The SPC Procedure

Constructing Charts for Standard Deviations

You produce control charts for standard deviations by using the SCHART or XSCHART statement. The following notation is used in this section:

	Process standard deviation (standard deviation of the population of measurements)
	Standard deviation of measurements in ith subgroup
	Sample size of ith subgroup
	Expected value of the standard deviation of n independent normally distributed variables with unit standard deviation
	Standard error of the standard deviation of n independent observations from a normal population with unit standard deviation

Subgroup Summary Statistics

Each point on an s chart indicates the value of a subgroup standard deviation (). For example, if the 10th subgroup contains the values 12, 15, 19, 16, and 13, the subgroup summary statistic is

Central Line

By default, the central line for the ith subgroup indicates an estimate for the expected value of , 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 .

Control Limits

The control limits are computed as a specified multiple (k) of the standard error of above and below the central line. The default limits are computed using k = 3 (these are referred to as limits).

Table 20.22 provides the formulas for the limits.

Table 20.22: Control Limits for s Charts

LCL = lower limit =

UCL = upper limit =

The formulas assume that the data are normally distributed. If a standard value is available for , replace with in Table 20.22. Note that the upper and lower limits vary with .

You can specify parameters for the limits as follows:

Specify k by using the SIGMAS= option or the variable _SIGMAS_ in a LIMITS= data table.
Specify a constant nominal sample size for the control limits by using the LIMITN= option or the variable _LIMITN_ in a LIMITS= data table.
Specify by using the variable _STDDEV_ in a LIMITS= data table.

Last updated: December 21, 2018