean of the X-bars
T = specification target
Sigma is an estimated sigma or sigma of the individual values, depending on how the histogram
is configured or whether you are calculating Cpk (estimated) or Ppk (actual).
Additional reference material
Additional sections from legacy actual-percent-f:
Actual percent out-of-spec formulas
Actual % out-of-spec = % above upper spec + % below lower spec
To find actual % above spec:
To find actual % below spec:
Related topic:
The formula for theoretical percent out of spec
Additional sections from legacy theoretical-f:
Theoretical percent out-of-spec formulas
To find theoretical % above spec:
Locate the value for Zupper in a standard normal table.
To find theoretical % below spec:
Locate the value for Zlower in a standard normal table.
Given:
- An X-bar value
- A sigma value and
- A set of specifications
And assuming:
In theory:
If the Z value from the standard normal table is multiplied by 100, then this process is expected to produce X% of its output outside specification.
Show me:
The standard normal table
The formulas for Target Z
Related topic:
The formula for actual percent out of spec
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