Design of Experiments CHM 585 Chapter 15

Experimentation is one of the most important methods in the Quality Movement -- the quest for continuous improvement in our products and processes. If you can measure aspects of quality in your product, and if you have factors under your control, then you can perform an experiment to find out which factor settings result in the best quality product.

Experimentation is usually expensive, so you want to get the most information from the least number of runs in the experiment.

One approach when looking for optimal factor settings is to pick starting values and then adjust one factor to see if it helps and keep fiddling with it until the response seems to get better. But even then sometimes it gets worse because of random or external factors. It's hard to tell.

Then, adjusting another factor improves the response more Then, adjusting another factor improves the response more. But after adjusting that factor, the first factor's supposedly optimal setting is no longer optimal because changing the second factor has affected how the first factor works (interaction). But there are dozens of potential factors that might affect the product. Each fiddle with a new control sends you back to adjusting all the other factors.

Hundreds of runs. Little progress Hundreds of runs. Little progress. No comprehensive understanding of the whole process after much effort.

Suppose that you first experiment with Factor1 and make runs 1 through 5 that improve the response. But when you complete run 6, the response is worse. So, for the next run, you backtrack to the value of Factor1 at point 5 and decide that Factor1 = .9 is the best when holding Factor2 constant. Now you hold Factor1 constant and do run 7, but the response is worse. So you experiment with Factor2 and make run 8 for a better response and 9 for worse. You again backtrack and find at point 10 that Factor2 = -.38 is its optimal value, holding Factor1 constant. Have you found the optimum? No. These are all conditional optimum values that depend on holding one factor constant, and do not yield the global optimum.

A more scientific approach to the problem is to reason out all the factors that might affect the response. After choosing the most promising 12 of them for investigation, a computer software program can help select a screening design that needs only 16 runs. Then perform the runs, and enter the responses into the computer. This complete analysis can quickly identify the three most important factors. Next the software performs a response-surface design for 20 runs. When the analysis is done, you have a complete understanding of the response surface, know what the optimal settings are, and what the variability in the process is.

Experimental Designs are used to identify or screen important factors affecting a process, and to develop empirical models of processes. Design of Experiment techniques enable teams to learn about process behavior by running a series of experiments, where a maximum amount of information will be learned, in a minimum number of runs. Tradeoffs as to amount of information gained for number of runs, are known before running the experiments. A typical plant Designed Experiment has 3 factors, each set at two levels - typically the maximum and minimum settings for each of the factors. A Designed Experiment with 3 factors each at 2 levels, is called a 23 factorial experiment (or Taguchi L8 experiment), and requires 8 runs, as follows:

<> run number Factor A Factor B Factor C 1 lo 2 hi 3 4 5 6 7 8

Bromination of acetone

Dithionite reduction

Evolutionary Operation (EVOP) It combines small variable perturbations and numerous replications of every process adjustment with statistical analysis. Every process contains random process fluctuations (noise) typically caused by such factors as raw-material variations, equipment deterioration, and instrument corrections. Because process responses to variable changes and the random noise may occasionally have comparable values, replication allows the effects of the noise to average out so the true effects of the variable changes can be determined

The Biological Neuron The most basic element of the human brain is a specific type of cell, which provides us with the abilities to remember, think, and apply previous experiences to our every action. These cells are known as neurons, each of these neurons can connect with up to 200000 other neurons. The power of the brain comes from the numbers of these basic components and the multiple connections between them.

All natural neurons have four basic components, which are dendrites, soma, axon, and synapses. Basically, a biological neuron receives inputs from other sources, combines them in some way, performs a generally nonlinear operation on the result, and then output the final result.

The brain basically learns from experience The brain basically learns from experience. Neural networks are sometimes called machine learning algorithms, because changing of its connection weights (training) causes the network to learn the solution to a problem. The strength of connection between the neurons is stored as a weight-value for the specific connection. The system learns new knowledge by adjusting these connection weights. The learning ability of a neural network is determined by its architecture and by the algorithmic method chosen for training.