· Xbar-R: for processes sampled in subgroups (e.g. 5 pieces per shift); n = 2–10.

· Xbar-s: for larger subgroups (n≥10) or readily available data — std dev is more sensitive than range.

· I-MR: for individual measurements or when grouping is impossible (one per batch, destructive testing).

· Green line = center line CL; red dashed lines = control limits UCL/LCL (P/U limits vary with sample size and are drawn as polylines).

· 8 out-of-control rules: 1 beyond 3σ / 9 in a row one side / 6 trending / 14 alternating / 2 of 3 beyond 2σ / 4 of 5 beyond 1σ / 15 within ±1σ / 8 all outside ±1σ.

· Attributes: P chart = proportion nonconforming (two columns per row, order free — auto-detected by size; variable n → limits follow n), NP chart = number nonconforming (fixed n), C chart = defects, U chart = defects per unit (variable units → limits follow u).

· Histogram / Q-Q plot: inspect distribution shape and normality — the Q-Q plot includes the Anderson-Darling test to decide whether your data are suitable for CpK.

· Out-of-control signals are alarms; find the root cause with 5 Why or 8D, then assess CpK once the process is stable.