Statistical analysis of Rayleigh competing risks model based on partially step stress Type-II censoring samples

Volume 12, Issue 4, pp 230--238 http://dx.doi.org/10.22436/jnsa.012.04.04

Publication Date: December 05, 2018 Submission Date: August 29, 2018 Revision Date: October 05, 2018 Accteptance Date: October 15, 2018

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Authors

Abdullah M. Almarashi - Statistic Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia. Ali Algarni - Statistic Department, Faculty of Science, King Abdulaziz University, Jaddeh, Saudi Arabia. G. A. Abd-Elmougod - Mathematics department, Faculty of Science, Taif University, Taif, Saudi Arabia. Sayed Abdel-Khalek - Mathematics department, Faculty of Science, Sohag University, Sohag, Egypt.

Abstract

This paper, discusses the problem of partially step-stress ALTs (accelerated life tests) form Rayleigh competing risks model. Type-II censored scheme is used in obtaining the observed censoring data. The method of MLE (maximum likelihood estimation) of the model parameters for point and approximate confidence intervals are considered. Also, bootstrap confidence intervals of model parameters are discussed. Simulation study is adopted to assess and compare our proposed method. Finally, some comment to illustrate the behavior of numerical results.

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Keywords

• Competing risk model
• accelerate life test
• Rayleigh distribution
• maximum likelihood estimations
• bootstrap confidence intervals

MSC

•  60E05
•  62E10
•  62N05

References

• [1] B. N. Al-Matrafi, G. A. Abd-Elmougod, Statistical Inferences with Jointly Type-II Censored Samples From Two Rayleigh Distributions, Global J. Pure Appl. Math., 13 (2017), 8361–8372.
  • Google Scholar


• [2] R. A. Bakoban, G. A. Abd-Elmougod , MCMC in analysis of progressively first failure censored competing risks data for Gompertz model, J. Comput. Theor. Nanoscience, 13 (2016), 1–9.
  • Google Scholar


• [3] N. Balakrishnan, A synthesis of exact inferential results for exponential step-stress models and associated optimal accelerated life-tests, Metrika, 69 (2009), 351–396.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] N. Balakrishnan, Q. Xie , Exact inference for a simple step-stress model with Type-II hybrid censored data from the exponential distribution, J. Statist. Plann. Inference, 137 (2007), 2543–2563.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] N. Balakrishnan, Q. Xie, D. Kundu , Exact inference for a simple step-stress model from the exponential distribution under time constraint, Ann. Inst. Statist. Math., 61 (2009), 251–274.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [6] M. J. Crowder, Classical Competing Risks, Chapman & Hall, Boca Raton (2001)
  • Google Scholar


• [7] A. C. Davison, D. V. Hinkley, Bootstrap Methods and their Applications, Cambridge University Press, Cambridge (1997)
  • View Article
  • MathSciNet
  • Google Scholar


• [8] B. Efron, Censored data and bootstrap, J. Amer. Statist. Assoc., 76 (1981), 312–319.
  • Google Scholar


• [9] B. Efron, R. J. Tibshirani, An introduction to the bootstrap, Chapman and Hall, New York (1993)
  • View Article
  • MathSciNet
  • Google Scholar


• [10] Q. Guan, Y. Tang, Optimal step-stress test under Type-I censoring for multivariate exponential distribution, J. Statist. Plann. Inference, 142 (2012), 1908–1923.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] R. D. Gupta, D. Kundu, Generalized exponential distributions: statistical inferences, J. Stat. Theory Appl., 1 (2002), 101–118.
  • MathSciNet
  • Google Scholar


• [12] P. Hall, Theoretical comparison of bootstrap confidence intervals, Ann. Statist., 16 (1988), 927–953.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [13] D. Han, D. Kundu, Inference for a step-stress model with competing risks for failure from the generalized exponential distribution under Type-I censoring, IEEE Tran. Reliab., 64 (2015), 31–43.
  • View Article
  • Google Scholar


• [14] D. Kundu, A. M. Sarhan, Analysis of incomplete data in the presence of competing risks among several groups, IEEE Tran. Reliab., 55 (2006), 262–271.
  • View Article
  • Google Scholar


• [15] C. T. Lin, C. C. Chou, Statistical inference for a lognormal step-stress model with Type-I censoring, IEEE Tran. Reliab., 61 (2012), 361–377.
  • View Article
  • Google Scholar


• [16] C. Park, Parameter estimation of incomplete data in competing risks using the EM algorithm, IEEE Tran. Reliab., 54 (2005), 282–290.
  • View Article
  • Google Scholar


• [17] A. M. Sarhan, Analysis of incomplete, censored data in competing risks models with generalized exponential distribution, IEEE Tran. Reliab., 56 (2007), 132–138.
  • View Article
  • Google Scholar


• [18] A. M. Sarhan, Analysis of incomplete, censored data in competing risks models with generalized Exponential distribution, IEEE Transactions on Reliability, 56 (2007), 132–138.
  • View Article
  • Google Scholar


• [19] A. A. Soliman, G. A. Abd-Elmougod, M. M. Al-Sobhi, Estimation in step-stress partially accelerated life tests for the Chen distribution using progressive Type-II censoring, Appl. Math. Infor. Sci., 11 (2017), 325–332.
  • View Article
  • Google Scholar