Daily inspection defects

What it is good for

• Build a p-chart with limits that vary with sample size and identify an out-of-control day.
• Distinguish defectives (p/np charts) from defects (c/u charts).
• Check whether daily defect counts are consistent with a Poisson model.
• Build a Pareto chart of defect types.

Methods: p-chart, np-chart, c-chart, u-chart, Poisson distribution, Pareto chart, chi-square goodness of fit.

Data quality notes

• Day 41 has a much higher defective rate (≈7.5% vs ≈3.2%) and should fall above the p-chart's upper limit.
• Sample sizes vary from day to day: use a u-chart rather than a c-chart for defects, or standardise.
• No missing values.

Provenance and licence

Units inspected ~ 380–620 (uniform). Defective units ~ Binomial(units, 0.032), except day 41 where p = 0.075 (assignable cause). Each defective unit carries 1 + Poisson(0.3) defects, each assigned to a type with probabilities scratch 0.40, dent 0.25, misalignment 0.20, paint 0.15. So defects_total ≥ defective_units and the four type counts add up to defects_total. Only working days (Sunday–Thursday) appear.

Synthetic data · CC0-1.0 (synthetic data generated by Statistics Quest) · generated deterministically (seed 20241008). It does not describe real people or organisations; any resemblance is coincidental.