[KSCI] Korea Science Citation Index Service

A Bayesian Inference for Power Law Process with a Single Change Point

Kim, Kiwoong (Department of Statistics, Seoul National University)
Inkwon Yeo (Division of Mathematics and Statistical Informatics Chonbuk National University)
Sinsup Cho (Department of Statistics, Seoul National University)
Kim, Jae-Joo (Department of Statistics, Seoul National University)

Publication Information

International Journal of Quality Innovation / v.5, no.1, 2004 , pp. 1-9 More about this Journal

Abstract

The nonhomogeneous poisson process (NHPP) is often used to model repairable systems that are subject to a minimal repair strategy, with negligible repair times. In this situation, the system can be characterized by its intensity function. There have been many NHPP models according to intensity functions. However, the intensity function of system in use can be changed because of repair or its aging. We consider the single change point model as the modification of the power law process. The shape parameter of its intensity function is changed before and after the change point. We detect the presence of the change point using Bayesian methodology. Some numerical results are also presented.

Keywords

Repairable System; Nonhomogeneous Poisson Process; Change Point; Bayes Factor; Power Law Process; Markov Chain and Monte Carlo technique;

Citations & Related Records

Reference

1	Achcar, J. A., Dey, D. K. and Niverthi, M. (1997). 'A Bayesian approach using nonhomogeneous Poisson process for software reliability model', Frontiers in Reliability, IAPQR.
2	Cox, D. R. and Lewis, P. A. (1966). 'The Statistical Analysis of Series of Events', Methuem, London
3	Crow, L. H. (1990). 'Evaluating the reliability of reparirable systems', Proceedings of the Annual Reliability and Maintainability Symposium: IEEE, 275-279
4	Duane, J. T. (1964). 'Learning curve approach to reliability monitoring', IEEE Transactions on Aerospace, 2, 263-566
5	Thompson Jr., W. A. (1988). 'Point Process Models with Applications to Safety and Reliability', Chapman and Hall, New York
6	Goel, A. L. and Okumoto, K. (1979). 'Time-dependent error detection rate model for software reliability and other performance measures', IEEE Transactions on Reliability, 28, 206-211 DOI ScienceOn
7	Ascher, H and Feingold, H. (1984). 'Repairable Systems Reliability : Modeling, Inference, Misconceptions and Their Causes', Marcel Dekker, New York.
8	Carlin, B. P., Gelfand A. E. and Smith, A. F. M. (1992). 'Hierarchical Bayesian Analysis of Change Point Problems', Journal of the Royal Statistical Society C, 41, 389-405
9	Gilks, W. R., S. Richardson, and D. J. Spiegelhalter (1996). 'Markov chain Monte Carlo in practice', Chapman and Hall, New York