International Journal of Management and Fuzzy Systems

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Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution

Received: 07 April 2017    Accepted: 16 May 2017    Published: 16 June 2017
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Abstract

The exponential distribution is applied to a very wide range of life analysis models, therefore, the research on it is of great significance in the practice of life. Based on the basic theory of general reliability and fuzzy reliability, on account of the Marshall-Olkin binary exponential distribution model, by establishing the fuzzy probability density function of the linear combination of two - dimensional random variables, this paper gives the fuzzy reliability function of the linear combination of the most widely used two - dimensional exponential distribution in reliability engineering.

DOI 10.11648/j.ijmfs.20170302.12
Published in International Journal of Management and Fuzzy Systems (Volume 3, Issue 2, April 2017)
Page(s) 28-31
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fuzzy Reliability, Binary Exponential Distribution, Non-Independent, Linear Combination

References
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[5] Zhang Ping. Statistical Analysis of Bivariate Exponential Distribution [D]. Shanghai Normal University, 2011.
[6] Han Zhu. Research on Characterization and Parameter Estimation of Bivariate Exponential Distributions and Other Related Problems [D]. Ningbo University, 2009.
[7] Arjun K,Gupta and SaraleesNadarajah. Exact and approximate distributions for the linear combination of inverted Dirichlet components [J]. Journal of Japan Statistical Society, 2006, 36 (2): 225-236.
[8] Li Dongna, Zhang Minyue, Ma Changqing. Fuzzy reliability analysis of parallel series system [J]. Journal of Gansu science, 2007, (04): 141-144.
[9] Li Tingjie, Gao He. Fuzzy Reliability of Series System [J]. Fuzzy Systems and Mathematics, 1989, (01): 38-45.
[10] GuoYunfei, Yin Zhe. The distribution of linear combinations of non - independent random variables subjecting to two- dimensional exponential distribution [J]. Mathematical Practice and Understanding, 2010, 40 (16): 179-183.
[11] Zhou Juling, Liang Xiaojia. Marshall-Olkin binary exponential distribution [J]. Journal of Xinjiang Normal University (Natural Science Edition), 2013, (04): 63-65.
[12] Li Guoan. Independence and Uniqueness of Exponential Distribution of Binary Marshall ~ Olkin Type [J]. University Mathematics, 2013,29 (4): 91-93. DOI: 10.3969/ j.issn.1672-1454.2013.04.019.
[13] Saralees Narajah and Samuel Kotz. Reliability for some Bivariate exponential distributions, Mathematical Problems in Engineering, 1-14, 2006.
[14] LI Tingjie, Gao He. Fuzzy Reliability [J]. Systems Engineering and Electronics, 1988, (10): 1-9.
[15] Cheng Kan, Cao Jinhua, Introduction to Reliability Mathematics. Beijing: Higher Education Press, 2006.
[16] Guo Yunfei, Reliability function of linear combination of marshall and olkin’s bivariate exponential distribution, Scientific Advances Publishers, 2015.
[17] Li Guoan. Exponential Distribution Sampling Fundamental Theorem and Its Application in Parameter Estimation of Two-parameter Binary Marshall-Olkin Exponential Distribution Parameter [J]. Statistical Research, 2016, (07): 98-102.
[18] Wang Junfang, Zhang Minyue. Fuzzy reliability of [J]. Journal of Sichuan University of Science and Engineering two interdependent parts in parallel system and series system with cold standby components (NATURAL SCIENCE EDITION), 2015, (01): 80-82.
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[20] Li Guoan. Characteristic and Parameter Estimation of Multivariate Marshall-Olkin Exponential Distribution [J]. Journal of Engineering Mathematics, 2005, (06): 109-116.
Author Information
  • Mathematics Department, Yanbian University, Yanji, P. R. China

  • Mathematics Department, Yanbian University, Yanji, P. R. China

  • Mathematics Department, Yanbian University, Yanji, P. R. China

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  • APA Style

    Yangjing Chong, Fangfang Guo, Wenyuan Sun. (2017). Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution. International Journal of Management and Fuzzy Systems, 3(2), 28-31. https://doi.org/10.11648/j.ijmfs.20170302.12

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    ACS Style

    Yangjing Chong; Fangfang Guo; Wenyuan Sun. Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution. Int. J. Manag. Fuzzy Syst. 2017, 3(2), 28-31. doi: 10.11648/j.ijmfs.20170302.12

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    AMA Style

    Yangjing Chong, Fangfang Guo, Wenyuan Sun. Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution. Int J Manag Fuzzy Syst. 2017;3(2):28-31. doi: 10.11648/j.ijmfs.20170302.12

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  • @article{10.11648/j.ijmfs.20170302.12,
      author = {Yangjing Chong and Fangfang Guo and Wenyuan Sun},
      title = {Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution},
      journal = {International Journal of Management and Fuzzy Systems},
      volume = {3},
      number = {2},
      pages = {28-31},
      doi = {10.11648/j.ijmfs.20170302.12},
      url = {https://doi.org/10.11648/j.ijmfs.20170302.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijmfs.20170302.12},
      abstract = {The exponential distribution is applied to a very wide range of life analysis models, therefore, the research on it is of great significance in the practice of life. Based on the basic theory of general reliability and fuzzy reliability, on account of the Marshall-Olkin binary exponential distribution model, by establishing the fuzzy probability density function of the linear combination of two - dimensional random variables, this paper gives the fuzzy reliability function of the linear combination of the most widely used two - dimensional exponential distribution in reliability engineering.},
     year = {2017}
    }
    

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  • TY  - JOUR
    T1  - Fuzzification of Linear Combination Based on Marshall-Olkin Bivariate Exponential Distribution
    AU  - Yangjing Chong
    AU  - Fangfang Guo
    AU  - Wenyuan Sun
    Y1  - 2017/06/16
    PY  - 2017
    N1  - https://doi.org/10.11648/j.ijmfs.20170302.12
    DO  - 10.11648/j.ijmfs.20170302.12
    T2  - International Journal of Management and Fuzzy Systems
    JF  - International Journal of Management and Fuzzy Systems
    JO  - International Journal of Management and Fuzzy Systems
    SP  - 28
    EP  - 31
    PB  - Science Publishing Group
    SN  - 2575-4947
    UR  - https://doi.org/10.11648/j.ijmfs.20170302.12
    AB  - The exponential distribution is applied to a very wide range of life analysis models, therefore, the research on it is of great significance in the practice of life. Based on the basic theory of general reliability and fuzzy reliability, on account of the Marshall-Olkin binary exponential distribution model, by establishing the fuzzy probability density function of the linear combination of two - dimensional random variables, this paper gives the fuzzy reliability function of the linear combination of the most widely used two - dimensional exponential distribution in reliability engineering.
    VL  - 3
    IS  - 2
    ER  - 

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