Keep processes in control, capable, and well-measured — the Six Sigma toolkit.
Quality engineering asks three recurring questions: is the process stable, is it capable of meeting spec, and can I trust the measurement system that tells me so. This guide walks the DMAIC-flavored toolkit for each.
The work is usually framed as DMAIC (Define–Measure–Analyze–Improve–Control) and sits under standards like ISO 9001. A few conventional thresholds recur: a process is judged capable at Cpk ≥ 1.33 (≈ 4σ); a measurement system is acceptable when Gage R&R consumes < 10% of tolerance (10–30% is marginal); and out-of-control signals are read with the Western Electric / Nelson run rules, not only points beyond 3σ.
Is the process in control? (ISO 7870 · Nelson 1984)
Statistical process control charts separate normal, expected variation from special-cause signals. Pick the chart for your data: Xbar-R/S for subgrouped measurements, I-MR for individuals, p/np/c/u for defect counts, and EWMA/CUSUM for detecting small sustained shifts.
▸ — Shewhart + time-weighted control charts with run rules.
▸ — Quick standalone control-chart plot.
▸ — Test a sequence for non-randomness.
Is the process capable? (ISO 22514 · AIAG)
Once stable, compare the process spread to the specification limits. Cp/Cpk describe short-term (potential) capability, Pp/Ppk the long-term (actual) performance, with a sigma level and expected nonconforming rate.
▸ — Cp / Cpk / Pp / Ppk vs spec limits, with a sigma level.
▸ — Reliability / time-to-failure — the workhorse life distribution.
▸ — Accelerated-failure-time fits when you need to extrapolate a lifetime.
▸ — Interval containing a set proportion of the population.
Can I trust the measurement system? (AIAG MSA)
A capable process still fails if the gauge is noisy. Gauge R&R partitions measurement variation into repeatability and reproducibility so you know how much of the spread is the process vs the measurement.
▸ — Repeatability + reproducibility of the measurement system.
▸ — Variance components when operators are nested inside sites, not crossed.
▸ — Is one instrument genuinely more variable than another?
▸ — Nested variance components for a measurement procedure.
Improve: designed experiments (Montgomery DOE)
To find which factors drive the outcome efficiently, run a designed experiment rather than one-factor-at-a-time. The design generator builds factorial / fractional / response-surface plans; the analysis fits main effects and interactions.