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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  
s_{i}  standard deviation of the measurements
x_{i1}, ... ,x_{ini} in the i^{ th} subgroup

n_{i}  sample size of i^{ th} subgroup 
N  number of subgroups 
weighted average of subgroup means  
z_{p}  100p^{ th} percentile of the standard normal distribution 
c_{4}(n)  expected value of the standard deviation of n independent normally distributed variables with unit standard deviation 
c_{5}(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 distribution with n degrees of freedom 
On the s chart, by default, the central line for the i^{ th} subgroup indicates an estimate for the expected value of s_{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 44.22: Limits for and s ChartsControl Limits  
Chart  LCL = lower limit 
UCL = upper limit  
s Chart  LCL = lower limit 
UCL = upper limit = 
Probability Limits  
Chart  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 n_{i} and that the probability limits for s_{i} are asymmetric about the central line.
You can specify parameters for the limits as follows:
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