Product and Process Control
What to master
Control questions separate people who understand where limits come from. Control limits are computed from the process (typically the mean plus or minus three standard deviations of the plotted statistic); specification limits come from the customer or design. A process can be in statistical control and still be incapable, and capable but out of control - two different questions.
Know the chart families: variables charts (X̄-R, X̄-s, individuals-MR) and attributes charts (p, np, c, u). Recognize out-of-control signals: a point beyond 3σ, two of three beyond 2σ, four of five beyond 1σ, eight consecutive on one side, and trends of six or more. Understand how subgroup size changes the limits (X̄ limits = X̄̄ ± A₂R̄).
Capability: Cp = (USL − LSL)/6σ measures spread only; Cpk = min(USL − X̄, X̄ − LSL)/3σ adds centering. Pp/Ppk use the overall standard deviation; Cp/Cpk use within-subgroup variation.
Also required: control plan contents (characteristic, specification, measurement method, sample size and frequency, control method, reaction plan), MSA and gage R&R (%GRR under 10 acceptable, 10–30 conditional, over 30 unacceptable), calibration traceability, acceptance sampling (AQL, LTPD, OC curve, producer's versus consumer's risk), and nonconforming material control with MRB disposition options.
Worked example. USL = 10.10, LSL = 9.90, X̄ = 10.02, σ = 0.02. Cpu = (10.10 − 10.02)/0.06 = 1.33. Cpl = (10.02 − 9.90)/0.06 = 2.00. Cpk = 1.33. Cp = 0.20/0.12 = 1.67. The process is capable in spread but off-center - centering the mean is the improvement lever.