The XBarControlLimits command computes the upper and lower control limits for the X-bar chart. Unless explicitly given, the mean and the standard deviation of the underlying quality characteristic 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.

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

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

mu=deduce or realcons -- This option specifies the mean of the underlying quality characteristic.

sigma=deduce, sbar, or rbar -- This option specifies how standard deviation of the underlying quality characteristic should be computed. It can be estimated either using the ranges or using the standard deviations of the individual samples. By default, the ranges are used for samples sizes less than 10. The range option cannot be uses for sample sizes larger than 25.

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

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

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

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

$\mathrm{XBarControlLimits}\left(A\,\mathrm{\sigma }=\mathrm{sbar}\right)$

Sample Size:              constant

$\left[73.9868662301027\,74.0154857698973\right]$

$\mathrm{XBarControlLimits}\left(A\,\mathrm{\sigma }=\mathrm{rbar}\right)$

Sample Size:              constant

$\left[73.9877711281404\,74.0145808718596\right]$

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

Sample Size:              constant

$\left[73.9877711281404\,74.0145808718596\right]$

$\mathrm{XBarControlLimits}\left(A\,\mathrm{confidencelevel}=0.95\right)$

Sample Size:              constant

$\left[73.9924183113334\,74.0099336886665\right]$

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

Sample Size:              variable

$\left[\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9781548564698\,74.0234971435302\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9846822408552\,74.0169697591448\right]\,\left[73.9846822408552\,74.0169697591448\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9846822408552\,74.0169697591448\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9781548564698\,74.0234971435302\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9781548564698\,74.0234971435302\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9781548564698\,74.0234971435302\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9880440739927\,74.0136079260073\right]\,\left[73.9880440739927\,74.0136079260073\right]\right]$

$\mathrm{XBarControlLimits}\left(B\,\mathrm{confidencelevel}=0.95\right)$

Sample Size:              variable

$\left[\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9860144584327\,74.0156375415672\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9902789378588\,74.0113730621412\right]\,\left[73.9902789378588\,74.0113730621412\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9902789378588\,74.0113730621412\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9860144584327\,74.0156375415672\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9860144584327\,74.0156375415672\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9860144584327\,74.0156375415672\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9924752951441\,74.0091767048559\right]\,\left[73.9924752951441\,74.0091767048559\right]\right]$

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