Adaptive One-Factor-at-a-Time Experimentation and Expected Value of Improvement

• Published in: Technometrics Vol. 48; no. 3; pp. 418 - 431
• Main Authors: Frey, Daniel D, Wang, Hungjen
• Format: Journal Article
• Language: English
• Published: Alexandria, VI Taylor & Francis 01.08.2006; Milwaukee, WI The American Society for Quality and The American Statistical Association; American Society for Quality Control; American Statistical Association; American Society for Quality
• Subjects: Adaptation; Adaptive experimentation; Aircraft; Applied sciences; Computer science; control theory; systems; Data processing. List processing. Character string processing; Design; Design engineering; Design of experiments; Designers; Error rates; Exact sciences and technology; Expected values; Experiment design; Experimentation; Factorial design; Factorial experiments; Flight time; Fractional factorial design; Mathematical models; Mathematical theorems; Mathematics; Mechanical engineering. Machine design; Memory organisation. Data processing; One factor at a time; Parameter estimation; Probability and statistics; Sciences and techniques of general use; Software; Statistics; Trends; One factor at a time; Probabilistic approach; Electric vehicle; Fractional factorial design; Modeling; Adaptive method; Adaptive experimentation; Engineering design; Systems engineering; Experimental design; Factorial design; Aircraft; Design of experiments
• ISSN: 0040-1706; 1537-2723
• DOI: 10.1198/004017006000000075

This article concerns adaptive experimentation as a means for making improvements in design of engineering systems. A simple method for experimentation, called "adaptive one-factor-at-a-time," is described. A mathematical model is proposed and theorems are proven concerning the expected value of the improvement provided and the probability that factor effects will be exploited. It is shown that adaptive one-factor-at-a-time provides a large fraction of the potential improvements if experimental error is not large compared with the main effects and that this degree of improvement is more than that provided by resolution III fractional factorial designs if interactions are not small compared with main effects. The theorems also establish that the method exploits two-factor interactions when they are large and exploits main effects if interactions are small. A case study on design of electric-powered aircraft supports these results.