Statistical Techniques
Statistical thinking separates common-cause variation (inherent and stable) from special-cause variation (assignable and sporadic). Control charts are built on that distinction: control limits are computed from the process - typically ±3σ of the plotted statistic - and never from the specification. Confusing control limits with spec limits is the most frequent exam trap.
Descriptive measures (mean, median, mode, range, variance, standard deviation) describe location and spread. The normal distribution's ±1σ/±2σ/±3σ areas (68.27/95.45/99.73%) anchor most area questions, and the central limit theorem lets you chart subgroup averages even when individual data are not normal.
Attribute charts: p (fraction defective, variable sample size), np (count defective, constant n), c (defect count, constant sample size/area), u (defects per unit, variable size). Variables charts: X̄-R for small subgroups, X̄-s for larger ones, individuals/moving range for slow processes.
Acceptance sampling: AQL is the quality level at which the producer risks rejection (α, producer's risk); LTPD/RQL is the poor level the consumer risks accepting (β, consumer's risk). The OC curve plots lot fraction defective against probability of acceptance; larger n steepens it.
Worked example. USL = 10.0, LSL = 9.0, process mean = 9.7, σ = 0.1. Cp = (10.0 − 9.0) / (6 × 0.1) = 1.67. Cpk = min(10.0 − 9.7, 9.7 − 9.0) / (3 × 0.1) = 0.3/0.3 = 1.0. Cp says the spread is capable; Cpk exposes that the process is off-center.