# The Six Sigma Guide to Robust Design

Robust design is particularly important in ensuring that the performance of a product will be consistently good over a wide range of conditions of use. This sample chapter explains how to quantify design, discusses the Taguchi approach to robust design, provides alternative approaches to robust design, and shows you how to deal with variation.
This chapter is from the book

### This chapter is from the book 

Customers expect excellent performance from the products they purchase, and producers of products expect excellent process performance in the production of those products. Performance excellence includes at least two dimensions: a high average level of performance and consistent performance at that level. In statistical terms, this means an average performance that is close to target with low variation about that average.

Some causes of variation are identifiable, and it is often possible to quantify the contributions of those causes to the overall variation in product or process performance. Overall variation may also change with the settings of controllable inputs that impact the performance. In such cases, it may be possible to identify settings of controllable inputs that minimize overall variation in performance while ensuring that the level of performance is close to its target. Achievement of those dual objectives is the role of Robust Design.1, 2 Data for this chapter are contained in the Minitab Project file Chapter 31—Robust Design. MPJ.

## Quantifying Robust Design Performance

Robust design is particularly important in ensuring that the performance of a product will be consistently good over a wide range of conditions of use. For example, an automobile should perform well at extremely high and extremely low temperatures, as well at normal temperatures. It should also perform equally as well in extremely dry and extremely wet climates, as well as in normal climates. The dual objectives of:

1. achieving average performance close to target, and
2. achieving low variation about that target

can be evaluated by the Mean Squared Deviation (MSD)

where yi is the measured performance value for observation i and n is the number of observations.

MSD can be divided into two components, as demonstrated by the equation:

where is a measure of the departure of performance from target, and

is a measure of the variation about the average performance.

Minimizing these two components of MSD requires the following:

• Adjusting the settings of controllable inputs to center the performance of a product or process at its target value
• Adjusting the settings of controllable inputs to minimize the variation in performance of a product or process about its average value.

### Using Critical Input Variables to Improve Robustness

Selection of the appropriate adjustments to achieve both of these objectives requires that we accomplish the following two tasks:

• Identification of the controllable inputs that influence the average performance and an equation describing the relationship between average performance and those controllable inputs.
• Identification of the controllable inputs that influence the variation in performance and an equation describing the relationship between variation in performance and those controllable inputs.

A robust design study can identify the critical controllable input variables for each of these tasks and provide the data required to develop an equation that describes the required relationship for each task. Once equations have been developed for average performance and variation in performance, one strategy for achieving the dual objectives uses the following steps:

• Bring average performance as close to target as possible using controllable inputs that impact average performance but not variation in performance. If no such controllable inputs can be identified, use those controllable inputs that affect both average performance and variation in performance but that have the smallest effects on variation in performance.
• Reduce the variation in performance as much as possible using controllable inputs that affect variation in performance but not average performance. If no such controllable inputs can be identified, use those controllable inputs that were not used to minimize departure of average performance from target in step 1.
• Set controllable inputs that impact neither average performance nor variation in performance at their most cost-effective settings.
• Carry out a capability study of performance at the recommended settings of all controllable inputs.

If the controllable inputs that influence average performance are different from the controllable inputs that influence variation in performance, the two objectives may be achieved independently of one another. In many cases, however, some controllable input variables affect both average performance and variation in performance, thereby creating a potential conflict between the two objectives. In such cases, a compromise optimum may be required using multiple response optimization, which is described in Chapter 33.

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