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Section A

The Lp-norm estimation of the parameters for the Jelinski–Moranda model in software reliability

Pages 467-481 | Received 19 May 2011, Accepted 14 Nov 2011, Published online: 16 Dec 2011

References

  • Almering , V. , van Genuchten , M. , Cloudt , G. and Sonnemans , P. J.M. 2007 . Using software reliability growth models in practice . IEEE Softw. , 24 ( 6 ) : 82 – 88 .
  • Atieg , A. and Watson , G. A. 2004 . Use of lp norms in fitting curves and surfaces to data . ANZIAM J. , 45(E) : C187 – C200 .
  • Bjorck , Å. 1996 . “ Numerical Methods for Least Squares Problems ” . Philadelphia , PA : SIAM .
  • Cai , K.-Y. 1998 . On estimating the number of defects remaining in software . J. Syst. Softw. , 40 : 93 – 114 .
  • Carnes , P. Software reliability in weapon systems . Proceedings of the 8th International Symposium on Software Reliability Engineering: Case Studies . Albuquerque , NM , USA. pp. 95 – 100 .
  • DasGupta , A. 2010 . “ Fundamentals of Probability: A First Course ” . Berlin : Springer .
  • David , H. A. and Nagaraja , H. N. 2003 . Order Statistics , 3 , New Jersey : Wiley .
  • Demidenko , E. Z. 2006 . Criteria for global minimum of sum of squares in nonlinear regression . Comput. Statist. Data Anal. , 51 : 1739 – 1753 .
  • Demidenko , E. Z. 2008 . Criteria for unconstrained global optimization . J. Optim. Theory Appl. , 136 : 375 – 395 .
  • Dunham , C. B. 1975 . Nonlinear mean-square approximation on finite sets . SIAM J. Numer. Anal. , 12 : 105 – 110 .
  • Gonin , R. and Money , A. H. 1989 . “ Nonlinear L p -Norm Estimation ” . New York : Marcel Dekker .
  • Hadeler , K. P. , Jukić , D. and Sabo , K. 2007 . Least-squares problems for Michaelis-Menten kinetics . Math. Methods Appl. Sci. , 30 : 1231 – 1241 . doi:10.1002/mma.835
  • Hardy , G. H. , Littlewood , J. E. and Pòlya , G. 1988 . Inequalities , 2 , Cambridge : Cambridge University Press .
  • Jelinski , Z. and Moranda , P. 1972 . “ Software reliability research ” . In Statistical Computer Performance Evaluation , Edited by: Freiberg , W. 465 – 484 . New York : Academic Press .
  • Jukić , D. 2009 . On the existence of the best discrete approximation in l p -norm by reciprocals of real polynomials . J. Approx. Theory , 156 : 212 – 222 .
  • Jukić , D. 2011 . Total least squares fitting Bass diffusion model . Math. Comput. Model , 53 : 1756 – 1770 . doi:10.1016/j.mcm.2010.12.054
  • Jukić , D. and Scitovski , R. 1997 . Existence of optimal solution for exponential model by least squares . J. Comput. Appl. Math. , 78 : 317 – 328 .
  • Kanoun , K. , Martini , M. B. and De Souza , J. M. 1991 . A method for software reliability analysis and prediction application to the TROPICO-R switching system . IEEE Trans. Softw. Eng. , 17 ( 4 ) : 334 – 344 .
  • Langberg , N. and Singpurwalla , N. 1985 . A unification of some software reliability models . SIAM J. Sci. Stat. Comput. , 6 : 781 – 790 .
  • Littlewood , B. and Verall , B. 1973 . A Bayesian reliability growth model for computer software . J. R. Statist. Soc. Ser. C , 22 : 332 – 346 .
  • Marković , D. and Jukić , D. 2010 . On nonlinear weighted total least squares parameter estimation problem for the three-parameter Weibull density . Appl. Math. Model , 34 : 1839 – 1848 .
  • Miller , D. R. 1986 . Exponential order statistic models of software reliability growth . IEEE Trans. Softw. Eng. , 12 : 12 – 24 .
  • Musa , J. D. 2004 . “ Software Reliability Engineering: More Reliable Software, Faster and Cheaper ” . New York : McGraw-Hill .
  • Nikora , A. P. 2000 . “ Computer Aided Software Reliability Estimation (CASRE), User's Guide, Version 3 ” . Pasadena : Jet Propulsion Laboratory .
  • Pham , H. 2006 . “ System Software Reliability ” . In Springer Series in Reliability Engineering , London : Springer .
  • Ross , G. J.S. 1990 . “ Nonlinear Estimation ” . New York : Springer .
  • Schneidewind , N. F. 2007 . A quantitative approach to software development using IEEE 982.1 . IEEE Softw. , 24 ( 1 ) : 65 – 72 .
  • Schneidewind , N. F. and Keller , T. W. 1992 . Application of reliability models to the space shuttle . IEEE Softw. , 9 ( 4 ) : 28 – 33 .
  • Seber , G. A.F. and Wild , C. J. 1989 . “ Nonlinear Regression ” . New York : Wiley .
  • J. Tal, Development and Evaluation of Software Reliability Estimates, Systems Research Laboratory, UTEC SR 77-013, University of Utah, 1976.
  • Wilson , S. P. and Samaniego , F. J. 2007 . Nonparametric analysis of the order-statistic model in software reliability . IEEE Trans. Softw. Eng. , 33 : 197 – 208 .
  • Xie , M. 1991 . “ Software Reliability Modelling ” . Singapore : World Scientific .
  • Yamada , S. Software reliability models and their applications: A survey . Proceedings of the International Seminar on Software Reliability of Man–Machine Systems . pp. 56 – 80 . Kyoto , , Japan : Kyoto University .

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