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Beyond Quality Control
Using design of experiments methodology means increased efficiency and improved product quality.

by K.N. Amarnath, June, 2004

Using design of experiments methodology means increased efficiency and improved product quality.

Product quality in any arena can be traced back to variations in parts, materials, people, and processes. And since it has been observed that all work can be broken down into processes, all processes, manufacturing or administrative in nature, have inherent variability. That variability has a directly proportional effect on process quality: The larger the variations, the poorer the quality.

Figure 1: Systat's DOE Wizard provides an alternative interface consisting of a series of questions defining the structure of a design.

Basic statistical process control techniques such as Pareto analysis, cause and effect diagrams, and control charts have been successfully incorporated in many industries. And while these tools are useful in identifying variations and in keeping the process quality from deteriorating, they do little to dramatically improve quality of the end product, and are used primarily for maintenance and monitoring purposes.

To make those improvements, experiments must be completed to determine how a system responds to a change in some factors. These types of experiments are undertaken to optimize the system's performance, or to characterize the system as part of a validation effort. Careful planning at the outset of such experiments can save a great deal of time and effort.

Figure 2: Systat's Classic DOE provides a standard dialog interface for generating complete (full) and incomplete (fractional) factorial designs.The Systat Design command interface.

The Usual Suspects
If the system response depends on just one factor, the strategy is simple: Measure the response at several different values of the factor and fit a curve to the results. But when there is more than one factor, things become more complicated.

The traditional approach would be to vary each factor individually while holding the others constant. This approach does work (i.e., one gets an idea how the system responds to changes in the factors), but it is not the most efficient way to go about the investigation. When investigating a process, you often have to consider many factors that may influence the process. The simple approach of testing one factor at a time can lead to problems due to interactions.

For example, the effect of temperature on a chemical process may be very different at low pressure than at high pressure. If you did two simple experiments, one examining temperature and one examining pressure, you would never see the effects of temperature changes at different pressures.

A more accurate way to study the effects of changes on a system is through design of experiments (DOE), or statistical experimental design. DOE, a planned approach for determining cause-and-effect relationships, can be applied to any process with measurable inputs and outputs. Factorial designs enable evaluation of multiple factors simultaneously. A factorial design for the example above could include observations at four points: high temperature/high pressure, high temperature/low pressure, low temperature/high pressure, and low temperature/low pressure. This helps you see the effects of different temperatures at different pressures.

DOE provides a statistical means for analyzing how numerous variables interact and has been applied to improving quality in numerous types of systems since Sir Ronald Aylmer Fisher applied it to agricultural experimentation early in the 20th Century. Since then DOE has spread to numerous fields and has found wide acceptance in engineering.

Various Matrices for Various Analyses
Systat DOE generates design matrices for a variety of analysis of variance. You can use Systat DOE as both an online library and a search engine for experimental designs, saving any design to a Systat file. You can run the associated experiment, add the values of a dependent variable to the same file, and analyze the experimental data by using a General Linear Model (or another Systat statistical procedure). Systat offers Classic DOE, the DOE Wizard, and the Design command for generating experimental designs.

Figure 3: The Systat Design command interface.

Different kinds of factorial designs can be generated in Systat, including homogeneous fractional, mixed-level fractional, Box-Hunter, Placzkett-Burman, Taguchi, and Latin square designs.

In many industrial situations, you need to find the best combination of factors for your process, as measured by some response variable. In such instances, response surface methods can help you find the optimal conditions for your process. The basic approach is to take measurements at different levels of each factor and then to build a model of the response in terms of those factors. The model is expressed as a polynomial approximation.

The process of fitting a response surface is usually an iterative one, using a hill-climbing strategy. You start with some set of factor values (chosen because they are thought to be close to the optimum or because they are convenient), and you conduct an experiment to find a linear model, a model with only main effects. (Two-level factorial designs are useful for this stage of the process.) If the linear model fits, it is used to find the direction of steepest ascent (or descent for minimization problems), and the factor levels are adjusted in this direction to bring them closer to the optimum. This is repeated until you find that a linear model does not fit the data and that a quadratic model, a model that includes interaction terms and squared main effects, is required. Then a final experiment is conducted to estimate the quadratic model and identify the optimum values. (While the quadratic surface may not fit the global response function very well, it usually fits quite well for localized regions of the factor space.)

Two general response surface designs are available in Systat, namely, Central Composite and Box-Behnken designs. Apart from all the others previously mentioned, Systat also provides mixture designs and optimal designs. The former takes into account this interdependence of factors by assuming that the factors must have a sum equal to a constant value. The latter minimizes a variance criterion (the objective function) within the constraints of the experiment that include the following methods: Fedorov, k-exchange, and coordinate exchange algorithms. There are three optimality criteria available for Fedorov and k-exchange algorithms, and two available for coordinate exchange algorithms.

DOE's potential for application in industry includes, but is not limited to, reduced time in product and process design and development; reducing the effect of variations in manufacturing conditions; improving process performance; increasing process productivity by reducing scrap or rework; and making products robust to withstand environmental variations. It is a very powerful problem-solving technique that assists engineers in tackling quality control problems effectively and economically; independent research has shown that DOE can help to improve a company's position in the marketplace, from securing a competitive advantage to increasing profit margins.

Quality Improvement for Robust Design
A large measure of the popularity of design of experiments (DOE) methodology in industry can be traced back to the quality engineering methods of Dr. Genichi Taguchi, who was recruited to help correct postwar Japan's crippled telephone system. In the 1950s he developed his own methods for identifying design problems, and were it not for the advancements Taguchi made, Japan might not have stayed afloat after World War II let alone flourish.

Japanese manufacturers were struggling to survive with very limited resources, and Taguchi revolutionized the manufacturing process in Japan through cost savings. He understood, like many other engineers, that all manufacturing processes are affected by outside influences, or noise. However, Taguchi realized methods of identifying noise sources with the greatest effects on product variability. His ideas have been adopted by successful manufacturers around the globe because of their results in creating superior production processes at much lower costs. He is widely acknowledged as a leader in the U.S. industrial quality movement, and is credited for starting the Robust Design movement. K.N.A.

K.N. Amarnath is a Product Analyst with Systat Software. He has more than 10 years of experience in synthesis, modeling, and analyzing data. His research interests include interdependent multivariate data analytical methods and data mining techniques.