s Chart: In this section we described control charts for R and x based on ranges. Control charts for monitoring variation and center (mean) can also be based on standard deviations. An s chart for monitoring variation is constructed by plotting sample standard deviations with a centerline at s (the mean of the sample standard deviations) and control limits at B4s and B3s,where B4and B3 are found in Table 14-2 on page 660 in this section. Construct an s chart for the data of Table 14-1 on page 655. Compare the result to the R chart given in Example 3 “R Chart of Altimeter Errors.”

Refer to the table 14-1 is taken to construct the s-chart.

S-chart contains a sequential mapping of sample standard deviation measure over time.It includes three values:

• Centerline\(\left( {\bar s} \right)\): mean of all sample standard deviation.
• Lower control limit (LCL)
• Upper control limit (UCL)

From the given values of sample standard deviation, the mean for sample standard deviation is computed as,

\(\begin{array}{c}\bar s = \frac{{\sum s }}{{{\rm{Number}}\;{\rm{of}}\;{\rm{days}}}}\\ = \frac{{4.02 + 5.18 + ... + 28.5}}{{20}}\\ = 12.274\end{array}\)

Thus, the centerline of the s-chart is 12.274.

The upper and lower control limits are computed as,

\(\begin{array}{l}L.C.L = {B_3}\bar s\\U.C.L = {B_4}\bar s\end{array}\)

The values of control limits constant is taken from table 14-2 (control tables constant) as\({B_4} = 2.089,\;{B_3} = 0\).

Thus, the values are:

\(\begin{array}{c}L.C.L = 0\left( {12.274} \right)\\ = 0\\U.C.L = 2.089\left( {12.274} \right)\\ = 25.640\end{array}\)

Steps to construct the s-chart are:

Thus, the s-chart is described as follows:

Refer to R-chart from example 3 for altimeter errors, which has the following measure of centerline, lower control limit and upper control limit:

\(\begin{array}{c}\bar R = 30.65\\U.C.L = 64.79\\L.C.L = 0\end{array}\)

It is observed that the pattern of R-chart is almost same as the s-chart expressed above, though the reference scale for the observations are different.