IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i14p2478-d864202.html
   My bibliography  Save this article

Inferences of the Multicomponent Stress–Strength Reliability for Burr XII Distributions

Author

Listed:
  • Yuhlong Lio

    (Department of Mathematical Sciences, University of South Dakota, Vermillion, SD 57069, USA
    These authors contributed equally to this work.)

  • Tzong-Ru Tsai

    (Department of Statistics, Tamkang University, Tamsui District, New Taipei City 25137, Taiwan
    These authors contributed equally to this work.)

  • Liang Wang

    (School of Mathematics, Yunnan Normal University, Kunming 650500, China
    These authors contributed equally to this work.)

  • Ignacio Pascual Cecilio Tejada

    (Department of Mathematics, Universidad de Almería, 04120 Almería, Spain
    These authors contributed equally to this work.)

Abstract

Multicomponent stress–strength reliability (MSR) is explored for the system with Burr XII distributed components under Type-II censoring. When the distributions of strength and stress variables have Burr XII distributions with common or unequal inner shape parameters, the existence and uniqueness of the maximum likelihood estimators are investigated and established. The associated approximate confidence intervals are obtained by using the asymptotic normal distribution theory along with the delta method and parametric bootstrap procedure, respectively. Moreover, alternative generalized pivotal quantities-based point and confidence interval estimators are developed. Additionally, a likelihood ratio test is presented to diagnose the equivalence of both inner shape parameters or not. Conclusively, Monte Carlo simulations and real data analysis are conducted for illustration.

Suggested Citation

  • Yuhlong Lio & Tzong-Ru Tsai & Liang Wang & Ignacio Pascual Cecilio Tejada, 2022. "Inferences of the Multicomponent Stress–Strength Reliability for Burr XII Distributions," Mathematics, MDPI, vol. 10(14), pages 1-28, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2478-:d:864202
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/14/2478/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/14/2478/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Liang Wang & Huizhong Lin & Kambiz Ahmadi & Yuhlong Lio, 2021. "Estimation of Stress-Strength Reliability for Multicomponent System with Rayleigh Data," Energies, MDPI, vol. 14(23), pages 1-23, November.
    2. Fatih Kızılaslan, 2018. "Classical and Bayesian estimation of reliability in a multicomponent stress–strength model based on a general class of inverse exponentiated distributions," Statistical Papers, Springer, vol. 59(3), pages 1161-1192, September.
    3. Sanku Dey & Josmar Mazucheli & M. Z. Anis, 2017. "Estimation of reliability of multicomponent stress–strength for a Kumaraswamy distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(4), pages 1560-1572, February.
    4. Fatih Kızılaslan & Mustafa Nadar, 2018. "Estimation of reliability in a multicomponent stress–strength model based on a bivariate Kumaraswamy distribution," Statistical Papers, Springer, vol. 59(1), pages 307-340, March.
    5. Kızılaslan, Fatih, 2017. "Classical and Bayesian estimation of reliability in a multicomponent stress–strength model based on the proportional reversed hazard rate mode," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 136(C), pages 36-62.
    6. Tanmay Kayal & Yogesh Mani Tripathi & Sanku Dey & Shuo-Jye Wu, 2020. "On estimating the reliability in a multicomponent stress-strength model based on Chen distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(10), pages 2429-2447, May.
    7. Dallas Wingo, 1993. "Maximum likelihood methods for fitting the burr type XII distribution to multiply (progressively) censored life test data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 203-210, December.
    8. G. Srinivasa Rao & Muhammad Aslam & Debasis Kundu, 2015. "Burr-XII Distribution Parametric Estimation and Estimation of Reliability of Multicomponent Stress-Strength," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(23), pages 4953-4961, December.
    9. Nahed A. Mokhlis & Emad J. Ibrahim & Dina M. Gharieb, 2017. "Stress−strength reliability with general form distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(3), pages 1230-1246, February.
    10. Y. L. Lio & Tzong-Ru Tsai, 2012. "Estimation of δ= P ( X > Y ) for Burr XII distribution based on the progressively first failure-censored samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 309-322, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nanami Taketomi & Kazuki Yamamoto & Christophe Chesneau & Takeshi Emura, 2022. "Parametric Distributions for Survival and Reliability Analyses, a Review and Historical Sketch," Mathematics, MDPI, vol. 10(20), pages 1-23, October.
    2. Amit Singh Nayal & Bhupendra Singh & Vrijesh Tripathi & Abhishek Tyagi, 2024. "Analyzing stress-strength reliability $$\delta =\text{ P }[U," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(6), pages 2453-2472, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liang Wang & Huizhong Lin & Kambiz Ahmadi & Yuhlong Lio, 2021. "Estimation of Stress-Strength Reliability for Multicomponent System with Rayleigh Data," Energies, MDPI, vol. 14(23), pages 1-23, November.
    2. M. S. Kotb & M. Z. Raqab, 2021. "Estimation of reliability for multi-component stress–strength model based on modified Weibull distribution," Statistical Papers, Springer, vol. 62(6), pages 2763-2797, December.
    3. Shubham Saini & Renu Garg, 2022. "Reliability inference for multicomponent stress–strength model from Kumaraswamy-G family of distributions based on progressively first failure censored samples," Computational Statistics, Springer, vol. 37(4), pages 1795-1837, September.
    4. Hossein Pasha-Zanoosi, 2024. "Estimation of multicomponent stress-strength reliability based on a bivariate Topp-Leone distribution," OPSEARCH, Springer;Operational Research Society of India, vol. 61(2), pages 570-602, June.
    5. Prashant Kumar Sonker & Mukesh Kumar & Agni Saroj, 2023. "Stress–strength reliability models on power-Muth distribution," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(1), pages 173-195, March.
    6. Devendra Pratap Singh & Mayank Kumar Jha & Yogesh Mani Tripathi & Liang Wang, 2023. "Inference on a Multicomponent Stress-Strength Model Based on Unit-Burr III Distributions," Annals of Data Science, Springer, vol. 10(5), pages 1329-1359, October.
    7. Kundan Singh & Amulya Kumar Mahto & Yogesh Mani Tripathi & Liang Wang, 2024. "Estimation in a multicomponent stress-strength model for progressive censored lognormal distribution," Journal of Risk and Reliability, , vol. 238(3), pages 622-642, June.
    8. Akram Kohansal, 2019. "On estimation of reliability in a multicomponent stress-strength model for a Kumaraswamy distribution based on progressively censored sample," Statistical Papers, Springer, vol. 60(6), pages 2185-2224, December.
    9. Amulya Kumar Mahto & Yogesh Mani Tripathi, 2020. "Estimation of reliability in a multicomponent stress-strength model for inverted exponentiated Rayleigh distribution under progressive censoring," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1043-1069, December.
    10. Amit Singh Nayal & Bhupendra Singh & Vrijesh Tripathi & Abhishek Tyagi, 2024. "Analyzing stress-strength reliability $$\delta =\text{ P }[U," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(6), pages 2453-2472, June.
    11. Amal S. Hassan & Ibrahim M. Almanjahie & Amer Ibrahim Al-Omari & Loai Alzoubi & Heba Fathy Nagy, 2023. "Stress–Strength Modeling Using Median-Ranked Set Sampling: Estimation, Simulation, and Application," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    12. Y. L. Lio & Tzong-Ru Tsai, 2012. "Estimation of δ= P ( X > Y ) for Burr XII distribution based on the progressively first failure-censored samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(2), pages 309-322, April.
    13. Filippo Domma & Sabrina Giordano, 2013. "A copula-based approach to account for dependence in stress-strength models," Statistical Papers, Springer, vol. 54(3), pages 807-826, August.
    14. Manoj Rastogi & Yogesh Tripathi, 2013. "Inference on unknown parameters of a Burr distribution under hybrid censoring," Statistical Papers, Springer, vol. 54(3), pages 619-643, August.
    15. Jessie Marie Byrnes & Yu-Jau Lin & Tzong-Ru Tsai & Yuhlong Lio, 2019. "Bayesian Inference of δ = P ( X < Y ) for Burr Type XII Distribution Based on Progressively First Failure-Censored Samples," Mathematics, MDPI, vol. 7(9), pages 1-24, September.
    16. Nesar Ahmad & A. Islam, 1996. "Optimal accelerated life test designs for Burr type XII distributions under periodic inspection and type I censoring," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(8), pages 1049-1077, December.
    17. Farha Sultana & Yogesh Mani Tripathi & Shuo-Jye Wu & Tanmay Sen, 2022. "Inference for Kumaraswamy Distribution Based on Type I Progressive Hybrid Censoring," Annals of Data Science, Springer, vol. 9(6), pages 1283-1307, December.
    18. M. Noori Asl & R. Arabi Belaghi & H. Bevrani, 2017. "On Burr XII Distribution Analysis Under Progressive Type-II Hybrid Censored Data," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 665-683, June.
    19. R. Arabi Belaghi & M. Arashi & S. Tabatabaey, 2014. "Improved confidence intervals for the scale parameter of Burr XII model based on record values," Computational Statistics, Springer, vol. 29(5), pages 1153-1173, October.
    20. M. E. Ghitany & S. Al-Awadhi, 2002. "Maximum likelihood estimation of Burr XII distribution parameters under random censoring," Journal of Applied Statistics, Taylor & Francis Journals, vol. 29(7), pages 955-965.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2478-:d:864202. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.