Achieving robust processes via three experiment-design options (part 3)

Richard Williams on May 1, 2024

The goal of robustness studies is to demonstrate that our processes will be successful upon implementation in the field when they are exposed to anticipated noise factors. There are several assumptions and underlying concepts that need to be understood when setting out to conduct a robustness study. Carefully considering these principles, three distinct types of designs emerge that address robustness:

I. Having settled on process settings, we desire to demonstrate the system is insensitive to external noise-factor variation, i.e., robust against Z factor influence.

II. Given we may have variation between our selected process settings and the actual factor conditions that may be seen in the field, we wish to find settings that are insensitive to this variation. In other words, we may set our controlled X factors, but these factors wander from their set points and cause variation in our results. Our goal is to achieve our desired Y values while minimizing the variation stemming from imperfect process factor control. The impact of external noise factors (Z’s) is not explored in this type of study.

III. Given a system having controllable factors (X’s) and non-controllable noise factors (Z’s) impacting one or more desirable properties (Y’s), we wish to find the ideal settings for the controllable factors that simultaneously maximize the properties of interest, while minimizing the impact of variation from both types of noise factors.

Read part 1 here.

Read part 2 here.

Design-Type III: A combination of the first two types

The idea here is to simultaneously involve the process factors (X’s) and the noise factors (Z’s) in the same DOE so as to identify the right process (controllable) factor settings to deliver the intended responses (Y’s) with the minimal variation when both the process and noise factors vary.

One of the first to consider this holistic approach was Taguchi in the 1980’s. Taguchi envisioned a factorial space whereby the controllable factors are changed in the usual way, and the noise factors are studied at each corner of the factorial space as a secondary factorial design. In his vocabulary, there was an inner array (of controllable factors) and an outer array (of noise factors). The design principle was as shown below, with 16 data points collected as indicated in blue (for 2 process factors, and two noise factors).

Taguchi array with 16 data points

The principle of Taguchi’s approach is sound. There were, however, challenges made regarding the analytical approach and that led to further efforts by others to advance the science. Several concepts have been proposed. A solid candidate would be a dual response surface approach, where process factors and noise factors are combined in the same study, and two responses are measured: the process mean (predicted Y values), and also the variance for the predicted Y values at any given point within the design space. Armed with this knowledge the experimenter can seek regions within the design space where the desired Y values are achieved but are also relatively insensitive to the variation of both process and noise factors.

How are these dual response surface studies done? Essentially the same as described before under Type II Robustness studies, with one key exception. The external noise factors are included as factors within the study, and their influence evaluated as though they were controllable factors (which they are, of course, during the DOE itself). And the propagated error from all factors upon the responses are evaluated as per Type II.

The difference comes during the numeric optimization. Since Z factors cannot be controlled in the field, these factors are set to their nominal value (usually the center of the range studied) in numeric optimization. The standard deviation for these factors will still influence the POE assessment for responses.

Then, the experimenter can use numeric optimization to achieve the desirable Y value criteria while simultaneously minimizing the POE response, resulting in the identification of a robust region that is relative insensitive to variation in X and Z factor variation.

For additional information on using a combined array, and an introduction to using POE to address both process factor and noise factor variation, read the 2002 white paper by Mark Anderson and Shari Kraber on Cost-Effective and Information-Efficient Robust Design For Optimizing Processes And Accomplishing Six Sigma Objectives.

Read a follow-up by Mark Anderson here.

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