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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
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:
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
Alpha value = 5%
Sigma of the individuals (actual sigma)
Estimated sigma
X-bar control limits are based on either range or sigma, depending on which chart it is paired with. When the X-bar chart is paired with a range chart, the most common (and recommended) method of computing control limits based on 3 standard deviations is:
Upper control limit
Lower control limit:
k is the number of subgroups
Lower control limit
The most common (and recommended) method of computing control limits for an individuals chart based on 3 standard deviations is: