Quality Engineering
Quality is quantified, and the exam tests both the formulas and the philosophy behind them.
Costs and philosophies
Costs are prevention, appraisal, internal failure, and external failure; external failure is usually the most expensive, so prevention dominates. Know Deming, Juran, Crosby (zero defects), Taguchi (loss function, robust design), and Six Sigma (DMAIC, 3.4 ppm with a 1.5σ shift).
Control charts
Variables charts: X̄-R for small subgroups, X̄-s for n above about 10, and individuals charts. Attributes charts: p (fraction defective, variable n), np (constant n), c (count of defects, constant opportunity), u (defects per unit, variable opportunity). Control limits come from the process - statistics times the average range - never from specification limits. Out-of-control signals include a point beyond 3σ, runs of points on one side, trends, and two of three points beyond 2σ.
Capability
Cp = (USL − LSL)/(6σ) measures potential spread; Cpk = min(USL − μ, μ − LSL)/(3σ) measures actual performance including centering. Cpk below 1 is incapable; 1.33 is the usual target; 1.67 for critical characteristics.
Acceptance sampling and DOE
OC curves: AQL is good lot quality with small producer's risk α; LTPD (RQL) is bad lot quality with consumer's risk β. Larger samples sharpen discrimination between accepted and rejected lots. In DOE, factorial designs estimate main effects and interactions, Taguchi uses orthogonal arrays and signal-to-noise ratios, blocking removes nuisance variation, and randomization guards against confounding.
Traps
Putting specification limits on a control chart; confusing Cp with Cpk; using constant-n formulas on a p-chart with varying n; blaming the process before checking gage variation with a Gage R&R study.
Worked example
USL 12, LSL 8, μ 10.5, σ 0.5: Cp = 4/3 = 1.33, so the spread is adequate, but Cpk = min(1.5, 2.5)/1.5 = 1.00 - the process is off-center and needs centering more than tightening.