DOE Simplified

Practical Tools for Effective Experimentation, Third Edition

Mark J. Anderson, Patrick J. Whitcomb

• Publisher: Productivity Press
• Year: 2017
• Print ISBN:
  9781482218947
• eBook ISBN:
  9781498760331
• Topic: Economics
• Subtopic: Industrial Management
• Index: Economics

Offering a planned approach for determining cause and effect, DOE Simplified: Practical Tools for Effective Experimentation, Third Edition integrates the authors decades of combined experience in providing training, consulting, and computational tools to industrial experimenters. Supplying readers with the statistical means to analyze how numerous variables interact, it is ideal for those seeking breakthroughs in product quality and process efficiency via systematic experimentation.Following in the footsteps of its bestselling predecessors, this edition incorporates a lively approach to learning the fundamentals of the design of experiments (DOE). It lightens up the inherently dry complexities with interesting sidebars and amusing anecdotes.The book explains simple methods for collecting and displaying data and presents comparative experiments for testing hypotheses. Discussing how to block the sources of variation from your analysis, it looks at two-level factorial designs and covers analysis of variance. It also details a four-step planning process for designing and executing experiments that takes statistical power into consideration.This edition includes a major revision of the software that accompanies the book (via download) and sets the stage for introducing experiment designs where the randomization of one or more hard-to-change factors can be restricted. Along these lines, it includes a new chapter on split plots and adds coverage of a number of recent developments in the design and analysis of experiments.Readers have access to case studies, problems, practice experiments, a glossary of terms, and a glossary of statistical symbols, as well as a series of dynamic online lectures that cover the first several chapters of the book.

Chapter 1

Basic Statistics for DOE

One thing seems certain—that nothing certain exists.

Pliny the Elder, Roman scholar (CE 23-79)

Statistics means never having to say you’re certain.

Slogan on shirt sold by the American Statistical Association (ASA)

Most technical professionals express a mixture of fear, frustration, and annoyance when confronted with statistics. It’s hard even to pronounce the word, and many people, particularly after enduring the typical college lecture on the subject, prefer to call it “sadistics.” Statistics, however, are not evil. They are really very useful, especially for design of experiments (DOE). In this chapter, we present basic statistics in a way that highlights the advantages of using them.

Statistics provide a way to extract information from data. They appear everywhere, not only in scientific papers and talks, but in everyday news on medical advances, weather, and sports. The more you know about statistics the better, because they can be easily misused and deliberately abused.

Imagine a technical colleague calling to give you a report on an experiment. It wouldn’t make sense for your colleague to read off every single measurement; instead, you would expect a summary of the overall result. An obvious question would be how things came out on average. Then you would probably ask about the quantity and variability of the results so you could develop some degree of confidence in the data. Assuming that the experiment has a purpose, you must ultimately decide whether to accept or reject the findings. Statistics are very helpful in cases like this; not only as a tool for summarizing, but also for calculating the risks of your decision.

Go Directly Tojail

When making a decision about an experimental outcome, minimize two types of errors:

1. Type I: Saying something happened when it really didn’t (a false alarm). This is often referred to as the alpha (α) risk. For example, a fire alarm in your kitchen goes off whenever you make toast.
2. Type II: Not discovering that something really happened (failure to alarm). This is often referred to as the beta (β) risk. For example, after many false alarms from the kitchen fire detector, you remove the battery. Then a piece of bread gets stuck in the toaster and starts a fire.

The following chart shows how you can go wrong, but it also allows for the possibility that you may be correct.

Decision-Making Outcomes		What You Say Based on Experiment:
		Yes	No
The Truth:	Yes	Correct	Type 2 Error
	No	Type 1 Error	Correct

The following story illustrates a Type I error. Just hope it doesn’t happen to you!

A sleepy driver pulled over to the side of the highway for a nap. A patrolman stopped and searched the vehicle. He found a powdery substance, which was thought to be an illegal drug, so he arrested the driver. The driver protested that this was a terrible mistake; that the bag contained the ashes from his cremated grandmother. Initial screening tests gave a positive outcome for a specific drug. The driver spent a month in jail before subsequent tests confirmed that the substance really was ashes and not a drug. To make matters worse, most of grandmother’s ashes were consumed by the testing. The driver filed a lawsuit seeking unspecified damages. (Excerpted from a copyrighted story in 1998 by the San Antonio Express-News.)

The “X” Factors

Let’s assume you are responsible for some sort of system, such as:

• 

  Computer simulation
• 

  Analytical instrument
• 

  Manufacturing process
• 

  Component in an assembled product
• 

  Any kind of manufactured “thing” or processed “stuff”

In addition, the system could be something people-related, such as a billing process or how a company markets its products via the layout of an Internet web page or point-of-purchase display. To keep the example generic, consider the system as a black box, which will be affected by various controllable factors (Figure 1.1). These are the inputs. They can be numerical (e.g., temperature) or categorical (e.g., raw material supplier). In any case, we will use the letter “X” to represent the input variables.

Presumably, you can measure the outputs or responses in at least a semiquantitative way. To compute statistics, you must at least establish a numerical rating, even if it’s just a 1 to 5 scale. We will use the letter “Y” as a symbol for the responses.

Unfortunately, you will always encounter variables, such as ambient temperature and humidity, which cannot be readily controlled or, in some cases, even identified. These uncontrolled variables are labeled “Z.” They can be a major cause for variability in the responses. Other sources of variability are deviations around the set points of the controllable factors, sampling and measurement error. Furthermore, the system itself may be composed of parts that also exhibit variability.

Figure 1.1 System variables.

Table 1.1 How DOE differs from SPC

	SPC	DOE
Who	Operator	Engineer
How	Hands-off (monitor)	Hands-on (change)
Result	Control	Breakthrough
Cause for Variability	Special (upset)	Common (systemic)

How can you deal with all this variability? Begin by simply gathering data from the system. Then make a run chart (a plot of data versus time) so you can see how much the system performance wanders. Statistical process control (SPC) offers more sophisticated tools for assessing the natural variability of a system. However, to make systematic improvements—rather than just eliminating special causes—you must apply DOE. Table 1.1 shows how the tools of SPC and DOE differ.

Talk To Your Process (And It Will Talk Back To You)

Bill Hunter, one of the co-authors of a recommended book on DOE called Statistics for Experimenters: Design, Innovation, and Discovery, 2nd ed. (Wiley-Interscience, 2005), said that doing experiments is like talking to your process. You ask questions by making changes in inputs, and then listen to the response. SPC offers tools to filter out the noise caused by variability, but it is a passive approach, used only for listening. DOE depends completely on you to ask the right questions. Asking wrong questions is sometimes called a Type III error (refer to the earlier text on Type I and II errors). Therefore, subject matter knowledge is an essential prerequisite for successful application of DOE.

“When I took math class, I had no problem with the questions, it was the answers I couldn’t give.”

Rodney Dangerfield

Does Normal Distribution Ring Your Bell?

When you ch...

Table of contents

• Cover
• Halftitle Page
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Introduction
• 1 Basic Statistics for DOE
• 2 Simple Comparative Experiments
• 3 Two-Level Factorial Design
• 4 Dealing with Nonnormality via Response Transformations
• 5 Fractional Factorials
• 6 Getting the Most from Minimal-Run Designs
• 7 General Multilevel Categoric Factorials
• 8 Response Surface Methods for Optimization
• 9 Mixture Design
• 10 Back to the Basics: The Keys to Good DOE
• 11 Split-Plot Designs to Accommodate Hard-to-Change Factors
• 12 Practice Experiments
• Appendix 1
• Appendix 2
• Glossary
• Recommended Readings
• Index
• About the Authors
• About the Software