Design, Analysis, and Applications of Failure Amplification Experiments

The main focus of this study is related to the Failure Amplification Method (FAMe) proposed by Joseph and Wu (2004). They suggested the use of an “amplification factor” to increase the information from experiments with a binary response variable. In addition to the amplification factor having a known effect, Joseph and Wu recommended that, for convenience of experimentation, this factor be taken as an easy to change, split unit factor. In such cases, the analysis ought to take into account the possibility of both whole unit and split unit error variation. I present such an analysis here, where the Bayesian approach not only permits proper accounting of the error structure, but also facilitates the subsequent optimization step.

FAMe can also be extended to categorical data with more than two categories. I helped design an experiment that was conducted at Huhtamaki Consumer Packaging West Inc., Los Angeles, CA, where the response variable was an ordinal variable characterizing the quality of the Tri Web Taco Bell Disk seal. An amplification factor – speed of the production line - was a whole-unit factor that was hard to change. Therefore an application of FAMe to ordinal data is presented here as well.

It is crucial to plan an experiment carefully, particularly with categorical responses. Levels of the split-unit factor can be chosen sequentially or set in advance. In the case of the sequential design, a rule for choosing a split-unit factor level will affect consistency and bias of the parameter estimates. Theory-based sequential rules often are impractical in real life situations. Properties of sequential ad hoc designs are studied and compared to fixed designs using complete enumeration and simulation techniques.