SControlLimits - Maple Help

ProcessControl

 SControlLimits
 compute control limits for the S chart

 Calling Sequence SControlLimits(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 sigma; specify options for computing the control limits

Description

 • The SControlLimits command computes the upper and lower control limits for the S chart. Unless explicitly given, the standard deviation of the underlying quality characteristic 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.

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 SControlLimits command. Missing values are represented by undefined or Float(undefined). So, if ignore=false and X contains missing data, the SControlLimits command returns undefined. If ignore=true, 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.

Examples

 > $\mathrm{with}\left(\mathrm{ProcessControl}\right):$
 > ${\mathrm{infolevel}}_{\mathrm{ProcessControl}}≔1:$
 > $A≔\left[\left[74.030,74.002,74.019,73.992,74.008\right],\left[73.995,73.992,74.001,74.011,74.004\right],\left[73.988,74.024,74.021,74.005,74.002\right],\left[74.002,73.996,73.993,74.015,74.009\right],\left[73.992,74.007,74.015,73.989,74.014\right],\left[74.009,73.994,73.997,73.985,73.993\right],\left[73.995,74.006,73.994,74.000,74.005\right],\left[73.985,74.003,73.993,74.015,73.988\right],\left[74.008,73.995,74.009,74.005,74.004\right],\left[73.998,74.000,73.990,74.007,73.995\right],\left[73.994,73.998,73.994,73.995,73.990\right],\left[74.004,74.000,74.007,74.000,73.996\right],\left[73.983,74.002,73.998,73.997,74.012\right],\left[74.006,73.967,73.994,74.000,73.984\right],\left[74.012,74.014,73.998,73.999,74.007\right],\left[74.000,73.984,74.005,73.998,73.996\right],\left[73.994,74.012,73.986,74.005,74.007\right],\left[74.006,74.010,74.018,74.003,74.000\right],\left[73.984,74.002,74.003,74.005,73.997\right],\left[74.000,74.010,74.013,74.020,74.003\right],\left[73.982,74.001,74.015,74.005,73.996\right],\left[74.004,73.999,73.990,74.006,74.009\right],\left[74.010,73.989,73.990,74.009,74.014\right],\left[74.015,74.008,73.993,74.000,74.010\right],\left[73.982,73.984,73.995,74.017,74.013\right]\right]:$
 > $B≔\left[\left[74.030,74.002,74.019,73.992,74.008\right],\left[73.995,73.992,74.001,\mathrm{undefined},\mathrm{undefined}\right],\left[73.988,74.024,74.021,74.005,74.002\right],\left[74.002,73.996,73.993,74.015,74.009\right],\left[73.992,74.007,74.015,73.989,74.014\right],\left[74.009,73.994,73.997,73.985,\mathrm{undefined}\right],\left[73.995,74.006,73.994,74.000,\mathrm{undefined}\right],\left[73.985,74.003,73.993,74.015,73.988\right],\left[74.008,73.995,74.009,74.005,\mathrm{undefined}\right],\left[73.998,74.000,73.990,74.007,73.995\right],\left[73.994,73.998,73.994,73.995,73.990\right],\left[74.004,74.000,74.007,74.000,73.996\right],\left[73.983,74.002,73.998,\mathrm{undefined},\mathrm{undefined}\right],\left[74.006,73.967,73.994,74.000,73.984\right],\left[74.012,74.014,73.998,\mathrm{undefined},\mathrm{undefined}\right],\left[74.000,73.984,74.005,73.998,73.996\right],\left[73.994,74.012,73.986,74.005,74.007\right],\left[74.006,74.010,74.018,74.003,74.000\right],\left[73.984,74.002,74.003,74.005,73.997\right],\left[74.000,74.010,74.013,\mathrm{undefined},\mathrm{undefined}\right],\left[73.982,74.001,74.015,74.005,73.996\right],\left[74.004,73.999,73.990,74.006,74.009\right],\left[74.010,73.989,73.990,74.009,74.014\right],\left[74.015,74.008,73.993,74.000,74.010\right],\left[73.982,73.984,73.995,74.017,74.013\right]\right]:$
 > $\mathrm{SControlLimits}\left(A\right)$
 Sample Size:              constant Estimated Sigma:          .0106658727200108
 $\left[{0.}{,}{0.0209438055041708}\right]$ (1)
 > $\mathrm{SControlLimits}\left(A,\mathrm{confidencelevel}=0.95\right)$
 Sample Size:              constant Estimated Sigma:          .0106658727200108
 $\left[{0.00289277927558015}{,}{0.0171587543316029}\right]$ (2)
 > $\mathrm{SControlLimits}\left(B\right)$
 Sample Size:              variable
 $\left[\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0263482486462044}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0232486093795974}\right]{,}\left[{0.}{,}{0.0232486093795974}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0232486093795974}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0263482486462044}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0263482486462044}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0263482486462044}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]{,}\left[{0.}{,}{0.0214321652247706}\right]\right]$ (3)
 > $\mathrm{SControlLimits}\left(B,\mathrm{confidencelevel}=0.95\right)$
 Sample Size:              variable
 $\left[\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.}{,}{0.0207706378059104}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.00177351030162367}{,}{0.0187455773681901}\right]{,}\left[{0.00177351030162367}{,}{0.0187455773681901}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.00177351030162367}{,}{0.0187455773681901}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.}{,}{0.0207706378059104}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.}{,}{0.0207706378059104}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.}{,}{0.0207706378059104}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]{,}\left[{0.00296023200659628}{,}{0.0175588556632175}\right]\right]$ (4)

References

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