MCHART Statement: SHEWHART Procedure
Constructing Median Charts
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 |
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sample size of |
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the number of subgroups |
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weighted average of subgroup means |
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median of the measurements in the
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average of the subgroup medians:
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median of the subgroup medians. Denote the
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standard error of the median of |
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100 |
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100 |
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100 |
th subgroup 
th measurement in the 
so that 
. Then 
independent, normally distributed variables with unit standard deviation (the value of 
th percentile 
of the distribution of the median of 
Plotted Points
Each point on a median chart indicates the value of a subgroup median (
). For example, if the tenth subgroup contains the values 12, 15, 19, 16, and 14, the value plotted for this subgroup is 
.
Central Line
The value of the central line indicates an estimate for 
, which is computed as
by default 
when you specify MEDCENTRAL=AVGMEAN 
when you specify MEDCENTRAL=MEDMED 
when you specify 
with the MU0= option
Control Limits
You can compute the limits
as a specified multiple (
) of the standard error of above and below the central line. The default limits are computed with 
(these are referred to as 
limits). as probability limits defined in terms of
, a specified probability that exceeds the limits
The following table provides the formulas for the limits:
Control Limits |
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LCLM |
UCLM |
Probability Limits |
LCLM |
UCLM |
lower limit = 
Note that the limits vary with 
. In Table 15.26, replace with if you specify MEDCENTRAL=AVGMEAN, and replace with if you specify MEDCENTRAL=MEDMED. Replace with if you specify with the MU0= option, and replace 
with 
if you specify with the SIGMA0= option. The formulas assume that the data are normally distributed.
You can specify parameters for the limits as follows:
Specify
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 the LIMITS= data set. Specify
with the SIGMA0= option or with the variable _STDDEV_ in the LIMITS= data set.