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ProcessControl

 RControlLimits
 compute control limits for the R chart

 Calling Sequence RControlLimits(X, n, options)

Parameters

 X - data n - (optional) sample size options - (optional) equation(s) of the form option=value where option is one of confidencelevel, ignore, or rbar; specify options for computing the control limits

Description

 • The RControlLimits command computes the upper and lower control limits for the R chart. Unless explicitly given, the average range of individual samples is 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.
 • 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 RControlLimits command. Missing values are represented by undefined or Float(undefined). So, if ignore=false and X contains missing data, the RControlLimits command returns undefined. If ignore=true, all missing items in X are ignored. The default value is true.
 • rbar=deduce or realcons -- This option specifies the average range of individual samples.

Examples

 > $\mathrm{with}\left(\mathrm{ProcessControl}\right):$
 > ${\mathrm{infolevel}}_{\mathrm{ProcessControl}}≔1:$
 > $A≔\left[\left[74.030,74.002,74.019,73.992,74.008\right],\left[73.995,73.992,74.001,74.011,74.004\right],\left[73.988,74.024,74.021,74.005,74.002\right],\left[74.002,73.996,73.993,74.015,74.009\right],\left[73.992,74.007,74.015,73.989,74.014\right],\left[74.009,73.994,73.997,73.985,73.993\right],\left[73.995,74.006,73.994,74.000,74.005\right],\left[73.985,74.003,73.993,74.015,73.988\right],\left[74.008,73.995,74.009,74.005,74.004\right],\left[73.998,74.000,73.990,74.007,73.995\right],\left[73.994,73.998,73.994,73.995,73.990\right],\left[74.004,74.000,74.007,74.000,73.996\right],\left[73.983,74.002,73.998,73.997,74.012\right],\left[74.006,73.967,73.994,74.000,73.984\right],\left[74.012,74.014,73.998,73.999,74.007\right],\left[74.000,73.984,74.005,73.998,73.996\right],\left[73.994,74.012,73.986,74.005,74.007\right],\left[74.006,74.010,74.018,74.003,74.000\right],\left[73.984,74.002,74.003,74.005,73.997\right],\left[74.000,74.010,74.013,74.020,74.003\right],\left[73.982,74.001,74.015,74.005,73.996\right],\left[74.004,73.999,73.990,74.006,74.009\right],\left[74.010,73.989,73.990,74.009,74.014\right],\left[74.015,74.008,73.993,74.000,74.010\right],\left[73.982,73.984,73.995,74.017,74.013\right]\right]:$
 > $B≔\left[\left[74.030,74.002,74.019,73.992,74.008\right],\left[73.995,73.992,74.001,\mathrm{undefined},\mathrm{undefined}\right],\left[73.988,74.024,74.021,74.005,74.002\right],\left[74.002,73.996,73.993,74.015,74.009\right],\left[73.992,74.007,74.015,73.989,74.014\right],\left[74.009,73.994,73.997,73.985,\mathrm{undefined}\right],\left[73.995,74.006,73.994,74.000,\mathrm{undefined}\right],\left[73.985,74.003,73.993,74.015,73.988\right],\left[74.008,73.995,74.009,74.005,\mathrm{undefined}\right],\left[73.998,74.000,73.990,74.007,73.995\right],\left[73.994,73.998,73.994,73.995,73.990\right],\left[74.004,74.000,74.007,74.000,73.996\right],\left[73.983,74.002,73.998,\mathrm{undefined},\mathrm{undefined}\right],\left[74.006,73.967,73.994,74.000,73.984\right],\left[74.012,74.014,73.998,\mathrm{undefined},\mathrm{undefined}\right],\left[74.000,73.984,74.005,73.998,73.996\right],\left[73.994,74.012,73.986,74.005,74.007\right],\left[74.006,74.010,74.018,74.003,74.000\right],\left[73.984,74.002,74.003,74.005,73.997\right],\left[74.000,74.010,74.013,\mathrm{undefined},\mathrm{undefined}\right],\left[73.982,74.001,74.015,74.005,73.996\right],\left[74.004,73.999,73.990,74.006,74.009\right],\left[74.010,73.989,73.990,74.009,74.014\right],\left[74.015,74.008,73.993,74.000,74.010\right],\left[73.982,73.984,73.995,74.017,74.013\right]\right]:$
 > $\mathrm{RControlLimits}\left(A\right)$
 Sample Size:              constant
 $\left[{0.}{,}{0.0491377128733060}\right]$ (1)
 > $\mathrm{RControlLimits}\left(A,\mathrm{confidencelevel}=0.95\right)$
 Sample Size:              constant
 $\left[{0.00632047186904479}{,}{0.0401595281309555}\right]$ (2)
 > $\mathrm{RControlLimits}\left(B\right)$
 Sample Size:              variable
 $\left[\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0570296043357637}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0505730160947950}\right]{,}\left[{0.}{,}{0.0505730160947950}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0505730160947950}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0570296043357637}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0570296043357637}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0570296043357637}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]{,}\left[{0.}{,}{0.0468542047019142}\right]\right]$ (3)
 > $\mathrm{RControlLimits}\left(B,\mathrm{confidencelevel}=0.95\right)$
 Sample Size:              variable
 $\left[\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.}{,}{0.0449410561635488}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.00359717063151698}{,}{0.0407228293684843}\right]{,}\left[{0.00359717063151698}{,}{0.0407228293684843}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.00359717063151698}{,}{0.0407228293684843}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.}{,}{0.0449410561635488}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.}{,}{0.0449410561635488}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.}{,}{0.0449410561635488}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]{,}\left[{0.00602674942418399}{,}{0.0382932505758173}\right]\right]$ (4)

References

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

 See Also

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