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p-Chart

A p-Chart is used to analyze the ratio of the proportion defective in a sample to each sample.

The upper control limit and lower control limit for a p-Chart are defined as:

UCL = ps + zσ
LCL = ps - zσ

where
        z is the number of standard deviations
        ps is the proportion defective
        σ is the standard deviation of the sample proportion

σ can be obtained by:

σ = √(ps * (1 - ps) / n), where n is the sample size

thus UCL and LCL can be rewritten as:

UCL = ps + z * √(ps * (1 - ps) / n)

LCL = ps - z * √(ps * (1 - ps) / n)
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