1997 DesignandAnalysisofExperiments
- (Montgomery, 1997) ⇒ Douglas C. Montgomery. (1997). “Design and Analysis of Experiments, 4th edition." John Wiley & Sons. ISBN:0471157465
Subject Headings: Analysis of Variance; average block design; confidence interval; expected mean squares; factorial experiment; fixed effects; fractional factorial design; Latin square
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Book Overview
This book describes the methods and techniques used in the design and analysis of experiments. It emphasizes the connection between the experiment and the model that the experimenter can develop from the results of the experiment and features a new chapter on experiments with random factors.
Chapter 1. Introduction
1-1 Strategy of Experimentation
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. More formally, we can define an experiment as a test or series of tests in which purposeful changes are made to the input variables of a process or system so that we may observe and identify the reason for changes in the output response.
This book is about planning and conducting experiments and about analyzing the resulting data so that conclusion and objective conclusions are obtained. Our focus is on experiments in the engineering, physical and chemical sciences. In engineering, experimentation plays an important role in new product design, manufacturing process development, and process improvement. The objective in many cases may be to develop a robust process, that is, a process affected minimally by external sources of variability.
As an example of an experiment, …
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In any experiment, the results and conclusions that can be drawn depend to a large extent on the manner in which the data were collected. …
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In general, experiments are used to study the performance of processes and systems. The process or system can be represented by the model shown in Figure 1-1. We can usually visualize the process as a combination of machines, methods, people, and other resources that transforms some input (often a material) into an output that has one or more observable responses. Some of the process variables [math]\displaystyle{ x_1, x_2, …, x_p }[/math], are controllable, whereas other variables [math]\displaystyle{ z_1, z_2, …, z_p }[/math], are uncontrollable (although they may be controllable for purposes of a test). The objectives of the experiment may include the following:
- Determining which variables are most influential on the response [math]\displaystyle{ y }[/math]
- Determining where to set the influential [math]\displaystyle{ x }[/math]’s so that [math]\displaystyle{ y }[/math] is almost always near the desired nominal value.
- Determining where to set the influential [math]\displaystyle{ x }[/math]’s so that variability in [math]\displaystyle{ y }[/math] is small.
- Determining where to set the influential [math]\displaystyle{ x }[/math]’s so that the effects of the uncontrollable variables
As you can see from the foregoing discussion, experiments often involve several factors. Usually, an objective of the person conducting the experiment called the experimenter, is to determine the influence that these factors have on the output response of the system. The general approach to planning and conducting the experiment is called the strategy of experimentation. There are several strategies that an experimenter could use. …
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Another strategy of experimentation that is used extensively in practice is one-factor-at-a-time approach. This method consists of selecting a starting point of or baseline set of levels for each factor, then successively varying each factor over its range with the other factors held constant at the baseline level. After all tests are performed, a series of graphs are usually constructed showing how the response variable is affected by varying each factor with all other factors held constant. …
The major disadvantage of the one-factor-at-a-time strategy is that it fails to consider any possible interaction between the factors. An interaction is the failure of one factor to produce the same effect on the response at different levels of another factor. …
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The correct approach to dealing with several factors is to conduct a factorial experiment. This is an experimental strategy in which factors are varied together, instead of one at a time. The factorial experimental design concept is extremely important, and several chapters in this book are developed to presenting basic factorial experiments and a number of useful variations and special cases.
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Geometrically, the four runs form the corners of a squere. This particular type of factorial experiment.
References
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| Author | volume | Date Value | title | type | journal | titleUrl | doi | note | year | |
|---|---|---|---|---|---|---|---|---|---|---|
| 1997 DesignandAnalysisofExperiments | Douglas C. Montgomery | Design and Analysis of Experiments | 1997 |