Statistics Quest

Applied case · Manufacturing · about 60 minutes

Are defects under control?

Build a p-chart with varying sample sizes, find the out-of-control day, see why a c-chart misleads when volumes vary, and focus root-cause work with a Pareto of defect types.

The brief

Corniche Fabrication (a fictional appliance-panel plant) inspects finished panels every working day. A major customer has complained about quality and asked for evidence that the process is stable, and the plant manager wants to know where to focus improvement work.

The quality engineer has 60 production days of final-inspection data and asks you to:

  1. check the data and choose the right control charts;
  2. build a p-chart for the proportion of defective panels and identify any out-of-control days;
  3. look at the number of defects (a panel can have several) and avoid a misleading chart;
  4. recommend next steps for root-cause investigation and for the customer.

The data. defects has one row per production day: units inspected (which varies from day to day), defective units, total defects, and defects by type (scratch, dent, misalignment, paint). It is synthetic — generated by documented code for teaching (the dataset page describes how, but try the analysis first) — and describes no real plant or customer.

Stakeholders. The plant manager (production), the quality engineer (owns the charts), line supervisors (who know what happened on each day), and the customer's quality team.

Dataset

Daily inspection defects

60 rows · one row = one production day · synthetic data

Production dayDateUnits inspected (units)Defective units (units)Total defects (defects)Scratches (defects)Dents (defects)Misalignments (defects)Paint defects (defects)
12024-02-0439515198560
22024-02-054479103511
32024-02-0646912166253
42024-02-07425182110452
52024-02-08618213215584
62024-02-1142019217824

Included with a Formula Quest membership

This case has 4 stages and 10 graded tasks, ending with a written report.

View Formula Quest memberships