The following notation is used in this section:
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process mean (expected value of the population of measurements) |
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process standard deviation (standard deviation of the population of measurements) |
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mean of measurements in ith subgroup |
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sample size of ith subgroup |
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N |
the number of subgroups |
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jth measurement in the ith subgroup, |
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jth largest measurement in the ith subgroup:
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weighted average of subgroup means |
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median of the measurements in the ith subgroup:
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average of the subgroup medians:
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median of the subgroup medians. Denote the jth largest median by so that .
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standard error of the median of n independent, normally distributed variables with unit standard deviation (the value of can be calculated with the STDMED function in a DATA step) |
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th percentile (0 < p < 1) of the distribution of the median of n independent observations from a normal population with unit standard deviation |
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th percentile of the standard normal distribution |
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th percentile of the distribution of the range of n independent observations from a normal population with unit standard deviation |
A box-and-whisker plot is displayed for the measurements in each subgroup on the box chart. Figure 17.14 illustrates the elements of each plot.
Figure 17.14: Box-and-Whisker Plot
The skeletal style of the box-and-whisker plot shown in Figure 17.14 is the default. You can specify alternative styles with the BOXSTYLE= option; see Example 17.2 or the entry for BOXSTYLE= in Dictionary of Options: SHEWHART Procedure.
You can compute the limits in the following ways:
as a specified multiple (k) of the standard error of (or ) above and below the central line. The default limits are computed with k = 3 (these are referred to as limits).
as probability limits defined in terms of , a specified probability that (or ) exceeds the limits
The CONTROLSTAT= option specifies whether control limits are computed for subgroup means (the default) or subgroup medians. The following tables provide the formulas for the limits:
Table 17.5: Control Limits and Central Line for Box Charts
CONTROLSTAT=MEAN |
CONTROLSTAT=MEDIAN |
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LCLX = lower limit = |
LCLM = lower limit = |
Central Line = |
Central Line = |
UCLX = upper limit = |
UCLM = upper limit = |
Table 17.6: Probability Limits and Central Line for Box Charts
CONTROLSTAT=MEAN |
CONTROLSTAT=MEDIAN |
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LCLX = lower limit = |
LCLM = lower limit = |
Central Line = |
Central Line = |
UCLX = upper limit = |
UCLM = upper limit = |
In the preceding tables, replace with if you specify MEDCENTRAL=AVGMEAN in addition to CONTROLSTAT=MEDIAN. Likewise, replace with if you specify MEDCENTRAL=MEDMED in addition to CONTROLSTAT=MEDIAN. If standard values and are available for and , replace with and with in Table 17.5 and Table 17.6.
Note that the limits vary with . The formulas for median limits assume that the data are normally distributed.
You can specify parameters for the limits as follows:
Specify k with the SIGMAS= option or with the variable _SIGMAS_
in a LIMITS= data set.
Specify with the ALPHA= option or with the variable _ALPHA_
in a LIMITS= data set.
Specify a constant nominal sample size for the control limits with the LIMITN= option or with the variable _LIMITN_
in a LIMITS= data set.
Specify with the MU0= option or with the variable _MEAN_
in a LIMITS= data set.
Specify with the SIGMA0= option or with the variable _STDDEV_
in a LIMITS= data set.
Note: You can suppress the display of the control limits with the NOLIMITS option. This is useful for creating standard side-by-side box-and-whisker plots.