Measure
Data and measurement
Measure establishes a trustworthy baseline. Classify data first: continuous versus discrete (attribute), and scale as nominal, ordinal, interval, or ratio. Discrete data carries far less information, so it needs much larger samples to detect a shift. A common trap is planning a 30-piece attribute sample to detect a 2% change in defect rate; that study has almost no power.
Measurement system analysis
Validate the measurement system before trusting the numbers: bias, linearity, stability, discrimination, and precision through Gage R&R, where repeatability is equipment variation and reproducibility is appraiser variation. Rule of thumb: %GRR below 10% is acceptable, 10-30% is marginal, and above 30% is unacceptable. Remember that a precise instrument can still be biased; accuracy and precision are different problems with different fixes.
Baseline capability
Capability indices compare process spread with specification width. Cp equals (USL minus LSL) divided by six sigma and ignores centering; Cpk accounts for where the mean sits. Pp and Ppk use overall sigma while Cp and Cpk use within-subgroup sigma. A Cpk of 1.33 corresponds roughly to a 4-sigma process.
Sampling
Use random, stratified, or systematic sampling as appropriate, and form rational subgroups that are homogeneous within but capture between-subgroup variation over time.
Worked example
USL 10, LSL 4, mean 8, sigma 1. Cp = 6/6 = 1.00, but Cpk = min(10-8, 8-4)/3 = 2/3 = 0.67. The process is perfectly centered yet not capable, because its spread is too wide for the specification.