Reliability estimation of Lomax distribution with fuzziness
Resumo
This paper considers the problem of estimating the reliability function for Lomax distribution with the presence of fuzziness through two procedures. The first procedure depends on fuzzy reliability definition that uses the composite trapezoidal rule in order to find the numerical integration and the second is Bayesian procedure which includes different cases depends on sample data and hyper-parameters of prior gamma distribution with squared error as a symmetric loss function and precautionary as an asymmetric loss function. In the Bayesian procedure, we proposed to consider three cases to estimate the fuzzy reliability with fuzzy observations, precise observations with fuzzy hyper-parameter, and fuzzy observations with fuzzy hyper-parameter.
Downloads
Referências
Al-Noor, N. H., and Alwan, S. S., (2015a). Non-Bayes, Bayes and Empirical Bayes Estimators for the Shape Parameter of Lomax Distribution, Mathematical Theory and Modeling 5(2): 17-27.
Al-Noor, N. H., and Alwan, S. S., (2015b). Non-Bayes, Bayes and Empirical Bayes Estimators for the Reliability and Failure Rate Functions of Lomax Distribution, Transactions on Engineering and Sciences, 3(2): 20-29.
Al-Zahrani, B., and Al-Sobhi, M., (2013). On parameters estimation of Lomax distribution under general progressive censoring, Journal of Quality and Reliability Engineering, Article ID 431541. https://doi.org/10.1155/2013/431541
Ashour, S. K. and Abdelfattah, A. M., (2011). Parameter Estimation of the Hybrid Censored Lomax Distribution, Pak. J. Stat. Oper. Res., 1: 1-19. https://doi.org/10.18187/pjsor.v7i1.136
Chen, C. H., and Mon, L., (1993). Fuzzy System reliability analysis by interval of confidence, Fuzzy sets and systems, 56: 29-36. https://doi.org/10.1016/0165-0114(93)90182-H
Cheng, C. H., (1996). Fuzzy Repairable Reliability Based on Fuzzy GERT, Microelectron. Reliab., 36(10):1557-1563. https://doi.org/10.1016/0026-2714(95)00200-6
Dahlquist, G., and Bjorck , A., (2008) . Numerical Methods in Scientific Computing, Volume 1, Society for Industrial and Applied Mathematics, ISBN 978-0-898716-44-3.
Hassan, A., and Al-Ghamdi, A., (2009). Optimum step stress accelerated life testing for Lomax distribution, Journal of Applied Sciences Research, 5: 2153-2164.
Jamkhaneh, E. B., (2012). Reliability Estimation under the Fuzzy Environments, The Journal of Mathematics and Computer Science, 5(1): 28-39. https://doi.org/10.22436/jmcs.05.01.04
Kilany, N.M., (2016). Weighted Lomax distribution, SpringerPlus, 5(1): articleno.1862. https://doi.org/10.1186/s40064-016-3489-2
Kim, H. C., (2016). A Performance Analysis of Software Reliability Modelusing Lomax and Gompertz Distribution Property, Indian Journal of Science and Technology 9(20). https://doi.org/10.17485/ijst/2016/v9i20/94668
Kumar, P., Kour, K., and Kour, J., (2018). Estimation of the probability density function of Lomax distribution. International Journal of statistics and Economics, 19(2): 78-88.
Lomax, K. S., (1954). Business Failures: Another Example of the Analysis of Failure Data, J. Amer. Statist. Assoc., 49: 847-852. https://doi.org/10.1080/01621459.1954.10501239
Mahmoud, M. A. W., El-Sagheer, R. M., Soliman, A. A., and Abd Ellah, A. H., (2016). Bayesian estimation of P[Y < X] based on record values from the Lomax distribution and MCMC technique. J Modern Appl Stat Methods 15(1(25)):488-510. https://doi.org/10.22237/jmasm/1462076640
Okasha, H. M., (2014). E-Bayesian estimation for the Lomax distribution based on type-II censored data, Journal of the Egyptian Mathematical Society 22, 489-495. https://doi.org/10.1016/j.joems.2013.12.009
Panahi, H., and Asadi, S., (2011). Inference of stress-strength model for a Lomax distribution. Int J Math Comput. Phys. Electr. Comput. Eng. 5(7): 937-940.
Parviz, N., (2016). Estimation parameter of R = P(Y < X)for Lomax distribution with presence of outliers. Int Math Forum 11(5): 239-248. https://doi.org/10.12988/imf.2016.512106
Rao, A. K., Pandey, H., and Singh, K. L., (2016). Estimation of Reliability Function of Lomax Distribution via Bayesian Approach, International Journal of Mathematics Trends and Technology 40(4): 252-254. https://doi.org/10.14445/22315373/IJMTT-V40P531
Singer, D., (1990). A fuzzy set approach to fault tree and reliability analysis, Fuzzy sets and systems, 34(2): 145-155. https://doi.org/10.1016/0165-0114(90)90154-X
Venkatesh, A., and Elango, S., (2013). Fuzzy Reliability Analysis for the Effect of TRH Based On Gamma Distribution, Journal of Engineering Research and Applications, 3(6): 1295-1298.
Vishwakarma, G. K., Paul, C., and Singh, N., (2018). Parameters Estimation of Weibull Distribution Based on Fuzzy Data Using Neural Network, Biostatistics and Biometrics, 6(5): 1-8. https://doi.org/10.19080/BBOAJ.2018.06.555696
Yadav, A. S., Singh, S. K., and Singh, U., (2019). Bayesian estimation of stress-strength reliability for Lomax distribution under type-II hybrid censored data using asymmetric loss function, Life Cycle Reliability and Safety Engineering,. https://doi.org/10.1007/s41872-019-00086-z
Zadeh, L. A., (1965). Fuzzy sets, Information and control, 8(3): 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
