Small subgroups measured together? See whether the average and the spread are stable, and whether the process is capable.
Counting defects or defectives instead of measuring? SPC Engine also covers p, np, c and u charts. Open SPC Engine
| # | x1 | x2 | x3 | x4 | x5 |
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Control limits follow the standard R̄ method: σ = R̄/d2, X̄ limits = X̿ ± 3σ/√n, R limits = R̄ ± 3·d3·σ (standard d2/d3 unbiasing constants). Capability uses σ within = pooled standard deviation / c4 (the standard default). Control chart rules follow the Nelson Rules (1-8). Anderson-Darling: AD is reported as in standard statistical software; its p-value uses the Stephens (1974) small-sample adjustment.
The X̄-R chart is for samples of 2 to 8 parts taken together (subgroups), for example 5 consecutive parts every hour. The X̄ chart follows the subgroup averages, which shows whether the process centre moves; the R chart follows the range inside each subgroup, which shows whether the short-term spread changes.
Keep the subgroup size the same throughout and take each subgroup close together in time. Twenty to 25 subgroups are a sensible minimum. With 9 or more parts per subgroup use the X̄-S chart.
Control limits, tests for special causes and capability indices follow the AIAG SPC manual and Montgomery, and the results are tested against reference data sets analysed in specialised statistical software. Normality is checked before capability is reported.
The data behind “Try an example”: 25 subgroups of 5 parts, specification 73.95 to 74.05.
| Result | Value |
|---|---|
| X̄ chart | X̿ 73.9991 · UCL 74.0115 · LCL 73.9867 |
| R chart | R̄ 0.02152 |
| Tests for special causes | No signals: stable |
| Cp · Cpk | 1.81 · 1.77 |
| Pp · Ppk | 1.83 · 1.80 |
The process is stable and well centred, and Cpk 1.77 is above both 1.33 and 1.67.