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The SHEWHART Procedure |
The following notation is used in this section:
|
process standard deviation (standard deviation of the population of measurements) |
|
range of measurements in |
|
sample size of |
|
expected value of the range of |
|
standard error of the range of |
|
100 |
Each point on an chart indicates the value of a subgroup range (
). For example, if the tenth subgroup contains the values 12, 15, 19, 16, and 14, the value plotted for this subgroup is
.
By default, the central line for the th subgroup indicates an estimate of the expected value of
, which is computed as
, where
is an estimate of
. If you specify a known value (
) for
, the central line indicates the value of
. Note that the central line varies with
.
You can compute the limits in the following ways:
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 |
---|
LCL |
UCL |
Probability Limits |
---|
LCL |
UCL |
The formulas assume that the data are normally distributed. Note that the control limits vary with and that the probability limits for
are asymmetric around the central line. If a standard value
is available for
, replace
with
in Table 13.48.
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 SIGMA0= option or with the variable _STDDEV_ in a LIMITS= data set.
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