Predictive analyses for nonhomogeneous Poisson processes with power law using Bayesian approach

Authors:
Jun-Wu Yu;Guo-Liang Tian;Man-Lai Tang
Affiliations:
School of Mathematics and Computation Science, Hunan University of Science and Technology, Xiangtan, Hunan 411201, PR China;Division of Biostatistics, University of Maryland Greenebaum Cancer Center, 22 South Greene Street, Baltimore, Maryland 21201, USA;Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, PR China
Venue:
Computational Statistics & Data Analysis
Year:
2007

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Abstract

Nonhomogeneous Poisson process (NHPP) also known as Weibull process with power law, has been widely used in modeling hardware reliability growth and detecting software failures. Although statistical inferences on the Weibull process have been studied extensively by various authors, relevant discussions on predictive analysis are scattered in the literature. It is well known that the predictive analysis is very useful for determining when to terminate the development testing process. This paper presents some results about predictive analyses for Weibull processes. Motivated by the demand on developing complex high-cost and high-reliability systems (e.g., weapon systems, aircraft generators, jet engines), we address several issues in single-sample and two-sample prediction associated closely with development testing program. Bayesian approaches based on noninformative prior are adopted to develop explicit solutions to these problems. We will apply our methodologies to two real examples from a radar system development and an electronics system development.