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XSCHART Statement |

See SHWXS4 in the SAS/QC Sample Library |

The standard
control limits for *s* charts (see Table 44.22)
are calculated under the assumption
that the data are normally distributed.
This example illustrates how a tranformation to normality
can be used in conjunction with and *s* charts.

The length of a metal brace is measured in centimeters for each of 20 braces sampled daily. Subgroup samples are collected for nineteen days, and the data are analyzed to determine if the manufacturing process is in statistical control.

data lengdata; informat day date7.; format day date5.; label length='Brace Length (cm)'; input day @; do i=1 to 5; input length @; output; end; drop i; datalines; 02JAN86 113.64 119.60 111.66 111.88 125.29 02JAN86 114.08 115.28 127.84 109.97 109.34 02JAN86 109.65 121.76 112.17 116.01 111.64 02JAN86 112.70 114.43 110.27 114.76 125.89 03JAN86 115.92 113.62 117.52 114.44 118.08 03JAN86 111.13 118.42 112.16 112.25 107.71 03JAN86 110.46 113.78 109.89 114.59 116.98 03JAN86 111.06 113.76 115.53 110.88 115.47 . . . . . . . . . . . . . . . . . . 20JAN86 112.84 109.01 110.03 114.44 115.21 20JAN86 115.15 112.34 114.99 109.70 111.20 20JAN86 117.81 119.51 109.03 111.61 118.01 20JAN86 113.55 114.78 112.91 111.87 118.54 ;

The following statements create preliminary and *s* charts
for the lengths:

title 'Mean and Standard Deviation Charts for Brace Length'; symbol v=dot c=salmon; proc shewhart data=lengdata; xschart length*day / cframe = lib cinfill = bwh cconnect = salmon; run;

The charts are shown in Output 44.3.1.

The

The following statements create a box chart for the lengths (for more information on box charts, see Chapter 32, "BOXCHART Statement").

title 'Box Chart for Brace Length'; proc shewhart data=lengdata; boxchart length*day / serifs nolegend nohlabel cinfill = bwh cboxfill = ywh cboxes = black cframe = lib; run;The chart, shown in Output 44.3.2, reveals that most of the subgroup distributions are skewed to the right. Consequently, the

No special cause for the skewness of the subgroup distributions is discovered. This indicates that the process is in statistical control and that the length distribution is naturally skewed.

The following statements apply a lognormal transformation to the length measurements and display a box chart for the transformed data:

data lengdata; set lengdata; logleng=log(length-105); label logleng='log(Length-105)'; run;

title 'Box Chart for log(Length-105)'; proc shewhart data=lengdata; boxchart logleng*day / serifs nohlabel nolegend cinfill = bwh cboxfill = ywh cboxes = black cframe = lib; run;

The chart, shown in Output 44.3.3, indicates that the subgroup distributions of LOGLENG are approximately normal (this can be verified with goodness-of-fit tests by using the CAPABILITY procedure).

Finally, and *s* charts, shown in Output 44.3.4,
are created for LOGLENG. They
indicate that the
variability and mean level of the transformed
lengths are in control.

title 'Mean and Standard Deviation Charts for log(Length)'; proc shewhart data=lengdata; xschart logleng*day / split = '/' cframe = lib cinfill = bwh cconnect = salmon; label logleng='Avg log of Length/Std Dev'; run;

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