Denote the standard deviation of the process by σ. The Process Capability platform provides two types of capability indices. The Ppk indices are based on an estimate of σ that uses all of the data in a way that does not depend on subgroups. This overall estimate may reflect special cause as well as common cause variation. The Cpk indices are based on an estimate that attempts to capture only common cause variation. The Cpk indices are constructed using within-subgroup, or short-term, estimates of σ. In this way, they attempt to reflect the true process standard deviation. When a process is not stable, the overall and within estimates of σ can differ markedly.
The overall sigma does not depend on subgroups. JMP calculates the overall estimate of σ as follows:
N = number of nonmissing values in the entire data set
= mean of nonmissing values in the entire data set
Caution: When the process is stable, the Overall Sigma estimates the process standard deviation. If the process is not stable, the overall estimate of σ is of questionable value, since the process standard deviation is unknown.
An estimate of σ that is based on within-subgroup variation can be constructed in one of three ways:
Within sigma estimated by the average of ranges is the same as the estimate of the standard deviation of an X/R chart:
d2(ni) = expected value of the range of ni independent normally distributed variables with unit standard deviation
N = number of subgroups for which
Within sigma estimated by the average of unbiased standard deviations is the same as the estimate for the standard deviation in an X/S chart:
c4(ni) = expected value of the standard deviation of ni independent normally distributed variables with unit standard deviation
N = number of subgroups for which
Within sigma estimated by moving range is the same as the estimate for the standard deviation for Individual Measurement and Moving Range charts:
d2(2) = expected value of the range of two independent normally distributed variables with unit standard deviation.
= mean of the observations on process 
= standard deviation of the observations on process This section provides details about the calculation of the mean shift and standard deviation standardized to specification quantities plotted in the Goal Plot. This section uses the notation defined in Notation for Goal Plots and Capability Box Plots.
The mean shift and the standard deviation standardized to the specification limits for the jth column are defined as follows:
Note: If either LSLj or USLj is missing, twice the distance from the target to the nonmissing specification limit is used in the denominators of the Goal Plot coordinates.
Suppose that the process has both a lower and an upper specification limit but no target. Then the formulas given in Goal Plot are used, replacing Tj with the midpoint of the two specification limits.
Suppose that the process has only one specification limit and no target. To obtain (x,y) coordinates for a point on the Goal Plot, the capability indices of the process are used. (See Capability Indices for definitions in terms of the theoretical mean and standard deviation.) For sample data, the following relationships hold:
Note: If either Cpu or Cpl is less than -0.6, then it is set to -0.6 in the formulas above. At the value -2/3, the denominator for x assumes the value 0. Bounding the capability values at -0.6 prevents the denominator from assuming the value 0 or switching signs.
A column with no target may have both upper and lower specification limits, or only a single specification limit. This section uses the notation defined in Notation for Goal Plots and Capability Box Plots.
When no target is specified for the jth column, the capability box plot is based on the following values for the transformed observations:
When no target is specified for the jth column, the capability box plot is based on the following values for the transformed observations:
For a process characteristic with mean μ and standard deviation σ, the capability indices are defined as follows:
LSL = lower specification limit
USL = upper specification limit
T = target value
For estimates of Within Sigma capability, σ is estimated using the subgrouping method that you specified. For estimates of Overall Sigma capability, σ is estimated using the sample standard deviation. With the default AIAG (Ppk) Labeling, the indices based on Overall Sigma are denoted by Pp, Ppl, Ppu, and Ppk. The labeling for the index Cpm does not change when Overall Sigma is used.