X-bar and sigma chart
The s chart replaces the R chart and provides an increase in sensitivity to variation of the spread of the data. The s-chart works better with 10 or more items per sample in order to obtain the s (standard deviation) estimate. The use of a spreadsheet or calculator expedites the calculation of the sample standard deviation.
The formula for the sample standard deviation is
Σ is the summation sign
X are the individual measurements
X-bar is the average of the individual measurements in a sample
n is the sample size
The X-bar chart construction is the same as described above except we use s for the control limit calculations with the following two formulas
X-double bar is the grand average
A3 is the factor to determine X-bar control limits based on sample size.
s-bar is the average standard deviation
The control limits for the s-chart use the following formulas
B3 and B4 are factors to determine the control limits adjusted for sample size.
S-bar is the average sample standard deviation and is the center line of the s-chart.
X-bar and s chart factors