Performance analysis of classical and fuzzy series components system of reliability estimation of New X-Lindley distribution simulation with comparative
DOI:
https://doi.org/10.62933/zkcxka52Keywords:
Series components, Fuzzy reliability, New X-Lindley, Monte Carlo, MAPEAbstract
This paper deal with analysis of classical and fuzzy series components systems of reliability shortly respectively R_s and R_Fs, based on estimation of these systems for New X –Lindley (NXL) distribution using eight different techniques. The techniques used include maximum likelihood estimation (MLE), weighted least squared (WLS), Approximate least squared (ALS), precise moments Method (PMM), percentile estimation (PE), and three shrinkage (Sh1, Sh2, and Sh3) techniques. Monte Carlo simulation is applied to test the performance of these techniques in estimating classical and fuzzy series distribution systems and analyze their accuracy according to criteria as mean absolute percentage error (MAPE), mean square error (MSE), and bias. The proofs of these distribution systems are presented, and then the extent of the impact of fuzziness in series components systems data on the estimation results is evaluated. This study founded that the performance of estimation techniques varied dependent on sample size, with MLE, Sh2, and Sh3 being the most accurate according to the evaluation criteria used. The results also showed that some traditional techniques, as WLS and ALS, suffer from greater bias when using fuzzy data, highlighting the impact of fuzzy estimation on the results of statistical models.
References
[1] Nasiri, Parviz. "Estimation of R= P (Y< X) for two-parameter exponential distribution." Australian Journal of Basic and Applied Sciences 5.12 (2011): 414-420.
[2] Zhangchun, Tang, and Lu Zhenzhou. "Reliability-based design optimization for the structures with fuzzy variables and uncertain-but-bounded variables." Journal of Aerospace Information Systems 11.6 (2014): 412-422.
[3] Kano, Liena, and Alain Verbeke. "The three faces of bounded reliability: Alfred Chandler and the micro-foundations of management theory." California Management Review 58.1 (2015): 97-122.
[4] Salman, Abbas N., Adel A. Hussein, and Ibtehal H. Farhan. "On Shrinkage Estimation for Stress-Strength Reliability in Case of Generalized Exponential Distribution."
[5] Kotlar, Josip, and Philipp Sieger. "Bounded rationality and bounded reliability: A study of nonfamily managers’ entrepreneurial behavior in family firms." Entrepreneurship theory and practice 43.2 (2019): 251-273.
[6] Kazemi, Mohammad Reza. "Interval estimation of stress-strength reliability parameter for exponential-inverted exponential model: Frequentist and Bayesian approaches." Journal of Statistical Modelling: Theory and Applications 1.2 (2020): 77-89.
[7] Qayoom, Danish, et al. "A new class of Lindley distribution: System reliability, simulation and applications." Heliyon 10.19 (2024).
[8] Maihulla, Anas Sani, et al. "Reliability Evaluation of an Industrial System Using Lomax-Lindley Distribution." International Journal of Reliability, Risk and Safety: Theory and Application 7.1 (2024): 45-50.
[9] Khodja, N., Gemeay, A. M., Zeghdoudi, H., Karakaya, K., Alshangiti, A. M., Bakr, M.E., Balogun, O. S., Muse, A. H. and Hussam, E. (2023), Modeling voltage real data set by a new version of Lindley distribution, IEEE Access, 11, 67220-67229.
[10] MirMostafaee, S. M. T. K. "The Exponentiated New XLindley Distribution: Properties, and Applications." Journal of Data Science and Modeling (2024): 185-208.
[11] Abdalrazaq, A.S. and Batah, F.S.M. (2022). Maximum Likelihood Estimates and a survival function for fuzzy data for the Weibull-Pareto parameters. Journal of Physics: Conference Series, 2322(1), 012022.
[12] Batah, F.S.M and Jalal, M.S. (2022). A general class of some inverted distributions. Bayesian Estimation for the Stress-Strength Reliability Exponentiated q-Exponential Distribution based on Singly Type II Censoring Data. Pakistan Journal of Statistics, 38(4), 399-429.
[13] Batah, F.S.M. (2023). Some methods of estimating the hazard function of exponentiated Q-exponential distribution. In AIP Conference Proceedings (Vol. 2820, No. 1). AIP Publishing.
[14] Batah, F.S.M. and Abdulrazaq, A.S. (2022). On Estimation of Hazard, Survival
and Density Functions for Weibull Pareto Distribution by Ranking Algorithm. In
5th International Conference on Engineering Technology and its Applications (IICETA) (pp. 97-101). IEEE.
[15] Noori, Noorldeen Ayad, Alaa Abdulrahman Khalaf, and Mundher Abdullah Khaleel. "A new expansion of the Inverse Weibull Distribution: Properties with Applications." Iraqi Statistians Journal 1.1 (2024): 52-62.
[16] Alsaab, Nooruldeen. "Estimation and Some Statistical Properties of the hybrid Weibull Inverse Burr Type X Distribution with Application to Cancer Patient Data." Iraqi Statisticians journal (2024): 8-29.
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