Estimations with Step-Stress Partially Accelerated Life Tests for Ailamujia Distribution under Type-I Censored Data

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Mohammad A. Amleh, Israa F. Al-Freihat

Abstract

This paper addresses the problem of estimating parameters in partial accelerated life tests following the Ailamujia distribution under Type-I censoring, employing both the maximum likelihood approach and the least squares method. The assessment of estimation methods involves a comprehensive simulation study, complemented by the analysis of a real dataset for illustrative purposes. The findings reveal the least square estimation method outperforms maximum likelihood estimation, considering biases and mean square errors.

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References

  1. W.B. Nelson, Accelerated Testing: Statistical Models, Test Plans, and Data Analysis, John Wiley & Sons, New York, 1990.
  2. A.F. Attia, A.A. Abdel-Ghaly, M.M. Abdel-Ghani, The Estimation Problem of Partially Accelerated Life Tests for Weibull Distribution by Maximum Likelihood Method With Censored Data, In: Proceeding of the 31st Annual Conference of Statistics, Computer Sciences and Operation Research, ISSR, Cairo University, Egypt, (1996), 128-138.
  3. M.M. Abdel-Ghani, Investigation of Some Lifetime Models Under Partially Accelerated Life Tests, Ph.D. Thesis, Department of Statistics, Faculty of Economics and Political Science, Cairo University, Giza, Egypt, 1998.
  4. A.A. Abdel-Ghaly, E.H. El-Khodary, A.A. Ismail, Maximum Likelihood Estimation and Optimal Design in Step Partially Accelerated Life Tests for the Pareto Distribution With Type-I Censoring, In: Proceedings of the 14th annual conference on Statistics and Computer Modeling in Human and Social Sciences, Faculty of Economics and Political Science, Cairo University, Egypt, (2002), 16-29.
  5. A.A. Abdel-Ghaly, E.H. El-Khodary, A.A. Ismail, Estimation and Optimal Design in Step Partially Accelerated Life Tests for The Compound Pareto Distribution Using Type II Censoring, In: Proceeding of the 15st Annual Conference on Statistics and Computer Modeling in Human and Social Sciences, Faculty of Economics and Political Science, Cairo University, Egypt, (2003), 35-47.
  6. M.M. Abdel-Ghani, The Estimation Problem of the Log Logistic Parameters in Step Partially Accelerated Life Tests Using Type-I Censored Data, Nat. Rev. Soc. Sci. 41 (2004), 1-19.
  7. A.A. Ismail, Inference for a Step-Stress Partially Accelerated Life Test Model With an Adaptive Type-II Progressively Hybrid Censored Data From Weibull Distribution, J. Comp. Appl. Math. 260 (2014), 533–542. https://doi.org/10.1016/j.cam.2013.10.014.
  8. A.A. Ismail, Likelihood and Bayesian Estimations for Step-Stress Life Test Model Under Type-I Censoring, Hacettepe J. Math. Stat. 44 (2015), 1235-1245.
  9. M.A. Fawzy, H. Athar, Inferences from Ailamujia Distribution based on Progressive Type-II Censored Data, J. Stat. Appl. Prob. 9 (2020), 483-493. https://doi.org/10.18576/jsap/090305.
  10. P.K. Goel, Some Estimation Problems in the Study of Tampered Random Variables, Technical Report No. 50, Department of Statistics, Carnegie-Mellon University, Pittsburgh, Pennsylvania, 1971.
  11. M.H. Degroot, P.K. Goel, Bayesian Estimation and Optimal Designs in Partially Accelerated Life Testing, Naval Res. Log. 26 (1979), 223-235. https://doi.org/10.1002/nav.3800260204.
  12. J.F. Lawless, Statistical Models and Methods for Lifetime Data, 2^nd ed., John Wiley & Sons, Hoboken, New Jersey, 2003.
  13. A.C. Cohen, B.J. Whitten, Parameter Estimation in Reliability and Life Span Models, Marcel Dekker /CRC Press, New York, 1988.
  14. A.C. Cohen, Truncated and Censored Samples: Theory and Applications, Marcel Dekker/CRC Press, New York, 1991.
  15. H.Q. Lv, L.H. Gao, C.L. Chen, Ailamujia Distribution and Its Application in Supportability Data Analysis, J. Acad. Armored Force Eng. 16 (2002), 48-52.
  16. G.T. Pan, B.H. Wang, C.L. Chen, Y.B. Huang, M.T. Dang, The Research of Interval Estimation and Hypothetical Test of Small Sample of Distribution, Appl. Stat. Manage. 28 (2009), 468-472.
  17. B. Long, Bayesian Estimation of Parameter on Ailamujia Distribution Under Different Prior Distribution, Math. Practice Theory, 4 (2015), 186-192.
  18. L.P. Li, Minimax Estimation of the Parameter of Ailamujia Distribution Under Different Loss Functions, Sci. J. Appl. Math. Stat. 4 (2016), 229-235.
  19. A.A. Rather, C. Subramanian, S. Shafi, K.A. Malik, P.J. Ahmad, B.A. Para, T.R. Jan, A New Size Biased Distribution with Applications in Engineering and Medical Science, Int. J. Sci. Res. Math. Stat. Sci. 5 (2018), 75-85.
  20. A. Aijaz, A. Ahmad, R. Tripathi, Inverse Analogue of Ailamujia Distribution with Statistical Properties and Applications, Asian Res. J. Math. 16 (2020), 36-46. https://doi.org/10.9734/arjom/2020/v16i930218.
  21. U. Jan, K. Fatima, S.P. Ahmad, On Weighted Ailamujia Distribution and Its Applications to Lifetime Data, J. Stat. Appl. Prob. 6 (2017), 619-633. https://doi.org/10.18576/jsap/060317.
  22. B.C. Arnold, N. Balakrishnan, H.N. Nagaraja, A First Course in Order Statistics, John Wiley & Sons, New York, 1992.
  23. M.A. Amleh, M.Z. Raqab, Prediction of Censored Weibull Lifetimes in a Simple Step-Stress Plan with Khamis-Higgins Model, Stat. Optim. Inf. Comp. 10 (2021), 658-677. https://doi.org/10.19139/soic-2310-5070-1069.
  24. L. Alkhalfan, Inference For A Gamma Step-Stress Model Under Censoring, PhD Thesis, McMaster University, Canada, 2012.
  25. M.A. Amleh, M.Z. Raqab, Inference for Step‐Stress Plan With Khamis‐Higgins Model Under Type‐II Censored Weibull Data, Qual. Reliab. Eng. Int. 39 (2023), 982-1000. https://doi.org/10.1002/qre.3275.
  26. M.A. Amleh, Prediction of Future Lifetimes for a Simple Step-Stress Model with Type-II Censoring and Rayleigh Distribution, WSEAS Trans. Math. 21 (2022), 131-143. https://doi.org/10.37394/23206.2022.21.20.
  27. M.A. Amleh, M.Z. Raqab, Inference in Simple Step-Stress Accelerated Life Tests for Type-II Censoring Lomax Data, J. Stat. Theory Appl. 20 (2021), 364-379. https://doi.org/10.2991/jsta.d.210406.001.
  28. J. J. Swain, S. Venkatraman, J.R. Wilson, Least Squares Estimation of Distribution Function in Johnsons Translation System, J. Stat. Comp. Simul. 29 (1988), 271-297. https://doi.org/10.1080/00949658808811068.
  29. D. P. Murthy, M. Xie & R. Jiang, Weibull models, John Wiley & Sons, Hoboken, New Jersey, 2004.
  30. M. Kamal, A. Rahman, S. Zarrin, H. Kausar, Statistical Inference Under Step Stress Partially Accelerated Life Testing for Adaptive Type-II Progressive Hybrid Censored Data, J. Reliab. Stat. Stud. 14 (2021), 585-614. https://doi.org/10.13052/jrss0974-8024.14211.