Manufacturing quality investigation

You are the quality analyst for a small (fictional) engineering group with two sites. Over the last month the group's customers have complained twice: a batch of steel shafts that did not fit their bearings, and appliance panels arriving with scratches. The plant manager has asked for one report that answers:

1. Is each process stable? Which signals are real (special causes that need action) and which are ordinary variation that nobody should "fix"?
2. Is each process capable of meeting its specification — and what does that capability mean in rejected parts and riyals?
3. Do lathes, shifts or operators differ, and can the data even tell?
4. What should we do first, given that every intervention costs downtime?

The data.

• machining — 300 measured shafts from the turning cell (target 25.000 mm, specification 24.950–25.050 mm). Each of two lathes (A and B) contributes 30 rational subgroups of 5 consecutive parts, one subgroup per shift (Day/Night) over 15 days, measured with a digital micrometer that reads to 0.001 mm. The maintenance log notes that a scheduled tool change on Lathe B was skipped after subgroup 20.
• defects — 60 working days of final inspection on the panel line: panels inspected (it varies from day to day), defective panels, and defects found by type.

Both datasets are synthetic: they were generated to behave like real shop-floor data (subgroup-to-subgroup variation, rounding, a drifting tool, a bad day), but they describe no real company and are not evidence about real processes.

Stakeholders and constraints. The plant manager (owns the downtime budget), the two shift supervisors (worried that "night shift is worse" will be read as a judgement on their people), the maintenance lead (assume a tool change on Lathe B costs about SAR 2,400 in inserts and lost machine time), and the key shaft customer, whose supplier quality agreement in this scenario asks for Cpk ≥ 1.33 on the shaft diameter (a common contractual threshold, but each customer sets its own). All costs and volumes in this project are scenario assumptions for a fictional group, not industry figures. Your deliverable is a written report to the plant manager built in the report workspace.