The SChart command generates control chart for the standard deviation (S chart) for the specified observations. The chart also contains the upper control limit (UCL), the lower control limit (LCL), and the standard deviation (represented by the center line) of the underlying quality characteristic. Unless explicitly given, the standard deviation and the control limits are computed based on the data.

The first parameter X is either a single data sample - given as a Vector or list - or a list of data samples. Each value represents an individual observation. Note, that the individual samples can be of variable size.

If X is a single data sample, the second parameter n is used to specify the size of individual samples.

All computations involving data are performed in floating-point; therefore, all data provided must have type realcons and all returned solutions are floating-point, even if the problem is specified with exact values.

For more information about computation in the ProcessControl package, see the ProcessControl help page.

The options argument can contain one or more of the following options.

color=list -- This option specifies colors of the various components of the S chart. The value of this option must be a list containing the color of the control limits, center line, data to be plotted, and the specification limits.

confidencelevel=realcons -- This option specifies the required confidence level. The default value is 0.9973, corresponding to a 3 sigma confidence level.

controllimits=deduce or [realcons, realcons] -- This option specifies the values for the control limits. The first element is the value of the lower control limit. The second element is the value of the upper control limit. For data with variable sample size, the value of this option must be a list of control limits for each sample. If this option is set to deduce (the default value), the control limits are computed based on the data.

ignore=truefalse -- This option controls how missing values are handled by the SChart command. Missing values are represented by undefined or Float(undefined). So, if ignore=false and X contains missing data, the SChart command returns undefined. If ignore=trues all missing items in X are ignored. The default value is true.

sigma=deduce or realcons -- This option specifies the standard deviation of the underlying quality characteristic.

speclimits=none, [realcons, realcons] -- This option specifies the values for the specification limits. The first element is the value of the lower specification limit. The second element is the value of the upper specification limit. The default value is none.

$\mathrm{with}\left(\mathrm{ProcessControl}\right)\:$

$\mathrm{infolevel}\left[\mathrm{ProcessControl}\right]≔1\:$

$A≔\left[\left[74.030\,74.002\,74.019\,73.992\,74.008\right]\,\left[73.995\,73.992\,74.001\,74.011\,74.004\right]\,\left[73.988\,74.024\,74.021\,74.005\,74.002\right]\,\left[74.002\,73.996\,73.993\,74.015\,74.009\right]\,\left[73.992\,74.007\,74.015\,73.989\,74.014\right]\,\left[74.009\,73.994\,73.997\,73.985\,73.993\right]\,\left[73.995\,74.006\,73.994\,74.000\,74.005\right]\,\left[73.985\,74.003\,73.993\,74.015\,73.988\right]\,\left[74.008\,73.995\,74.009\,74.005\,74.004\right]\,\left[73.998\,74.000\,73.990\,74.007\,73.995\right]\,\left[73.994\,73.998\,73.994\,73.995\,73.990\right]\,\left[74.004\,74.000\,74.007\,74.000\,73.996\right]\,\left[73.983\,74.002\,73.998\,73.997\,74.012\right]\,\left[74.006\,73.967\,73.994\,74.000\,73.984\right]\,\left[74.012\,74.014\,73.998\,73.999\,74.007\right]\,\left[74.000\,73.984\,74.005\,73.998\,73.996\right]\,\left[73.994\,74.012\,73.986\,74.005\,74.007\right]\,\left[74.006\,74.010\,74.018\,74.003\,74.000\right]\,\left[73.984\,74.002\,74.003\,74.005\,73.997\right]\,\left[74.000\,74.010\,74.013\,74.020\,74.003\right]\,\left[73.982\,74.001\,74.015\,74.005\,73.996\right]\,\left[74.004\,73.999\,73.990\,74.006\,74.009\right]\,\left[74.010\,73.989\,73.990\,74.009\,74.014\right]\,\left[74.015\,74.008\,73.993\,74.000\,74.010\right]\,\left[73.982\,73.984\,73.995\,74.017\,74.013\right]\right]\:$

$B≔\left[\left[74.030\,74.002\,74.019\,73.992\,74.008\right]\,\left[73.995\,73.992\,74.001\,\mathrm{undefined}\,\mathrm{undefined}\right]\,\left[73.988\,74.024\,74.021\,74.005\,74.002\right]\,\left[74.002\,73.996\,73.993\,74.015\,74.009\right]\,\left[73.992\,74.007\,74.015\,73.989\,74.014\right]\,\left[74.009\,73.994\,73.997\,73.985\,\mathrm{undefined}\right]\,\left[73.995\,74.006\,73.994\,74.000\,\mathrm{undefined}\right]\,\left[73.985\,74.003\,73.993\,74.015\,73.988\right]\,\left[74.008\,73.995\,74.009\,74.005\,\mathrm{undefined}\right]\,\left[73.998\,74.000\,73.990\,74.007\,73.995\right]\,\left[73.994\,73.998\,73.994\,73.995\,73.990\right]\,\left[74.004\,74.000\,74.007\,74.000\,73.996\right]\,\left[73.983\,74.002\,73.998\,\mathrm{undefined}\,\mathrm{undefined}\right]\,\left[74.006\,73.967\,73.994\,74.000\,73.984\right]\,\left[74.012\,74.014\,73.998\,\mathrm{undefined}\,\mathrm{undefined}\right]\,\left[74.000\,73.984\,74.005\,73.998\,73.996\right]\,\left[73.994\,74.012\,73.986\,74.005\,74.007\right]\,\left[74.006\,74.010\,74.018\,74.003\,74.000\right]\,\left[73.984\,74.002\,74.003\,74.005\,73.997\right]\,\left[74.000\,74.010\,74.013\,\mathrm{undefined}\,\mathrm{undefined}\right]\,\left[73.982\,74.001\,74.015\,74.005\,73.996\right]\,\left[74.004\,73.999\,73.990\,74.006\,74.009\right]\,\left[74.010\,73.989\,73.990\,74.009\,74.014\right]\,\left[74.015\,74.008\,73.993\,74.000\,74.010\right]\,\left[73.982\,73.984\,73.995\,74.017\,74.013\right]\right]\:$

$\mathrm{SChart}\left(A\right)$

Estimate for Sigma:       .0100257668035915
Sample Size:              constant
Estimated Sigma:          .0106658727200108
Estimated Control Limits: [0, .0209438055041708]

$\mathrm{SChart}\left(B\right)$

Estimate for Sigma:       .0102595438349069
Sample Size:              variable

$\mathrm{SControlLimits}\left(A\right)$

Sample Size:              constant
Estimated Sigma:          .0106658727200108

$\left[0.\,0.0209438055041708\right]$

$l≔\mathrm{SControlLimits}\left(A\,\mathrm{confidencelevel}=0.95\right)$

Sample Size:              constant
Estimated Sigma:          .0106658727200108

$l≔\left[0.00289277927558015\,0.0171587543316029\right]$

$\mathrm{SChart}\left(A\,\mathrm{controllimits}=l\right)$

Estimate for Sigma:       .0100257668035915
Estimated Control Limits: [.00289277927558015, .0171587543316029]

$l≔\mathrm{SControlLimits}\left(B\,\mathrm{confidencelevel}=0.95\right)$

Sample Size:              variable

$l≔\left[\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.\,0.0207706378059104\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.00177351030162367\,0.0187455773681901\right]\,\left[0.00177351030162367\,0.0187455773681901\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.00177351030162367\,0.0187455773681901\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.\,0.0207706378059104\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.\,0.0207706378059104\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.\,0.0207706378059104\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\,\left[0.00296023200659628\,0.0175588556632175\right]\right]$

$\mathrm{SChart}\left(B\,\mathrm{controllimits}=l\right)$

Estimate for Sigma:       .0102595438349069

Montgomery, Douglas C. Introduction to Statistical Quality Control. 2nd ed. New York: John Wiley & Sons, 1991.