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. Then
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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 . Then
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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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100pth 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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100pth percentile of the standard normal distribution |
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100pth percentile of the distribution of the range of n independent observations from a normal population with unit standard deviation |
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 .
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
You can compute the limits
as a specified multiple (k) of the standard error of 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 exceeds the limits
The following table provides the formulas for the limits:
Table 17.26: Limits for Median Charts
Control Limits |
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LCLM = lower limit = |
UCLM = upper limit = |
Probability Limits |
LCLM = lower limit = |
UCLM = upper limit = |
Note that the limits vary with . In Table 17.26, 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 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 the LIMITS= data set.
Specify with the SIGMA0= option or with the variable _STDDEV_
in the LIMITS= data set.