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Statistical and Probabilistic Models in Reliability pp 27–37Cite as

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CPIT Goodness-Of-Fit Tests for Reliability Growth Models

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Part of the book series: Statistics for Industry and Technology ((SIT))

Abstract

Assume that the n first failure times of a repairable system are observed. In order to choose an appropriate stochastic model for these data, goodness-of-fit tests have to be performed. The aim of this work is to study the goodness-of-fit tests based on the Conditional Probability Integral Transformation of O’Reilly-Quesenberry. The general CPIT methodology is described. Then the CPIT tests are derived for the Homogeneous Poisson Process, Jelinski-Moranda model, Goel-Okumoto model and the Power-Law Process. The power of these tests is assessed through simulations and finally, they are applied to real software reliability data.

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References

  1. Cretois E. and Gaudoin O. (1997). New results on goodness-of-fit tests for the power-law process and applications to software reliability, Proceedings of the 3rd ISSAT International Conference on Reliability and Quality in Design, Anaheim, 111–115.

    Google Scholar 

  2. Crow, L. H. (1974). Reliability analysis for complex repairable systems, In Reliability and Biometry — Statistical Analysis of Lifelength, SIAM Philadelphia, pp. 379–410.

    Google Scholar 

  3. D’Agostino R. B. and Stephens M. A. (1986). Goodness-of-fit Techniques, New York: Marcel Dekker.

    MATH  Google Scholar 

  4. Gaudoin O. (1998). CPIT Goodness-of-fit tests for the power law process, Communications in Statistics—Theory and Methods, 27, 1.

    Article  MathSciNet  Google Scholar 

  5. 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, 1, 206–211.

    Article  MATH  Google Scholar 

  6. Jelinski, Z. and Moranda, P. B. (1972). Statistical computer performance evaluation, In Software Reliability Research (Ed., W. Freiberger), pp. 465–497, New York: Academic Press.

    Google Scholar 

  7. Lee, L. and Finelli, G. B. (1989). A transformation for testing the fit of an exponential order statistics model, Stochastic Processes and Their Applications, 33, 299–307.

    Article  MathSciNet  MATH  Google Scholar 

  8. Lyu, M. R. (Ed.) (1996). Handbook of Software Reliability Engineering, IEEE Computer Society Press and McGraw-Hill Book Company.

    Google Scholar 

  9. Miller, D. R. (1986). Exponential order statistics models of software reliability growth, IEEE Transactions on Software Engineering, 12, 12–24.

    Article  MATH  Google Scholar 

  10. Moranda, P. B.(1979). Event altered rate models for general reliability analysis, IEEE Transactions on Reliability, 28, 5, 376–381.

    Article  MATH  Google Scholar 

  11. Musa J. D. (1979). Software reliability data, Technical Report, Rome Air Development Center.

    Google Scholar 

  12. O’Reilly, F. J. and Quesenberry, C. P. (1973). The conditional probability integral transform and applications to obtain composite chi-square goodness-of-fit tests, Annals of Statistics, 1, 74–83.

    Article  MathSciNet  MATH  Google Scholar 

  13. O’Reilly, F. J. and Stephens, M. A. (1982). Characterizations and goodness-of-fit tests, Journal of the Royal Statistical Society, Series B, 44, 353–360.

    MathSciNet  MATH  Google Scholar 

  14. Rigdon S. E. (1989). Testing goodness-of-fit for the power-law process, Communications in Statistics—Theory and Methods, 18, 4665–4676.

    Article  MATH  Google Scholar 

  15. Rosenblatt, M. (1952). Remarks on a multivariate transformation, Annals of Mathematical Statistics, 23, 470–472.

    Article  MathSciNet  MATH  Google Scholar 

  16. Xie, M. (1991). Software reliability modelling, Singapore: World Scientific.

    MATH  Google Scholar 

  17. Yamada, S., Ohba, M. and Osaki, S. (1983). S-shaped reliability growth modelling for software error detection, IEEE Transactions on Reliability, 35, 475–478.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Laboratoire IMAG-LMC, Grenoble, France

    Olivier Gaudoin

Authors
  1. Olivier Gaudoin
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Editor information

Editors and Affiliations

  1. Power Engineering Faculty, University Politehnica Bucharest, 77206, Bucharest, Romania

    D. C. Ionescu

  2. Division Mathématiques Appliquées, Université de Technologie de Compiègne, 60205, Compiègne Cedex, France

    N. Limnios

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© 1999 Springer Science+Business Media New York

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Gaudoin, O. (1999). CPIT Goodness-Of-Fit Tests for Reliability Growth Models. In: Ionescu, D.C., Limnios, N. (eds) Statistical and Probabilistic Models in Reliability. Statistics for Industry and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1782-4_2

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  • DOI: https://doi.org/10.1007/978-1-4612-1782-4_2

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7280-9

  • Online ISBN: 978-1-4612-1782-4

  • eBook Packages: Springer Book Archive

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