# 代写代考 Math 558 Lecture #0 – cscodehelp代写

Math 558 Lecture #0

Introduction
What do we mean by an experiment?

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An operation or procedure carried out under controlled condi- tions in order to discover an unknown effect or law, to test or establish a hypothesis, or to illustrate a known law.( Dictionary)

Introduction Experiment
we can define an experiment as a test or series of runs in which purposeful changes are made to the input variables of a process or system so that we may observe and identify the reasons for changes that may be observed in the output response. We may want to determine which input variables are responsible for the observed changes in the response, develop a model relating the response to the important input variables and to use this model for process or system improvement or other decision- making.(Montgomery, Design and Analysis of Experiments, Pg 1)

Introduction Some history
Montgomery has divided the history of modern development of Experimental design in four eras.
The first era started somewhere between 1920 and 1930 from the work of Fisher (Sir Ronald A. Fisher)1 in the field of Agricultural Experiments. Fisher was a statistician at Rothamsted Agricultural Experimental Station near London, England. He introduced three important rules which are considered fundamental in designing of an experiment. There rules2 are
Randomization replication blocking
1 https://rss.onlinelibrary.wiley.com/doi/10.1111/j. 2397- 2327.1963.tb01058.x
2details in the next lectures

Some History
Fisher’s two books Statistical Methods for Experimenters and Design of Experiments have a strong influence on the development of experimental design theory. An interesting reading ( though not directly related to this course) can be https://statmodeling.stat.columbia.edu/2020/08/ 01/ra-fisher-and-the-science-of-hatred/.
The second era started immediately after world war II. It is also designated as the first industrial era of experimental designs. The most important development of this era was the landmark publication by Box and Wilson (1951) in response surface designs, thinking of the output as a response function and trying to find the optimum conditions for this function.

Box and Wilson ” recognized and exploited the fact that many industrial experiments are fundamentally different from their agricultural counterparts in two ways: (1) the response vari- able can usually be observed (nearly) immediately, and (2) the experimenter can quickly learn crucial information from a small group of runs that can be used to plan the next experi- ment. Box (1999) calls these two features of industrial experi- ments immediacy and sequentiality. (Montgomery, pg 21)

Some History
3 played a great role in spreading the RSM in industrial experiments. However, due to lack of training of technical staff as well as the absence of a user friendly software the use statistical methods was still very limited.
Another important development of the industrial era was the introduction of optimal design of experiments. Kiefer (1959, 1961) and Kiefer and Wolfowitz (1959) proposed a formal “approach to selecting a design based on specific objective optimality criteria. Their initial approach was to select a design that would result in the model parameters being estimated with the best possible precision.”
3An interesting reading, not related to this course is, “An accidental Statistician”

Some History
The third era is the era of Statistical quality control. It started in early 70s. The important features of this era are quality improvement initiatives process robustness.
Taguchi advocated using designed experiments for what he termed robust parameter design, or
1. Making processes insensitive to environmental factors or other factors that are difficult to control
2. Making products insensitive to variation transmitted from components
3. Finding levels of the process variables that force the mean to a desired value while simultaneously reducing variability around this value.

Some History
The fourth era began in early 90s. It’s common features are the wide spread use of experimental design approaches in the industrial world, development of computer software for construction and asnalysis of experimental designs and formal experimental design courses were introduced at different levels of university education.

Some History