Introduction to Design of Experiments (DOE)

DOE is an essential piece of the reliability program pie. It plays an important role in Design for Reliability (DFR) programs, allowing the simultaneous investigation of the effects of various factors and thereby facilitating design optimization. This article introduces the concept of DOE. Future articles will cover more DOE fundamentals in addition to applications and discussion of DOE analyses accomplished with a soon-to-be-introduced ReliaSoft software product!

DOE helps in:

• Identifying relationships between cause and effect.
• Providing an understanding of interactions among causative factors.
• Determining the levels at which to set the controllable factors (product dimension, alternative material, alternative designs, etc.) in order to optimize reliability.
• Minimizing experimental error (noise).
• Improving the robustness of the design or process to variation.

Introduction

Much of our knowledge about products and processes in the engineering and scientific disciplines is derived from experimentation. An experiment is a series of tests conducted in a systematic manner to increase the understanding of an existing process or to explore a new product or process. Design of Experiments, or DOE, is a tool to develop an experimentation strategy that maximizes learning using a minimum of resources. Design of Experiments is widely used in many fields with broad application across all the natural and social sciences. It is extensively used by engineers and scientists involved in the improvement of manufacturing processes to maximize yield and decrease variability. Often times, engineers also work on products or processes where no scientific theory or principles are directly applicable. Experimental design techniques become extremely important in such situations to develop new products and processes in a cost-effective and confident manner.

Why DOE?

With modern technological advances, products and processes are becoming exceedingly complicated. As the cost of experimentation rises rapidly, it is becoming impossible for the analyst, who is already constrained by resources and time, to investigate the numerous factors that affect these complex processes using trial and error methods. Instead, a technique is needed that identifies the "vital few" factors in the most efficient manner and then directs the process to its best setting to meet the ever-increasing demand for improved quality and increased productivity. The techniques of DOE provide powerful and efficient methods to achieve these objectives. Designed experiments are much more efficient than one-factor-at-a-time experiments, which involve changing a single factor at a time to study the effect of the factor on the product or process. While the one-factor-at-a-time experiments are easy to understand, they do not allow the investigation of how a factor affects a product or process in the presence of other factors. When the effect that a factor has on the product or process is altered due to the presence of one or more other factors, that relationship is called an interaction. Many times the interaction effects are more important than the effects of individual factors. This is because the application environment of the product or process includes the presence of many of the factors together instead of isolated occurrences of single factors at different times. Consider an example of interaction between two factors in a chemical process where increasing the temperature alone increases the yield slightly while increasing pressure alone has no effect on the yield. However, in the presence of both higher temperature and higher pressure, the yield increases rapidly. Thus, an interaction is said to exist between the two factors affecting the chemical reaction.

The methodology of DOE ensures that all factors and their interactions are systematically investigated; thus, information obtained from a DOE analysis is much more reliable and complete than results from one-factor-at-a-time experiments that ignore interactions and may lead to misleading conclusions.

Stages of DOE

Designed experiments are usually carried out in five stages planning, screening, optimization, robustness testing and verification.

1. Planning

It is important to carefully plan for the course of experimentation before embarking upon the process of testing and data collection. A few of the considerations to keep in mind at this stage are a thorough and precise objective identifying the need to conduct the investigation, assessment of time and resources available to achieve the objective and integration of prior knowledge to the experimentation procedure. A team composed of individuals from different disciplines related to the product or process should be used to identify possible factors to investigate and the most appropriate response(s) to measure. A team approach promotes synergy that gives a richer set of factors to study and thus a more complete experiment. Carefully planned experiments always lead to increased understanding of the product or process. Well planned experiments are easy to execute and analyze. Botched experiments, on the other hand, may result in data sets that are inconclusive and may be impossible to analyze even when the best statistical tools are available.

2. Screening

Screening experiments are used to identify the important factors that affect the process under investigation out of the large pool of potential factors. These experiments are carried out in conjunction with prior knowledge of the process to eliminate unimportant factors and focus attention on the key factors that require further detailed analyses. Screening experiments are usually efficient designs requiring few executions, where the focus is not on interactions but on identifying the vital few factors.

3. Optimization

Once attention has been narrowed down to the important factors affecting the process, the next step is to determine the best setting of these factors to achieve the desired objective. Depending on the product or process under investigation, this objective may be to either increase yield or decrease variability or to find settings that achieve both at the same time.

4. Robustness Testing

Once the optimal settings of the factors have been determined, it is important to make the product or process insensitive to variations that are likely to be experienced in the application environment. These variations result from changes in factors that affect the process but are beyond the control of the analyst. Such factors (e.g. humidity, ambient temperature, variation in material, etc.) are referred to as noise or uncontrollable factors. It is important to identify such sources of variation and take measures to ensure that the product or process is made insensitive (or robust) to these factors.

5. Verification

This final stage involves validation of the best settings by conducting a few follow-up experimental runs to confirm that the process functions as desired and all objectives are met.