Propagation of Error

Propagation of error (POE) methods find factor settings that minimize variation transmitted to the response from a factor that isn’t under complete control. Settings that minimize the transmitted variation make the process more robust to variations in input factors.

In essence, the POE method involves application of partial derivatives to locate flat areas on the response surface.

POE techniques require two things: a second-order hierarchical response surface model and estimated standard deviations for the numeric factors.

The standard deviations can be entered for all factors on the Column Info Sheet. They can also be entered one factor at a time by selecting a column or cell and changing it on the Design Properties tool.

Using the factor standard deviation information, the software constructs a response surface map of the factor variation transmitted to each response. Multiple response optimization, including goals to minimize the POE, can find factor settings to achieve the response goals with minimal variation.


The response models MUST be hierarchical in order to generate the POE. Non-hierarchical models cannot be accurately converted from coded to actual units and POE is based on the actual units of measure.