Robust Product Design through Design of Experiments

Robust Design

A robust product is one that works as intended regardless of variation in a product’s manufacturing process, variation resulting from deterioration, and variation in use. Robust design can be achieved when the designer understands these potential sources of variation and takes steps to desensitize the rpoduct to these potential sources of variation. Robust design can be achieved through “brute force” techniques of added design margin or tighter tolerances or through “intelligent design” by understanding which product and process design parameters are critical to the achievement of a performance characteristic and what are the optimum values to both achieve the performance characteristic and minimize variation.

When the operation of the product or achievement of a performance characteristic can be mathmatically related to a product or process design parameter, optimum product and process design parameters can be calculated. When these relationships are unknown, design of experiments (DOE) can aid in determining these optimum parameter values and, thereby, developing a more robust design.

Design of Experiments

Design of Experiments is based on the objective of desensitizing a product’s performance characteristic(s) to variation in critical product and process design parameters. Genichi Taguchi developed the concept of “loss to society”. In this concept, variability in critical design parameters will increase the loss to society which is an expanded view of the traditional, internally-oriented cost of quality. This is a quadratic relationship of increasing costs (loss to society) as these critical design parameter values vary from the desired mean value of the parameter.

To consider quality implications during design, the design process can be segmented into three stages. The first stage, system design, establishes the functionality of the product, the physical product envelope, and general specifications. The second stage, parameter design, establishes specific values for design parameters related to physical and functional specifications. It is during these first two stages that the designer has the greatest opportunity to reduce product costs through effective functional design and parameter specification. The third stage, tolerance design, establishes the acceptable tolerances around each parameter or target. The third stage typically will add costs to the product through efforts to ensure compliance with the tolerances associated with product parameters.

Since an organization cannot cost-effectively inspect quality into the product, it must focus on minimizing variability in the product through product and process design and control of processes. However, some variability is uncontrollable or very difficult to control. This difficult to control variation is referred to as noise. Noise is the result of variation in materials, processes, the environment and the product’s use or misuse. Products need to be designed so that they are robust – their performance is insensitive to this naturally occurring, difficult to control variation.

Design of Experiments techniques provide an approach to efficiently designing industrial experiments which will improve the understanding of the relationship between product and process parameters and the desired performance characteristic. This efficient design of experiments is based on a fractional factorial experiment which allows an experiment to be conducted with only a fraction of all the possible experimental combinations of parameter values. Orthogonal arrays are used to aid in the design of an experiment. The orthogonal array will specify the test cases to conduct the experiment. Frequently, two orthogonal arrays are used: a design factor matrix and a noise factor matrix, the latter used to conduct the experiment is the presence of difficult to control variation so as to develop a robust design. This approach to designing and conducting an experiment to determine the effect of design factors (parameters) and noise factors on a performance characteristic is represented below.


These experimental results can be summarized into a metric called the signal to noise ratio which jointly considers how effectively the mean value (signal) of the parameter has been achieved and the amount of variability that has been experienced. As a result, a designer can identify the parameters that will have the greatest effect on the achievement of a product’s performance characteristic.

The design parameters or factors of concern are identified in an inner array or design factor matrix which specifies the factor level or design parameter test cases. The outer array or noise factor matrix specifies the noise factor or the range of variation the product will be exposed to in the manufacturing process, the environment or how the product used (conditions it is exposed to). This experimental set-up allows the identification of the design parameter values or factor levels that will produce the best performing, most reliable, or most satisfactory product over the expected range of noise factors or environmental conditions.

After the experiments are conducted and the signal to noise ratio determined for each design factor test case, a mean signal to noise ratio value is calculated for each design factor level or value. This data is statistically analyzed using analysis of variation (ANOVA) techniques. Very simply, a design factor with a large difference in the signal noise ratio from one factor setting to another indicates that the factor or design parameter is a significant contributor to the achievement of the performance characteristic. When there is little difference in the signal to noise ratio from one factor setting to another, this indicates that the factor is insignificant with respect to the performance characteristic.

With the resulting understanding from the experiments and subsequent analysis, the designer can:

  • Identify parameter values which maximize achievement of performance characteristic and minimize the effect of noise, thereby achieving a more robust design.
  • Identify parameters that have no significant effect on performance. In these cases, tolerances can be relaxed and cost reduced.
  • Identify parameter values which reduce cost without affecting performance or variation.

These steps take initial effort, but can reduce cost and improve the performance of the product. In the past, the designer selected design parameters and tolerances and made system design trade-offs in an intuitive manner, sometimes supported by limited analysis and trial and error experimentation. However, an overall framework was lacking to make these decisions. Design of Experiments techniques offer a framework for developing a more rigorous understanding of the relationship between product and process parameters and the achievement of a performance, reliability or quality characteristic, thereby leading to improved design decisions. These techniques present a comprehensive approach experimental design, analysis, and product and process design decision-making.