Analyzing Deficient Response Summaries from Designed Experiments

Abstract

ABSTRACT All too often statisticians do not have access to raw experimental data. These scenarios require additional methodology to properly account for the missing information. In this article, we demonstrate a technique for analyzing averages of lifetime data collected at various experimental conditions that provides inference for factor effects. To handle these summaries, we use some numerical techniques to calculate the probability density function of the average of independent and identically distributed lognormal random variables. We illustrate our method with an example from the literature and provide some R code that implements a Bayesian analysis. We also provide recommendations for more informative summary statistics than lifetime averages for lognormal data.

KEYWORDS:

• Bayesian inference
• EULER algorithm
• Euler’s formula
• fractional factorial design
• Laplace transform
• lifetime
• lognormal
• reliability
• robust design
• sufficient statistics
• sum of i.i.d. random variables

Additional information

Notes on contributors

M. S. Hamada

M. S. Hamada is a Scientist and holds a Ph.D. in Statistics from the University of Wisconsin– Madison. He is a Fellow of the American Statistical Association. His research interests include design and analysis of experiments, measurement system assessment, quality control, and reliability.

R. L. Warr

R. L. Warr is an Assistant Professor with a Ph.D. in Statistics from the University of New Mexico. His research interests include Bayesian statistics, reliability, and semi-Markov processes.