How is the standard deviation calculated for the different moving average control charts in JMP®?
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| Last Modified:
EWMA and UWMA Charts
The estimate for σ is
where N is the number of subgroups for which ni≥2, si is the standard deviation of the i th subgroup
and
Here
denotes the gamma function and
denotes the i th subgroup mean. A subgroup standard deviation si is included in the claculation only if ni≥2. If the observations are normally distributed, then the expected value of si is c4(ni)σ. Thus,
is the unweighted average of N unbiased estimates of σ.
When each subgroup sample contains a single observation (ni=1), the process standard deviation σ is estimated as
where N is the number of observations and xi,x2,...,xn are the individual measurements.
[Previously JMP Note 35442]