Optimal Blocking with One Hard-to-change Factor

• Activity Number: 211
• Type: Topic Contributed
• Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Quality and Productivity
• Author(s): Frank T. Anbari*+
• Companies: George Washington University
• Keywords: hard-to-change factors ; expensive-to-change factors ; prediction variance ; G-efficiency ; cost function ; fractional factorial designs

Abstract

This paper shows how to design, run and analyze 2**k and 2**k-p experimental designs for process improvement when there are hard-to-change or expensive-to-change factors. The paper discusses the different ways of running these experiments, and gives practical recommendations. It shows how to block designs to get a small prediction variance and low cost. It presents an algorithm to allow the selection of efficient confounding relation(s) in 2**k and 2**k-p designs, presents methods for calculating the prediction variance and G-efficiency when there are hard-to-change factors, and tabulates the results. The approach is extended to fractional factorial designs, and results are tabulated. The paper discusses the cost of running the experiment. It shows practical block patterns which have higher G-efficiencies and higher cost efficiencies than designs run in a random order. The paper shows that with one hard-to-change factor, a blocked design is both less expensive to run, because it requires fewer resets of the hard-to-change factor, and more precise as it gives a lower variance of prediction than a completely randomized design.