THERMAL SCIENCE

International Scientific Journal

Ahlam H. Tolba

,

Dina A. Ramadan

,

Ehab M. Almetwally

,

Taghreed M. Jawa

,

Neveen Sayed-Ahmed

STATISTICAL INFERENCE FOR STRESS-STRENGTH RELIABILITY USING INVERSE LOMAX LIFETIME DISTRIBUTION WITH MECHANICAL ENGINEERING APPLICATIONS

ABSTRACT
The inverse Lomax distribution has been extensively used in many disciplines, including stochastic modelling, economics, actuarial sciences, and life testing. It is among the most recognizable lifetime models. The purpose of this research is to look into a new and important aspect of the inverse Lomax distribution: the calculation of the fuzzy stress-strength reliability parameter RF = P(Y < X), as­suming X and Y are random independent variables that follow the inverse Lomax probability distribution. The properties of structural for the proposed reliability model are studied along with the Bayesian estimation methods, maximum product of the spacing and maximum likelihood. Extensive simulation studies are achieved to explore the performance of the various estimates. Subsequently, two sets of real data are considered to highlight the practicability of the model.
KEYWORDS
inverse Lomax distribution, fuzzy reliability, real data, maximum likelihood, Bayes estimation, simulation
PAPER SUBMITTED: 2022-09-03
PAPER REVISED: 2022-10-27
PAPER ACCEPTED: 2022-11-08
PUBLISHED ONLINE: 2023-01-21
DOI REFERENCE: https://doi.org/10.2298/TSCI22S1303T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Special issue 1, PAGES [303 - 326]
REFERENCES
  1. Bamber, D., The Area above the Ordinal Dominance Graph and the Area below the Receiver Operating Characteristic Graph, Journal of Mathematical Psychology, 12 (1975), 4, pp. 387-415
  2. Coolen, F. P. A., Newby, M. J., A Note on the Use of the Product of Spacings in Bayesian Inference, Department of Mathematics and Computing Science, University of Technology, Eindhoven, The Netherlands, 1990
  3. Raqab, M. Z., et al., Estimation of p (y < x) for the Three-Parameter Generalized Exponential Distribution, Communications in Statistics - Theory and Methods, 37 (2008), 18, pp. 2854-2864
  4. Wong, A., Interval Estimation of p (y < x) for Generalized Pareto Distribution, Journal of Statistical Planning and Inference, 142 (2012), 2, pp. 601-607
  5. El-Sagheer, R. M., et al., Inferences for Stress-Strength Reliability Model in the Presence of Partially Accelerated Life Test to Its Strength Variable, Computational Intelligence and Neuroscience, 2022 (2022), 4710536
  6. Asgharzadeh, A., et al., Estimation of the Stress-Strength Reliability for the Generalized Logistic Distribution, Statistical Methodology, 15 (2013), Nov., pp. 73-94
  7. Akgül, F. G., Senoglu, B., Estimation of p (x < y) Using Ranked Set Sampling for the Weibull Distribution, Quality Technology and Quantitative Management, 14 (2017), 3, pp. 296-309
  8. Al-Omari, A. I, et al., Estimation of the Stress-Strength Reliability for Exponentiated Pareto Distribution Using Median and Ranked set Sampling Methods, Comput Mater Contin, 64 (2020), 2, pp. 835-857
  9. Liu, Y., et al., Reliability and Mean Time to Failure of Unrepairable Systems with Fuzzy Random Lifetimes, IEEE Transactions on Fuzzy Systems, 15 (2007), 5, pp. 1009-1026
  10. Mohamed, R. A. H., et al., Inference of Reliability Analysis for Type II Half Logistic Weibull Distribution with Application of Bladder Cancer, Axioms, 11 (2022), 386
  11. Huang, H.-Z., Reliability Analysis Method in the Presence of Fuzziness Attached to Operating Time, Microelectronics Reliability, 35 (1995), 12, pp. 1483-1487
  12. Huang, H.-Z., et al., Bayesian Reliability Analysis for Fuzzy Lifetime Data, Fuzzy Sets and Systems, 157 (2006), 12, pp. 1674-1686
  13. Wu, H.-C., Fuzzy Reliability Estimation Using Bayesian Approach, Computers and Industrial Engineering, 46 (2004), 3, pp. 467-493
  14. Wu, H.-C., Fuzzy Bayesian System Reliability Assessment Based on Exponential Distribution, Applied Mathematical Modelling, 30 (2006), 6, pp. 509-530
  15. Buckley, J. J., Fuzzy Probability and Statistics, Springer, Heibelberg, Germany, 2006
  16. Chen, G., Pham, T. T., Introduction Fuzzy Sets, Fuzzy Logic, and Fuzzy Control Systems, CRC Press, Boca Raton, Fla., USA, 2000
  17. Lee, I.-S., et al., Comparison of Interval Estimations for p (x < y) in Marshall-Olkin's Model, Journal of the Korean Data and Information Science Society, 7 (1996), 1, pp. 93-104
  18. Zardasht, V., et al., On Non-Parametric Estimation of a Reliability Function, Munications in Statistics-Theory and Methods, 41 (2012), 6, pp. 983-999
  19. Neamah, M. W., Ali, B. K., Fuzzy Reliability Estimation for Frechet Distribution by Using Simulation, Periodicals of Engineering and Natural Sciences (PEN), 8 (2020), Jan., pp. 632-646
  20. Sabry, M. A. H., et al., Inference of Fuzzy Reliability Model for Inverse Rayleigh Distribution, AIMS Mathematics, 6 (2021), 9, pp. 9770-9785
  21. Kleiber, C., Kotz, S., Statistical Size Distributions in Economics and Actuarial Sciences, John Wiley and Sons, New York, USA, 2003, Vol. 70
  22. Ziegel, E. R., Statistical Size Distributions in Economics and Actuarial Sciences, Technometrics, 46 (2004), 4, pp. 499-500
  23. McKenzie, D., et al., The Landscape Ecology of Fire, Springer Science and Business Media, Berlin, Germany, 2011
  24. Greene, W., et al., Estimating Econometric Models with Fixed Effects, Department of Economics, Stern School of Business, New York University, New York, USA, 2001
  25. Washington, S., et al., Statistical and Econometric Methods for Transportation Data Analysis, Chapman and Hall/CRC, London, UK, 2020
  26. Almongy, H. M., et al., The Weibull Generalized Exponential Distribution with Censored Sample: Estimation and Application on Real Data, Complexity, 2021 (2021), ID6653534
  27. Muhammed, H. Z., Almetwally, E. M., Bayesian and Non-Bayesian Estimation for the Bivariate Inverse Weibull Distribution under Progressive Type-II Censoring, Annals of Data Science, 3 (2020), Nov., pp. 1-32
  28. Abd El-Raheem, A. M., et al., Accelerated Life Tests for Modified Kies Exponential Lifetime Distribution: Binomial Removal, Transformers Turn Insulation Application and Numerical Results, AIMS Mathematics, 6 (2021), 5, pp. 5222-5255
  29. Efron, B., Tibshirani, R. J., An Introduction the Bootstrap, CRC Press, Boca Raton, Fla., USA, 1994
  30. Hall, P., Theoretical Comparison of Bootstrap Confidence Intervals, The Annals of Statistics, 16 (1988), 3, pp. 927-953
  31. Tolba, A. H., et al., Bayesian Estimation of a One Parameter Akshaya Distribution with Progressively Type II Censord Data, Journal of Statistics Applications and Probability An International Journa, 11 (2022), 2, pp. 565-579
  32. Nassr, S. G., et al., Statistical Inference for the Extended Weibull Distribution Based on Adaptive Type-II Progressive Hybrid Censored Competing Risks Data, Thailand Statistician, 19 (2021), Jan., pp. 547-564
  33. Albert, J., Bayesian Computation with R., Springer Science and Business Media, Berlin Germany, 2009
  34. Abushal, T. A., et al., Estimation for Akshaya Failure Model with Competing Risks under Progressive Censoring Scheme with Analyzing of Thymic Lymphoma of Mice Application, Complexity, 2022 (2022), ID5151274
  35. Agiwal, V., Bayesian Estimation of Stress Strength Reliability from Inverse Chen Distribution with Application on Failure Time Data, Annals of Data Science, 3 (2021), Jan., pp. 1-31
  36. Chen, M.-H., Shao, Q.-M., Monte Carlo Estimation of Bayesian Credible and HPD Intervals, Journal of Computational and Graphical Statistics, 8 (1999), 1, pp. 69-92
  37. Caramanis, M., et al., Probabilistic Production Costing: An Investigation of Alternative Algorithms, International Journal of Electrical Power and Energy Systems, 5 (1983), 2, pp. 75-86
  38. Mazumdar, M., Gaver, D. P., On the Computation of Power-Generating System Reliability Indexes, Technometrics, 26 (1984), 2, pp. 173-185
  39. Khan, M. J. S., Arshad, M., Umvu Estimation of Reliability Function and Stress-Strength Reliability from Proportional Reversed Hazard Family Based on Lower Records, American Journal of Mathematical and Management Sciences, 35 (2016), 2, pp. 171-181
  40. Proschan, F., Theoretical Explanation of Observed Decreasing Failure Rate, Technometrics, 5 (1963), 3, pp. 375-383
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Statistical inference for stress-strength reliability using inverse Lomax lifetime distribution with mechanical engineering applications

© 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