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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
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weighted average of subgroup means | |
Mi | median of the measurements in the i th subgroup:
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average of the subgroup medians:
| |
median of the subgroup medians. Denote the
j th largest median by
M(j) so that . Then
| |
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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