To Survive or to Fail: What Is the Question?

• Activity Number: 67
• Type: Topic Contributed
• Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Refik Soyer*+
• Companies: The George Washington University
• Keywords: Entropy ; Predictive Information ; Failure Data Analysis ; Prediction

Abstract

A natural question arising in life testing is this: "During the conduct of the test do we want to observe more failures or more survivals?" Intuitively speaking, failures, because of their definitiveness, providemore information about the parameters of a failuremodel. But it has been shown before that this is not always true for an observation from the exponential model under the gamma prior for the failure rate, and that it depends on the particular parameter of interest. We show that the existing findings are more general, and that they hold for samples from a family of distributions which contains several lifetime models used in practice, under the gamma and Jeffreys' priors. We also provide results for the stochastic order of predictive distributions derived from failure and survival samples. These results enable us to compare the information provided by failure and survival times about prediction of lifetime of an untested item, without assuming a particular family of models for the likelihood or for the prior distribution.