CHAPTER 1
INTRODUCTION

1.1 Introduction to design of experiments

Experiments are performed by investigators in virtually all fields of inquiry, usually to discover something about a particular process or system. Literally, an experiment is a test. A designed experiment [1] is a test or series of tests in which purposeful changes are made to the input variables of a process or system so that the reasons for the changes in the output responses can be observed and identified. The investigator sets several factors in these experiments simultaneously and changes the factor settings from experiment to experiment in a specified manner. This procedure yields the maximum amount of information about the effect of input variables on the output response.

Some special statistical experiments require mere simple arithmetic calculations to yield sufficiently precise and reliable information. Each such special design has a rational relationship to the purpose of experimentation, the needs of the investigator and the physical limitations of the experiments. All such designs begin with the statement of the investigator's objective and the identification of the factors that have the greatest potential influence upon the response. Some common statistical designs are:

  1. Regression analysis [1]
  2. Statistical methods [1]
    • Randomized block
    • Completely randomized design
    • Factorial design
    • Blocked factorial design
    • Latin square etc.,
  3. Taguchi method [2]

1.2 Comparison of various methods

Among the above designs, the design of experiments based on the regression analysis is used to find out the exact mathematical relationship between the cause (independent input variable) and the effect (performance parameter) provided the independent variable and the performance parameters are quantitative figures. When the independent variable is an attribute that is not a measurable quantity (e.g., gender, geographic location, plant shift, etc.,) then the regression analysis can not be used. This poses a major limitation for generic cases where the independent variable is not a quantitative figure.

When the intention of the investigator is to understand the relationship between the cause and the effect rather than just obtaining the mathematical equations relating the cause and the effect, then the statistical approach and Taguchi methods are best suited.

The design of experiments using statistical approach is a simple and systematic approach by identifying various independent factors and levels, and conducting experiments by varying one variable at a time. In order to reduce the noise effect or error due to the order / sequence in which the experiments are conducted, randomization of the sequence of experiments and variables is done.

Statistical experiments consist of several well-planned individual experiments conducted together. The setting up of a statistical experiment [5] involves several steps such as the following.

  1. Selection of responses (performance characteristics of interest) that will be observed.
  2. Identification of the factors (the independent or influencing conditions) to be studied.
  3. The different treatments (or levels) at which these factors will be set in the different individual experiments.
  4. Consideration of blocks (the observable noise factors that may influence the experiments as a source of error of variability).

The main drawback of the statistical approach is that there are no precise guidelines for the sequence of experiments to be conducted and the level combinations of various independent variables for each experiment. Moreover, the number of experiments is, in most of the cases, more than that of experiments conducted using Taguchi method.

The design of experiments using Taguchi method is more efficient compared to statistical methods. By choosing proper level combinations of various independent variables, the number of experiments is reduced considerably. At the same time, there is no loss of any information due to reduction of number of experiments. The method has been described in the subsequent chapters.

1.3 Areas of application

While the design of experiments can be used in many engineering and non-engineering areas, the following are a few engineering areas where this technique can be effectively used.

1.3.1 Process development

Many processes typically have a large number of factors that influence the final outcome. Identification of their individual contributions and their intricate interrelationship is essential in the development of such processes. For example, the efficiency of a flow solder machine meant for soldering the printed circuit boards has several variables [2] that can be controlled. This includes solder temperature, preheat temperature, flux type, flux specific gravity, solder wave depth, etc.,

1.3.2 Test and development

Testing with prototypes [6] is an efficient way to see how the concepts work when they are put into a design. Since the experimental hardware is costly, the need to accomplish the objectives with the least number of tests is a top priority.

1.3.3 Analysis

In the design of engineering products and processes the analytical simulation plays an important role in transforming a concept into the final product design. The Taguchi approach can be utilized to arrive the best parameters for the near optimum design configuration with the least number of analytical investigations. Although there are several method available for optimization, the Taguchi method is the one that treats factors at discrete levels. This method significantly reduces computer time.

1.3.4 Design of experiments as applied to the finite element analysis

The finite element technique is used to predict the physical behavior of the models which are governed by the differential equations. Most of the common engineering problems can be solved using the finite element technique. By using the finite element method as an experimental tool, one can conduct experiments by varying the independent variables. Once the experiments are conducted, the output response/ performance can be statistically analyzed to predict the influence of each variable on the performance. This has been discussed in the subsequent chapters.

1.4 Scope of the project

In this research, a method has been developed and implemented to conduct design of experiments using the Taguchi method and the finite element analysis. Chapter 2 presents the basic concept of Taguchi method, orthogonal arrays, and setting up layout designs, analyzing the output data, procedure to find out the influence of each independent variable on objective function. Chapter 3 gives the picture of how the Taguchi method and the finite element analysis can be used together to carryout the design of experiments and arrive at near optimal solution for generic engineering problems that can be solved using ANSYSTM finite element solver. Chapter 4 discusses about the distributive cooperative problem solving approach using blackboard database. Chapter 5 presents the details of how the blackboard database approach is implemented in developing the INFINITE software for the integrated approach in the GBB environment. Chapter 6 illustrates a typical example of the above method. Chapter 7 consists of conclusion and future scope of work.