197
Views
2
CrossRef citations to date
0
Altmetric
Original Article

A Bivariate Gamma Model for a Latent Degradation Process

Pages 1924-1938 | Received 13 Nov 2011, Accepted 12 Mar 2012, Published online: 14 Apr 2014

References

  • Aalen, O.O., Gjessing, H.K. (2004). Survival models based on the Ornstein-Uhlenbeck process, Lifetime Data Anal. 407–423.
  • Albert, J. (2007). Bayesian Computation with R. New York: Springer.
  • Bagdonavicius, V., Nikulin, M. (2002). Estimation in degradation models with explanatory variables. Lifetime Data Anal. 7:85–103.
  • Birnbaum, Z.W., Saunders, S.C. (1969). A new family of life distribution. J. Appl. Probab. 6:319–327.
  • Balakrishnan, N., Lai, C.D. (2009). Continuous Bivariate Distributions, 2nd ed. Adelaide, Australia: Springer.
  • Bhattacharyya, G.K., Fries, A. (1982). Fatigue failure models-Birnbaum-Saunders vs. inverse Gaussian. IEEE Trans. Reliab. 31:439–440.
  • Chib, S., Greenberg, E. (1995). Understanding the Metropolis-Hastings algorithm. Amer. Statistician, 49(4):327–335.
  • Chhikara, R.S., Folks, J.L. (1989). The Inverse Gaussian Distribution: Theory, Methodology and Applications. New York: Marcel Dekker.
  • Doksum, K., Normand, S-L.T. (1995). Gaussian models for degradation process-Part I: Methods for the analysis of biomarker data. Lifetime Data Anal. 1:135–144.
  • Feller, W. (1970). An Intoduction to Probability Theory and Its Application.2nd ed. New York: John Wiley.
  • Iliopoulos, G., Karlis, D., Ntzoufras, I. (2005). Bayesian estimation in Kibble's bivariate gamma distribution. Can. J. Statist. 33(4):571–589.
  • Jewell, N. P., Kalbfleisch, J. D. (1996). Marker processes in survival analysis. Lifetime Data Anal. 2:15–29.
  • Lu, J. (1995). A reliability model based on degradation and lifetime data. Ph.D. thesis, McGill University, Montreal, Canada.
  • Lu, C. J., Meeker, W. Q. (1993). Using degradation measures to estimate time to failure distribution. Technometrics 35:161–174.
  • Lawless, J., Crowder, M. (2004). Covariates and random effects in a gamma process model with application to degradation failure. Lifetime Data Anal. 10:213–227.
  • Lee, M.L.T., Shubina, M., Zaslavsky, A. (2005). Bayesian analysis for marker and degradation. Applied Stochastic and Data Analysis Conference, . Brest, France.
  • Petit, L. I., Young, K. D. S. (1999). Bayesian analysis for inverse gaussian lifetime data with measures of degradation. J. Statist. Comput. Simul. 63:217–234.
  • Padgett, W. J., Tomlinson, M. A. (2004). Inference from accelerated degradation anf failure data based on Gaussian process models. Lifetime Data Anal. 10:191–206.
  • Park, C., Padgett, W. J. (2005). Accelerated degradation models for failure based on geometric Brownian motion and Gamma processes. Lifetime Data Anal. 11:511–527.
  • Prabhu, N.U. (1965). Stochastic Process: Basic Theory and Its Applications. New York: Macmillan Company.
  • Singpurwalla, N.D. (1995). Survival in daynamic environments. Statist. Sci., 10:86–103.
  • Whitmore, G. A. (1995). Estimating degradation by a wiener diffusion process subject to measurement error. Lifetime Data Anal. 1:307–319.
  • Whitmore, G. A., Schenkelberg, F. (1997). Modelling accelerated degradation data using wiener diffusion with a time scale transformation. Lifetime Data Anal. 3:1–19.
  • Whitmore, G. A., Crowder, M. J., Lawless, J. F. (1998). Failure inference from a marker process based on bivariate Wiener model. Lifetime Data Anal. 4:229–251.
  • Yuan, L., Kalbfleisch, J.D. (2000). On the Bessel distribution and related problems. Ann. Inst. Statist. Math. 52(3):438–447.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.