Process Performance Indices

When monitoring a process via a quality control chart (e.g., the X-bar and R-chart; Quality Control Charts) it is often useful to compute the process capability indices for the process. Specifically, when the data set consists of multiple samples, such as data collected for the quality control chart, then we can compute two different indices of variability in the data. One is the regular standard deviation for all observations, ignoring the fact that the data consist of multiple samples; the other is to estimate the process's inherent variation from the within-sample variability. For example, when plotting X-bar and R-charts one may use the common estimator R-bar/d2 for the process sigma (e.g., see Duncan, 1974; Montgomery, 1985, 1991). Note however, that this estimator is only valid if the process is statistically stable. For a detailed discussion of the difference between the total process variation and the inherent variation refer to ASQC/AIAG reference manual (ASQC/AIAG, 1991, page 80).

When the total process variability is used in the standard capability computations, the resulting indices are usually referred to as process performance indices (as they describe the actual performance of the process; common indices are Pp, Pr, and Ppk), while indices computed from the inherent variation (within-sample sigma) are referred to as capability indices (since they describe the inherent capability of the process; common indices are Cp, Cr, and Cpk).

For additional information, see Process Capability Indices; for computational details, see Process Capability Indices in the Process (Machine) Capability Analysis overview.