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XSCHART Statement |
The following notation is used in this section:
![]() | process mean (expected value of the population of measurements) |
![]() | process standard deviation (standard deviation of the population of measurements) |
![]() | mean of measurements in i th subgroup |
si | standard deviation of the measurements
xi1, ... ,xini in the i th subgroup
|
ni | sample size of i th subgroup |
N | number of subgroups |
![]() | weighted average of subgroup means |
zp | 100p th percentile of the standard normal distribution |
c4(n) | expected value of the standard deviation of n independent normally distributed variables with unit standard deviation |
c5(n) | standard error of the standard deviation of n independent observations from a normal population with unit standard deviation |
![]() | 100p th percentile (0<p<1) of the ![]() |
On the s chart, by default, the central line
for the i th subgroup
indicates an estimate for the expected value of si, 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 ni.
The following table provides the formulas for the limits:
Table 44.22: Limits forControl Limits | |
![]() | LCL = lower limit ![]() |
UCL = upper limit ![]() | |
s Chart | LCL = lower limit ![]() |
UCL = upper limit = ![]() |
Probability Limits | |
![]() | LCL = lower limit ![]() |
UCL = upper limit ![]() | |
s Chart | LCL = lower limit ![]() |
UCL = upper limit ![]() |
The formulas for s charts
assume
that the data are normally distributed.
If standard values and
are available
for
and
, respectively,
replace
with
and
with
in Table 44.22.
Note that the limits vary with
ni and that the probability limits
for si are asymmetric about the central line.
You can specify parameters for the limits as follows:
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