We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 November 2024
Call for Paper
December Edition
IJCA solicits high quality original research papers for the upcoming December edition of the journal. The last date of research paper submission is 20 November 2024

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

Software Reliability Data Analysis with Marshall-Olkin Extended Weibull Model using MCMC Method for Non-Informative Set of Priors

by Ashwini K. Srivastava, Vijay Kumar
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 18 - Number 4
Year of Publication: 2011
Authors: Ashwini K. Srivastava, Vijay Kumar
10.5120/2271-2926

Ashwini K. Srivastava, Vijay Kumar . Software Reliability Data Analysis with Marshall-Olkin Extended Weibull Model using MCMC Method for Non-Informative Set of Priors. International Journal of Computer Applications. 18, 4 ( March 2011), 31-39. DOI=10.5120/2271-2926

@article{ 10.5120/2271-2926,
author = { Ashwini K. Srivastava, Vijay Kumar },
title = { Software Reliability Data Analysis with Marshall-Olkin Extended Weibull Model using MCMC Method for Non-Informative Set of Priors },
journal = { International Journal of Computer Applications },
issue_date = { March 2011 },
volume = { 18 },
number = { 4 },
month = { March },
year = { 2011 },
issn = { 0975-8887 },
pages = { 31-39 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume18/number4/2271-2926/ },
doi = { 10.5120/2271-2926 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:05:26.506759+05:30
%A Ashwini K. Srivastava
%A Vijay Kumar
%T Software Reliability Data Analysis with Marshall-Olkin Extended Weibull Model using MCMC Method for Non-Informative Set of Priors
%J International Journal of Computer Applications
%@ 0975-8887
%V 18
%N 4
%P 31-39
%D 2011
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, the two-parameter Marshall-Olkin Extended Weibull (MOEW) model is considered to analyze the software reliability data. The Markov Chain Monte Carlo (MCMC) method is used to compute the Bayes estimates of the model parameters. In this paper, it is assumed that the parameters have non-informative set of priors and they are independently distributed. Under the above priors, we use Gibbs algorithm in OpenBUGS to generate MCMC samples from the posterior density function. Based on the generated samples, we can compute the Bayes estimates of the unknown parameters and also can construct highest posterior density credible intervals. We also compute the maximum likelihood estimate and associated confidence intervals to compare the performances of the Bayes estimators with the classical estimators. One data analysis is performed for illustrative purposes.

References
  1. Chen, M. H. and Shao, Q. M. (1999). Monte Carlo estimation of Bayesian credible intervals and HPD intervals, Journal of Computational and Graphical Statistics. 8(1).
  2. Chen, M., Shao, Q. and Ibrahim, J.G. (2000). Monte Carlo Methods in Bayesian Computation, Springer, NewYork.
  3. Cid, J. E. R. and Achcar, J. A., (1999). Bayesian inference for nonhomogeneous Poisson processes in software reliability models assuming nonmonotonic intensity functions, Computational Statistics & Data Analysis 32:147–159.
  4. Hornik, K., (2004). The R FAQ (on-line). Available at http://www.ci.tuwien. ac.at/~hornik/R/.
  5. Ihaka, R.; Gentleman, R.R. (1996). R: A language for data analysis and graphics, Journal of Computational and Graphical Statistics, 5, 299–314.
  6. Jalote, P. (1991). An Integrated Approach to Software Engineering. Springer – Verlag, New York.
  7. Jiang, R. and Murthy,D.N.P. (1999). Exponentiated Weibull family: A graphical approach, IEEE Transactions on Reliability, 48(1), 68–72.
  8. Kumar, V. and Ligges, U. (2011). reliaR : A package for some probability distributions. http://cran.r-project.org/web/packages/reliaR/index.html.
  9. Lawless, J. F., (2003). Statistical Models and Methods for Lifetime Data, 2nd ed., John Wiley and Sons, New York.
  10. Lyu M.R., (1996). Handbook of Software Reliability Engineering, IEEE Computer Society Press, McGraw Hill, 1996.
  11. Marshall, A.W., Olkin, I. (1997). A new method for adding a parameter to a family of distributions with application to the Weibull and Weibull families. Biometrika, 84(3): 641- 652.
  12. Marshall, A. W., Olkin, I. (2007). Life Distributions: Structure of Nonparametric, Semiparametric and Parametric Families. Springer, New York.
  13. Mudholkar, G.S. and Srivastava, D.K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42(2), 299–302.
  14. Mudholkar, G.S., Srivastava, D.K., and Freimer, M. (1995). The exponentiated Weibull family—a reanalysis of the bus-motor-failure data, Technometrics, 37(4), 436–445.
  15. Nassar, M.M., and Eissa, F. H. (2003). On the Exponentiated Weibull Distribution, Communications in Statistics - Theory and Methods, 32(7), 1317 –1336.
  16. R Development Core Team (2008). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, URL http://www.R-project.org.
  17. Singpurwalla, N.D. and S. Wilson (1994). Software Reliability Modeling. International Statistic. Rev., 62 3:289-317.
  18. Srivastava, A.K. and Kumar V. (2011). Analysis of Software Reliability Data using Exponential Power Model. International Journal of Advanced Computer Science and Applications, Vol. 2, No. 2, February 2011, 38-45.
  19. Thomas, A. (2007). OpenBUGS, URL http://mathstat.helsinki.fi/openbugs/.
  20. Thomas, A. (2010). OpenBUGS Developer Manual, Version 3.0.2. URL http://mathstat.helsinki.fi/openbugs/
  21. Zhang T,Xie M (2007) Failure data analysis with extended Weibull distribution. Commun Statist Simul Comp, 36:579–592.
  22. Tang,Y., Xie,M., Goh,T.N.(2003).Statistical analysis of a Weibull extension model. Communications in Statistics:Theory & Methods 32(5):913 –928.
  23. Wang,R.H., Fei,H.F.(2003).Uniqueness of the maximum likelihood estimate of the Weibull distribution tampered failure rate model. Communications in Statistics:Theory & Methods 32:2321 –2338.
  24. Xie,M., Tang,Y., Goh,T.N.(2002).A modified Weibull extension with bathtub-shaped failure rate function. Reliability Engineering System Safety 76(3):279 –285.
  25. Xie,M., Goh,T.N., Tang,Y.(2004).On changing points of mean residual life and failure rate function for some generalized Weibull distributions.Reliability Engineering &System Safety 84:293 –299.
Index Terms

Computer Science
Information Sciences

Keywords

Marshall-Olkin Extended Weibull (MOEW) model Parameter estimation Maximum likelihood estimate (MLE) Bayes estimates Markov Chain Monte Carlo (MCMC)

Powered by PhDFocusTM