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XRCHART 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 | |
R_{i} | range of measurements in i^{ th} subgroup |
n_{i} | sample size of i^{ th} subgroup |
N | number of subgroups |
weighted average of subgroup means | |
d_{2}(n) | expected value of the range of n independent normally distributed variables with unit standard deviation |
d_{3}(n) | standard error of the range of n independent observations from a normal population with unit standard deviation |
z_{p} | 100p^{ th} percentile of the standard normal distribution |
D_{p}(n) | 100p^{ th} percentile of the distribution of the range of n independent observations from a normal population with unit standard deviation |
If you specify a known value () for ,the central line indicates the value of .
On an R chart, by default, the central line for the i^{ th} subgroup indicates an estimate for the expected value of R_{i}, 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 n_{i}.
The following table provides the formulas for the limits:
Table 43.22: Limits for and R ChartsControl Limits | |
Chart | LCL = lower limit |
UCL = upper limit | |
R Chart | LCL = lower limit |
UCL = upper limit = |
Probability Limits | |
Chart | LCL = lower limit |
UCL = upper limit | |
R Chart | LCL = lower limit |
UCL = upper limit |
The formulas for R charts assume that the data are normally distributed. If standard values and are available for and , respectively, replace with and with in Table 43.22. Note that the limits vary with n_{i} and that the probability limits for R_{i} are asymmetric around the central line.
You can specify parameters for the limits as follows:
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