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 ith subgroup 

range of measurements in ith subgroup 

sample size of ith subgroup 
N 
number of subgroups 

weighted average of subgroup means 

100pth percentile of the standard normal distribution 
Each point on an chart indicates the value of a subgroup mean (). For example, if the tenth subgroup contains the values 12, 15, 19, 16, and 14, the value plotted for this subgroup is

By default, the central line on an chart indicates an estimate for , which is computed as

If you specify a known value () for , the central line indicates the value of .
You can compute the limits in the following ways:
as a specified multiple (k) of the standard error of above and below the central line. The default limits are computed with k = 3 (these are referred to as limits).
as probability limits defined in terms of , a specified probability that exceeds the limits
The following table provides the formulas for the limits:
Table 17.66: Limits for Charts
Control Limits 

LCL = lower limit = 
UCL = upper limit = 
Probability Limits 

LCL = lower limit = 
UCL = upper limit = 
Note that the limits vary with . If standard values and are available for and , respectively, replace with and with in Table 17.66.
You can specify parameters for the limits as follows:
Specify k with the SIGMAS= option or with the variable _SIGMAS_
in a LIMITS= data set.
Specify with the ALPHA= option or with the variable _ALPHA_
in a LIMITS= data set.
Specify a constant nominal sample size for the control limits with the LIMITN= option or with the variable _LIMITN_
in a LIMITS= data set.
Specify with the MU0= option or with the variable _MEAN_
in a LIMITS= data set.
Specify with the SIGMA0= option or with the variable _STDDEV_
in a LIMITS= data set.