Applied Statistics and Probability for Engineers, 6th Edition

Design of Experiments with Several Factors

Chapter Outline

14-1 Introduction

14-2 Factorial Experiments

14-3 Two-Factor Factorial Experiments

14-3.1 Statistical Analysis of the Fixed-Effects Model

14-3.2 Model Adequacy Checking

14-3.3 One Observation per Cell

14-4 General Factorial Experiments

14-5 2^k Factorial Designs

14-5.1 2² DESIGN

14-5.2 2^k Design for k ≥ 3 Factors

14-5.3 Single Replicate of the 2^k Design

14-5.4 Addition of Center Points to a 2^k Design

14-6 Blocking and Confounding in the 2^k Design

14-7 Fractional Replication of the 2^k Design

14-7.1 One-Half Fraction of the 2^k Design

14-7.2 Smaller Fractions: The 2^k–p Fractional Factorial

14-8 Response Surface Methods and Designs

Carotenoids are fat-soluble pigments that occur naturally in fruits in vegetables and are recommended for healthy diets. A well-known carotenoid is beta-carotene. Astaxanthin is another carotenoid that is a strong antioxidant and commercially produced. An exercise later in this chapter describes an experiment in Biotechnology Progress to promote astaxanthin production. Seven variables were considered important to production: photon flux density and concentrations of nitrogen, phosphorous, magnesium, acetate, ferrous, and NaCl. It was important to study the effects of these factors as well as the effects ...