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MRCHART 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 | |
Ri | range 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 |
d2(n) | expected value of the range of n independent normally distributed variables with unit standard deviation |
d3(n) | standard error of the range 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 |
On the range chart, by default, the central line for the i th subgroup indicates an estimate for the expected value of Ri, which is computed as ,where is an estimate of . If you specify a known value () for , the central line indicates the value of .The central line on the range chart varies with ni.
The following table provides the formulas for the limits:
Table 36.22: Limits for Median and Range ChartsControl Limits | |
Median Chart | LCL = lower limit |
UCL = upper limit | |
Range Chart | LCL = lower control limit |
UCL = upper control limit = | |
Probability Limits | |
Median Chart | LCL = lower limit |
UCL = upper limit | |
Range Chart | LCL = lower limit |
UCL = upper limit |
In Table 36.22, 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. Note that the limits for both charts vary with ni and that the probability limits for Ri are asymmetric around the central line.
You can specify parameters for the limits as follows:
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