Estimated standard deviation
- Last UpdatedNov 04, 2024
- 3 minute read
The estimated sigma is calculated based on the chart type linked to a characteristic. If sigma_est for a variable is set to 1= use std.dev, the estimated sigma is calculated using the standard population deviation method.
The methods for calculating estimated standard deviation from sample information (when sigma_est = 0) for individual chart types are described in the following table.
|
Default Chart Type |
Calculation |
Description of Terms |
|---|---|---|
|
XBar and Range Chart |
|
S is the number of samples used in calculating the estimated sigma. R is the range from a sample. d2 is the constant (adjustment) factor for the estimated sigma.
|
|
XBar and Sigma Chart |
|
S is the number of samples used in calculating the estimated sigma.
c4 is the constant (adjustment) factor for the estimated sigma.
|
|
Individual and Moving Range Chart |
|
N is the total number of individual readings from all the samples.
d2 is the constant (adjustment) factor for the estimated sigma. |
|
Moving Average and Range Chart |
|
N is the total number of individual readings from all the samples. s is the moving average span configured for a characteristic.
d2 is the constant (adjustment) factor for the estimated sigma. |
|
Moving Average and Sigma Chart |
The moving sigma is calculated as:
The estimated standard deviation is calculated as:
|
Moving sigma: σ is the standard deviation. s is the moving average span configured for a characteristic.
Estimated standard deviation:
N is the total number of individual readings from all the samples. s is the moving average span configured for a characteristic. c4 is the constant (adjustment) factor for the estimated sigma. |
is the estimated standard deviation.
is the number of individual readings for a sample.
is the sample standard deviation.
is the individual result data.
is the individual result data.
is the arithmetic mean from the results data.