Applied Statistics and Probability for Engineers

470 CHAPTER 13 DESIGN AND ANALYSIS OF SINGLE-FACTOR EXPERIMENTS: THE ANALYSIS OF VARIANCE

Experimental design methods are also useful in engineering designactivities, where new

products are developed and existing ones are improved. Some typical applications of statisti-

cally designed experiments in engineering design include

1. Evaluation and comparison of basic design configurations


2. Evaluation of different materials


3. Selection of design parameters so that the product will work well under a wide vari-
   ety of field conditions (or so that the design will be robust)


4. Determination of key product design parameters that affect product performance
   The use of experimental design in the engineering design process can result in products that
   are easier to manufacture, products that have better field performance and reliability than their
   competitors, and products that can be designed, developed, and produced in less time.
   Designed experiments are usually employed sequentially.That is, the first experiment
   with a complex system (perhaps a manufacturing process) that has many controllable variables
   is often a screening experimentdesigned to determine which variables are most important.
   Subsequent experiments are used to refine this information and determine which adjustments
   to these critical variables are required to improve the process. Finally, the objective of the ex-
   perimenter is optimization, that is, to determine which levels of the critical variables result in
   the best process performance.
   Every experiment involves a sequence of activities:


5. Conjecture—the original hypothesis that motivates the experiment.


6. Experiment—the test performed to investigate the conjecture.


7. Analysis—the statistical analysis of the data from the experiment.


8. Conclusion—what has been learned about the original conjecture from the experi-
   ment. Often the experiment will lead to a revised conjecture, and a new experiment,
   and so forth.
   The statistical methods introduced in this chapter and Chapter 14 are essential to good
   experimentation. All experiments are designed experiments;unfortunately, some of them
   are poorly designed, and as a result, valuable resources are used ineffectively. Statistically
   designed experiments permit efficiency and economy in the experimental process, and the
   use of statistical methods in examining the data results in scientific objectivitywhen draw-
   ing conclusions.

13-2 THE COMPLETELY RANDOMIZED SINGLE-FACTOR

EXPERIMENT

13-2.1 An Example

A manufacturer of paper used for making grocery bags is interested in improving the tensile

strength of the product. Product engineering thinks that tensile strength is a function of the

hardwood concentration in the pulp and that the range of hardwood concentrations of practi-

cal interest is between 5 and 20%. A team of engineers responsible for the study decides to in-

vestigate four levels of hardwood concentration: 5%, 10%, 15%, and 20%. They decide to

make up six test specimens at each concentration level, using a pilot plant. All 24 specimens

are tested on a laboratory tensile tester, in random order. The data from this experiment are

shown in Table 13-1.

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