THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Abdullah M. Almarashi

,

Gamal A. Abd-Elmougod

ACCELERATED COMPETING RISKS MODEL FROM GOMPERTZ LIFETIME DISTRIBUTIONS WITH TYPE-II CENSORING SCHEME

ABSTRACT
Time to failure under normal stress conditions may take a long period of time and statistical inferences under this condition is more serious. Then, the experiment is loaded under stress higher than normal one which is defined as accelerated life tests. This problem in this paper is discussed in the form of partially step-stress accelerated life test model when the lifetime of the product has Gompertz lifetime distribution and unites are fails under the two independent risks. The maximum likelihood method under type-II censoring scheme is used to formulate the point and asymptotic confidence interval estimators of model parameters. The two boot­strap methods are also used to formulate the point and approximate interval estimators. The numerical results are adopted in the form of Monte Carlo studying to illustrate, assess and compare all of the theoretical results. Finally, results are discussed in points to clarify results validity.
KEYWORDS
Gompertz distribution, accelerated model, computing risks model, estimation with maximum likelihood and bootstrap method
PAPER SUBMITTED: 2020-04-15
PAPER REVISED: 2020-05-29
PAPER ACCEPTED: 2020-06-10
PUBLISHED ONLINE: 2020-10-25
DOI REFERENCE: https://doi.org/10.2298/TSCI20S1165A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2020, VOLUME 24, ISSUE Supplement 1, PAGES [S165 - S175]
REFERENCES
  1. Nelson, W., Accelerated Testing Statistical Models, Test, Plans and Data Analyses, Wiley, New York, USA, 1990
  2. Bagdanavicius, V. B., Nikulin, M., Accelerated Life Models: Modelling and Statistical Analysis, Chapman and Hall CRC Pres, Boca Raton, Fla., USA, 2002
  3. Balakrishnan, N. A, Synthesis of Exact Inferential Results for Exponential Step-Stress Models and Associated Optimal Accelerated Life-Tests, Metrika, 69 (2009), 2, pp. 351-396
  4. Abd-Elmougod, G. A., Mahmoud, E. E., Paramters Estimation of Compound Rayleigh Distribution under an Adaptive Type-II Progressively Hybrid Censored Data for Constant Partially Accelerated Life Tests, Global Journal of Pure and Applied Mathematics, 13 (2016), Jan., pp. 8361-8372
  5. Algarni, A., et al., Two Compound Rayleigh Lifetime Distributions in Analyses the Jointly Type-II Censoring Samples, Journal of Mathematical Chemistry, 58 (2019), Aug., pp. 950-966
  6. Ganguly, A., Kundu, D., Analysis of Simple Step-Stress Model in Presence of Competing Risks, Journal of Statistical Computation and Simulation, 86 (2016), 10, pp. 1989-2006
  7. Wang, R., Fei, H., Statistical Inference of Weibull Distribution for Tampered Failure Rate Model in Progressive Stress Accelerated Life Testing, Journal of Systems Science and Complexity, 17 (2004), 2, pp. 237-243
  8. Abdel-Hamid, A. H., Al-Hussaini, E. K., Progressive Stress Accelerated Life Tests under Finite Mixture Models, Metrika, 66 (2007), Jan., pp. 213-231
  9. Cox, D. R., The Analysis of Exponentially Distributed Lifetimes with Two Types of Failures, Journal of the Royal Statistical Society, 21 (1959), 2, pp. 411-421
  10. Balakrishnan, N., Han, D., Exact Inference for a Simple Step-Stress Model with Competing Risks for Failure from Exponential Distribution under Type-II Censoring, Journal of Statistical Planning and Inference, 138 (2008), 12, pp. 4172-4186
  11. Hanaa, H., et al., Competing Risks Model with Partially Step-Stress Accelerate Life Tests Analyses Lifetime Chen Data under Type-II Censoring Scheme, Open Phys., 17 (2019), 1, pp. 192-199
  12. Algarni, A., et al., Statistical Analysis of Competing Risks Lifetime Data from Nadarajaha and Haghighi Distribution under Type-II Censoring, Journal of Intelligent and Fuzzy Systems, 38 (2020), 3 pp. 2591-2601
  13. Han, D., Kundu, D., Inference for a Step-Stress Model with Competing Risks for Failure from the Generalized Exponential Distribution under Type-I Censoring, IEEE Transactions on Reliability, 64 (2015), 1, pp. 31-43
  14. Yusuf, A., Qureshi, S., A Five Parameter Statistical Distribution with Application to Real Data, Journal of Statistics Applications and Probability, 8 (2019), 1, pp. 11-26
  15. Mohie El-Din, M., et al., Estimation of the Coefficientof Variation for Lindley Distribution based on Progressive First Failure Censored Data, Journal of Statistics Applications and Probability, 8 (2019), July, pp. 83-90
  16. Sabry, M. A., et al., Parameter Estimation for the Power Generalized WeibullDistribution Based on One- and Two-Stage Ranked Set Sampling Designs, Journal of Statistics Applications and Probability, 8 (2019), 2, pp. 113-128
  17. Abdel-Khalek, S., Fisher Information Due to a Phase Noisy Laser under Non-Markovian Environment, Annals of Physic, 351 (2014), Dec., pp. 952-959
  18. Abdel-Khalek, S., Quantum Fisher Information Flow and Entanglement in Pair Coherent States, Optical and Quantum Electronics, 46 (2014), 8, pp. 1055-1064
  19. Abdel-Khalek, S., et al., Some Features of Quantum Fisher Information and Entanglement of Two Atoms Based on Atomic State Estimation, Appl. Math., 11 (2017), 3, pp. 677-681
  20. Davison, A. C., Hinkley, D. V., Bs Bootstrap Methods and Their Applications, 2nd ed., Cambridge University Press, Cambridge, UK, 1997
  21. Efron, B., Censored Data and Bootstrap, Journal of the American Statistical Association, 76 (1981), 374, pp. 312-319
  22. Efron, B., Tibshirani, R. J., Bootstrap Method for Standard Errors, Confidence Intervals and Other Measures of Statistical Accuracy, Statistical Science, 1 (1986), 1, pp. 54-75
  23. Efron, B., Tibshirani, R. J., An Introduction the Bootstrap, New York Chapman and Hall, New York, USA, 1993
PDF VERSION [DOWNLOAD]
Accelerated competing risks model from Gompertz lifetime distributions with type-II censoring scheme

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence