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ProcessControl

 XBarChart
 generate the X-bar chart

 Calling Sequence XBarChart(X, n, options, plotoptions)

Parameters

 X - data n - (optional) sample size options - (optional) equation(s) of the form option=value where option is one of color, confidencelevel, controllimits, ignore, mu, sigma, or speclimits; specify options for generating the X-bar chart plotoptions - (optional) parameters to pass to the plot command

Description

 • The XBarChart command generates control chart for the average mean level (X-bar chart) for the observations. The chart also contains the upper control limit (UCL), the lower control limit (LCL), and the mean value (represented by the center line) of the underlying quality characteristic. Unless explicitly given, the mean, 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.

Computation

 • 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.

Options

 The options argument can contain one or more of the following options.
 • color=list -- This option specifies colors of the various components of the X-bar 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 XBarChart command. Missing values are represented by undefined or Float(undefined). So, if ignore=false and X contains missing data, the XBarChart 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.
 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{ProcessControl}\right):$
 > $\mathrm{infolevel}\left[\mathrm{ProcessControl}\right]≔1:$
 > $A≔\left[\left[74.030,74.002,74.019,73.992,74.008\right],\left[73.995,73.992,74.001,74.011,74.004\right],\left[73.988,74.024,74.021,74.005,74.002\right],\left[74.002,73.996,73.993,74.015,74.009\right],\left[73.992,74.007,74.015,73.989,74.014\right],\left[74.009,73.994,73.997,73.985,73.993\right],\left[73.995,74.006,73.994,74.000,74.005\right],\left[73.985,74.003,73.993,74.015,73.988\right],\left[74.008,73.995,74.009,74.005,74.004\right],\left[73.998,74.000,73.990,74.007,73.995\right],\left[73.994,73.998,73.994,73.995,73.990\right],\left[74.004,74.000,74.007,74.000,73.996\right],\left[73.983,74.002,73.998,73.997,74.012\right],\left[74.006,73.967,73.994,74.000,73.984\right],\left[74.012,74.014,73.998,73.999,74.007\right],\left[74.000,73.984,74.005,73.998,73.996\right],\left[73.994,74.012,73.986,74.005,74.007\right],\left[74.006,74.010,74.018,74.003,74.000\right],\left[73.984,74.002,74.003,74.005,73.997\right],\left[74.000,74.010,74.013,74.020,74.003\right],\left[73.982,74.001,74.015,74.005,73.996\right],\left[74.004,73.999,73.990,74.006,74.009\right],\left[74.010,73.989,73.990,74.009,74.014\right],\left[74.015,74.008,73.993,74.000,74.010\right],\left[73.982,73.984,73.995,74.017,74.013\right]\right]:$
 > $B≔\left[\left[74.030,74.002,74.019,73.992,74.008\right],\left[73.995,73.992,74.001,\mathrm{undefined},\mathrm{undefined}\right],\left[73.988,74.024,74.021,74.005,74.002\right],\left[74.002,73.996,73.993,74.015,74.009\right],\left[73.992,74.007,74.015,73.989,74.014\right],\left[74.009,73.994,73.997,73.985,\mathrm{undefined}\right],\left[73.995,74.006,73.994,74.000,\mathrm{undefined}\right],\left[73.985,74.003,73.993,74.015,73.988\right],\left[74.008,73.995,74.009,74.005,\mathrm{undefined}\right],\left[73.998,74.000,73.990,74.007,73.995\right],\left[73.994,73.998,73.994,73.995,73.990\right],\left[74.004,74.000,74.007,74.000,73.996\right],\left[73.983,74.002,73.998,\mathrm{undefined},\mathrm{undefined}\right],\left[74.006,73.967,73.994,74.000,73.984\right],\left[74.012,74.014,73.998,\mathrm{undefined},\mathrm{undefined}\right],\left[74.000,73.984,74.005,73.998,73.996\right],\left[73.994,74.012,73.986,74.005,74.007\right],\left[74.006,74.010,74.018,74.003,74.000\right],\left[73.984,74.002,74.003,74.005,73.997\right],\left[74.000,74.010,74.013,\mathrm{undefined},\mathrm{undefined}\right],\left[73.982,74.001,74.015,74.005,73.996\right],\left[74.004,73.999,73.990,74.006,74.009\right],\left[74.010,73.989,73.990,74.009,74.014\right],\left[74.015,74.008,73.993,74.000,74.010\right],\left[73.982,73.984,73.995,74.017,74.013\right]\right]:$
 > $\mathrm{XBarChart}\left(A\right)$
 Sample Size:              constant Estimated Control Limits: [73.9877711281404, 74.0145808718596]
 > $\mathrm{XBarChart}\left(B\right)$
 Sample Size:              variable
 > $\mathrm{XBarControlLimits}\left(A\right)$
 Sample Size:              constant
 $\left[{73.9877711281404}{,}{74.0145808718596}\right]$ (1)
 > $l≔\mathrm{XBarControlLimits}\left(A,\mathrm{confidencelevel}=0.95\right)$
 Sample Size:              constant
 ${l}{≔}\left[{73.9924183113334}{,}{74.0099336886665}\right]$ (2)
 > $\mathrm{XBarChart}\left(A,\mathrm{controllimits}=l\right)$
 Estimated Control Limits: [73.9924183113334, 74.0099336886665]
 > $l≔\mathrm{XBarControlLimits}\left(B,\mathrm{confidencelevel}=0.95\right)$
 Sample Size:              variable
 ${l}{≔}\left[\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9860144584327}{,}{74.0156375415672}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9902789378588}{,}{74.0113730621412}\right]{,}\left[{73.9902789378588}{,}{74.0113730621412}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9902789378588}{,}{74.0113730621412}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9860144584327}{,}{74.0156375415672}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9860144584327}{,}{74.0156375415672}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9860144584327}{,}{74.0156375415672}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]{,}\left[{73.9924752951441}{,}{74.0091767048559}\right]\right]$ (3)
 > $\mathrm{XBarChart}\left(B,\mathrm{controllimits}=l\right)$

References

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

 See Also