THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

ESTIMATION AND PREDICTION OF TWO RAYLEIGH LIFETIME DISTRIBUTIONS UNDER JOINT CENSORING SCHEME

ABSTRACT
Comparative life tests of a life product have received considerable attention in the past few years for measuring the relative merits of a product in competing duration. In this paper, we are adopting the problem of estimation and prediction of Rayleigh lifetime distributions under joint Type-I censoring scheme. The point and interval estimation is formulated with maximum likelihood and the Bayes methods for the unknown parameters. Also, Bayesian approach is applied in viewpoint both point and interval prediction. The results of estimation and prediction are discussed through analysis the set of real data and bulding Monte-Carlo simulation studies. Finally, we built a numerical discussion of the most important results and future recommendations.
KEYWORDS
PAPER SUBMITTED: 2022-08-20
PAPER REVISED: 2022-10-17
PAPER ACCEPTED: 2022-11-04
PUBLISHED ONLINE: 2023-01-21
DOI REFERENCE: https://doi.org/10.2298/TSCI22S1247A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Special issue 1, PAGES [247 - 259]
REFERENCES
  1. Balakrishnan, N. Aggarwala, R., Progressive Censoring: Theory, Methods and Applications, Birkhuser, Boston, Mass., USA, 2000
  2. Balakrishnan, N., Progressive Censoring Methodology: An Appraisal (with Discussions), Test, 16 (2007), June, pp. 211-296
  3. Kundu, D., Bayesian Inference and Life Testing Plan for Weibull Distribution in Presence of Progressive Censoring, Technometrics, 50 (2008), 2, pp. 144-154
  4. Soliman, A. A., et al., Estimation of the Parameters of Life for Gompertz Distribution Using Progressive First-Failure Censoring Data, Computational Statistics and Data Analysis, 56 (2012), 8, pp. 2471-2485
  5. Rao, U. V. R., et al., Contributions to the Theory of Rank Order Statistics: The Two-Sample Censored Case, Ann Math Stat, 31 (1960), 2, pp. 415-426
  6. Basu, A. P., On a Generalized Savage Statistic with Applications to Life Testing, Ann Math Stat, 39 (1976), 5, pp. 1591-1604
  7. Johnson, R. A., Mehrotra, K. G., Locally Most Powerful Rank Tests for the Two-Sample Problem with Censored Data, Ann Math Stat, 43 (1972), 3, pp. 823-831
  8. Mehrotra, K. G., Johnson, R. A., Asymptotic Sufficiency and Asymptotically Most Powerful Tests for the Two Sample Censored Situation, Ann Stat, 4 (1976), 3, pp. 589-596
  9. Bhattacharyya, G. K., Mehrotra, K. G., On Testing Equality of Two Exponential Distributions under Combined Type-II Censoring, Journal Am Stat Assoc, 76 (1981), 376, pp. 886-894
  10. Mehrotra, K. G., Bhattacharyya, G. K., Confidence Intervals with Jointly Type-II Censored Samples from Two Exponential Distributions, Journal Am Stat Assoc, 77 (1982), 378, pp. 441-446
  11. Balakrishnan, N., Rasouli, A., Exact Likelihood Inference for Two Exponential Populations under Joint Type-II Censoring, Comput Stat Data Anal, 52 (2008), 5, pp. 2725-273
  12. Shafaya, A. R., et al., Bayesian Inference Based on a Jointly Type-II Censored Sample from Two Exponential Populations, Journal of Statistical Computation and Simulation, 84 (2014), 11, pp. 2427-2440
  13. Al-Matrafi, B. N., Abd-Elmougod, G. A., Statistical Inferences with Jointly Type-II Censored Samples from Two Rayleigh Distributions, Global Journal of Pure and Applied Mathematics, 13 (2017), 12, pp. 8361-8372
  14. 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
  15. Mondal, S., Kundu, D., Bayesian Inference for Weibull Distribution under the Balanced Joint Type-II Progressive Censoring Scheme, American Journal of Mathematical and Management Sciences, 39 (2019), 1, pp. 56-74
  16. Mondal, S., Kundu, D., Inferences of Weibull Parameters under Balance Two Sample Type-II Progressive Censoring Scheme, Quality and Reliability Engineering International, 36 (2020), 5, pp. 1-17
  17. Almarashi, A. M., et al., Inferences for Joint Hybrid Progressive Censored Exponential Lifetimes under Competing Risk Model, Mathematical Problems in Engineering, 2021 (2021), ID3380467
  18. Dyer, D. D., Whisenand, C. W., Best Linear Unbiased Estimator of the Parameter of the Rayleigh Distribution - Part I: Small Sample Theory for Censored Order Statistics, IEEE Transactions on Reliability, 22 (1973), 1, pp. 27-34
  19. Dyer, D. D., Whisenand, C. W., Best Linear Unbiased Estimator of the Parameter of the Rayleigh Distribution - Part II: Optimum Theory for Selected Order Statistics, IEEE Transactions on Reliability, 22 (1973), 4, pp. 229-231
  20. Polovko, A. M., Fundamentals of Reliability Theory, Academic Press, New York, USA, 1986
  21. Algarni, A., et al.,Two Compound Rayleigh Lifetime Distributions in Analyses the Jointly Type-II Censoring Samples, Journal of Mathematical Chemistry, 58 (1968), Aug., pp. 950-966
  22. Harter, H. L., Moore, A. H., Point and Interval Estimators, Based on m Order Statistics, for the Scale Parameter of a Weibull Population with Known Shape Parameter, Technometrics, 7 (1965), 3, pp. 405-422
  23. Lalitha, S., Mishra, A., Modified Maximum Likelihood Estimation for Rayleigh Distribution, Communications in Statistics, Theory and Methods, 25 (1996), 2, pp. 389-401
  24. Kong, F., Fei, H., Limits Theorems for the Maximum Likelihood Estimate under General Multiply Type II Censoring, Annals of the Institute of Statistical Mathematics, 48 (1996), Dec., pp. 731-755
  25. Howlader, H. A., Hossain, A., On Bayesian Estimation and Prediction from Rayleigh Based on Type II Censored Data, Communications in Statistics, Theory and Methods, 24 (1995), 9, pp. 2249-2259
  26. Fernandez, A. J. Bayesian Inference from Type II Doubly Censored Rayleigh Data, Statistics and Probability Letters, 48 (2000), 4, pp. 393-399
  27. AL-Hussaini, E. K., Ahmad, A. A., On Bayes Predictive Distributions of Generalized Order Statistics, Metrika, 57 (2003), May, pp. 165-176
  28. AL-Hussaini, E. K., Ahmad, A. A., On Bayes Interval Prediction of Future Records, Test, 12 (2003), 1, pp. 79-99
  29. Kundu, D., Joarder, A., Analysis of Type-II Progressively Hybrid Censored Data, Computational Statistics and Data Analysis, 50 (2006), 10, pp. 2509-2528
  30. Hoel, D. G., A Representation of Mortality Data by Competing Risks, Biometrics, 28 (1972), pp. 475-488

© 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