Q
AshToolbox Quality Lean Six Sigma Suite
Intermediate Category: Statistical Process Control (SPC) • ~7 min read

p Chart for Fraction Defective

Track defect rates across varying production lot sizes while accounting for overdispersion.

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Q:

What is a p-Chart and how are limits calculated for variable subgroup sizes?

A p-chart monitors the proportion (fraction) of nonconforming items across inspection lots. Because sample size n can vary per lot, control limits expand and contract dynamically based on binomial standard error √(p̄(1-p̄)/n_i).
UCL = Min(1, p̄ + 3√(p̄(1-p̄)/n_i)), LCL = Max(0, p̄ - 3√(p̄(1-p̄)/n_i))

Average Proportion (p̄)

2.88%

Total: 173 / 6000
Out of Control

0 Subgroups

0.0% of series

p Control Chart (Fraction Nonconforming)

p̄123456789101112

Binomial Fraction Nonconforming Monitoring

When quality inspection classifies parts dichotomously as Pass or Fail, and daily production batch quantities fluctuate, the p-chart provides rigorous statistical signaling while adjusting limits for varying lot sizes.

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