Variance Components

To determine improvement opportunity, the relative contributions of the sources of variation around target should be assessed. The total variance about target, τ2, can be decomposed into the various components that can be compared to assess improvement priority.

Tau Variance Components

σ2 potential is estimated and may also be decomposed into σ2product and σ2measurement. See discussion in Cp(potential).

σ2 off-target is simply estimated as follows:

Variance - Off-target

The variance from process stream differences may be estimated many ways. If the data have not been stratified, studies may be conducted to determine the variance contribution from process stream differences. These studies may include all streams of interest or a random selection of streams. Methods such as Analysis of Variance (ANOVA) may be used to estimate this component. Remember though, that the process is not assumed to be stable and these assessments should be considered approximate.

If the variance from process streams is obtained separately from the data undergoing analysis in the software, the standard deviation from process streams may be entered in User Set Standard Deviations.

If the data have been stratified by all process streams of interest and included within the analysis, the process stream variance is estimated as follows.

Process Stream Variance

where

  • s2 is the sample variance from all combined data, and
  • s2within stream may be found as described in Pp(process stream).

The variance from through-time process changes, σ2time, is estimated as follows.

sigma2-time-eqn

These components may be placed in a Pie or 100% Stacked Bar Chart. For example, using a Pie chart:

Pie chart

or, as a 100% Stacked bar chart:

Stacked Bar