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The p formula (for the proportion of nonconforming units from subgroups that can vary in size):
To calculate control limits for the p-chart:
The np-chart formula (for number of nonconforming units from subgroups with a constant size):
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).
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%