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MCHART Statement |
![]() | 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 |
ni | sample size of i th subgroup |
N | the number of subgroups |
xij | j th measurement in the i th subgroup, j = 1,2,3, ... , ni |
xi(j) | j th largest measurement in
the i th subgroup. Then
|
![]() | weighted average of subgroup means |
Mi | median of the measurements in the i th subgroup:
|
![]() | average of the subgroup medians:
|
![]() | median of the subgroup medians. Denote the
j th largest median by
M(j) so that ![]() |
eM(n) | standard error of the median of n independent, normally distributed variables with unit standard deviation (the value of eM(n) can be calculated with the STDMED function in a DATA step) |
Qp(n) | 100p th percentile (0<p<1) of the distribution of the median of n independent observations from a normal population with unit standard deviation |
zp | 100p th percentile of the standard normal distribution |
Dp(n) | 100p th percentile of the distibution of the range of n independent observations from a normal population with unit standard deviation |
The following table provides the formulas for the limits:
Table 35.22: Limits for Median ChartsControl Limits |
LCLM = lower limit ![]() |
UCLM = upper limit ![]() |
Probability Limits |
LCLM = lower limit ![]() |
UCLM = upper limit ![]() |
Note that the limits vary with ni.
In Table 35.22,
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:
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