Quality Engineering and Statistical Process Control
Quality engineering spans the cost of quality, control charts, process capability, and acceptance sampling. Know the four quality costs: prevention, appraisal, internal failure, and external failure; external failure is the most expensive and prevention is the least. Quality gurus (Deming, Juran, Crosby, Taguchi) appear in conceptual questions; Taguchi's loss function penalizes deviation from target, not just conformance to limits.
SPC is heavily tested. Distinguish variables charts (X̄-R, X̄-s) from attributes charts (p, np, c, u). Control limits are at ±3 standard deviations from the center line and are computed from the process, not from specification limits. For X̄-R: UCL = X̄̄ + A₂R̄, LCL = X̄̄ − A₂R̄; for R: UCL = D₄R̄, LCL = D₃R̄. Out-of-control signals include a point beyond limits, runs of seven on one side, and nonrandom patterns. Traps: confusing control limits with specification limits; using σ of individuals where σ of the mean (σ/√n) is needed; and misreading a process that is in control but not capable.
Process capability: Cp = (USL − LSL)/(6σ) measures potential; Cpk = min[(USL − μ)/(3σ), (μ − LSL)/(3σ)] measures actual centering. Cpk ≥ 1.33 is a common minimum; Cpk = 1.0 means the process barely fits. A process can have Cp > 1 but Cpk < 1 if off-center. Acceptance sampling uses OC curves, AQL, LTPD, and producer's/consumer's risk (α, β).
Worked example
USL = 12, LSL = 8, μ = 10.5, σ = 0.5. Cp = 4/(3.0) = 1.33. Cpk = min[(12−10.5)/1.5, (10.5−8)/1.5] = min[1.0, 1.67] = 1.0. The process is potentially capable but off-center.