TESTING HYPOTHESES ABOUT THE POWER LAW PROCESS UNDER FAILURE TRUNCATION USING INTRINSIC BAYES FACTORS

RAMA T. LINGHAM^{1} AND S. SIVAGANESAN^{2}

1Division of Statistics, Northern Illinois University, DeKalb, IL 60115-2854, U.S.A.

2Department of Mathematical Sciences, University of Cincinnati, Old Chemistry Building (ML25), Cincinnati, OH 45221-0025, U.S.A.

(Received February 7, 1996; revised October 3, 1996)

Abstract. Conventional Bayes factors for hypotheses testing cannot typically accommodate the use of standard noninformative priors, as such priors are defined only up to arbitrary constants which affect the values of the Bayes factors. To circumvent this problem, Berger and Pericchi (1996, J. Amer. Statist. Assoc., 91, 109–122) introduced a new criterion called the Intrinsic Bayes Factor (IBF). In this paper, we use their methodology to test several hypotheses regarding the shape parameter of the power law process. Assuming that we have data from the process according to the failure-truncation sampling scheme, we derive the arithmetic and geometric IBF’s using the reference priors. We deduce a set of intrinsic priors that correspond to these IBF’s, as the observed number of failures tends to infinity. We then use these results to analyze an actual data set on the failures of an aircraft generator.

Key words and phrases: Automatic Bayes factor, Intrinsic Bayes factors, (nonhomogeneous) Poisson process, reference prior, repairable systems, tests of hypotheses, Weibull process.