S chart

An S-chart is a type of control chart used to monitor the process variability (as the standard deviation) when measuring subgroups (n ≥ 5) at regular intervals from a process.

Each point on the chart represents the value of a subgroup standard deviation.

The center line for each subgroup is the expected value of the standard deviation statistic. Note that the center line varies when the subgroup sizes are unequal.

The control limits are either:
  • A multiple (k) of sigma above and below the center line. Default k=3.
  • Probability limits, defined as the probability (alpha) of a point exceeding the limits. Default alpha=0.27%.
If unspecified, the process sigma is the weighted average of the unbiased subgroup estimates of sigma based on the standard deviation statistics.

The individual observations are assumed to be independent and normally distributed. Although the chart is fairly robust and nonnormality is not a serious problem unless there is a considerable deviation from normality (Burr, 1967).

For subgroup sizes less than 6 with k-sigma control limits, the lower limit is zero. In these cases, probability limits may be more appropriate.