Subgroups of 9 or more? The S chart tracks the spread inside each subgroup more precisely than the range.
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 use the standard Xbar-S constants (A3, B3, B4), derived from the c4 bias-correction factor for the given subgroup size. Sigma is estimated from the pooled within-subgroup standard deviation, bias-corrected with c4. 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-S chart is for subgroups of 9 parts or more. The X̄ chart follows the subgroup averages; the S chart follows the standard deviation inside each subgroup. With larger subgroups the standard deviation uses every reading and estimates the spread better than the range, which only looks at the largest and smallest value.
Keep the subgroup size constant and take each subgroup close together in time. For 2 to 8 parts per subgroup use the X̄-R 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”: 20 subgroups of 10 parts, specification 4.80 to 5.25.
| Result | Value |
|---|---|
| X̄ chart | X̿ 5.0230 · UCL 5.0673 · LCL 4.9788 |
| S chart | S̄ 0.04538 |
| Tests for special causes | No signals: stable |
| Cp · Cpk | 1.60 · 1.59 |
| Pp · Ppk | 1.59 · 1.58 |
The process is stable and capable, with Cpk 1.59 above the common 1.33 target.