IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i13p2805-d1176581.html
   My bibliography  Save this article

The NBRULC Reliability Class: Mathematical Theory and Goodness-of-Fit Testing with Applications to Asymmetric Censored and Uncensored Data

Author

Listed:
  • Walid B. H. Etman

    (Faculty of Computer and Artificial Intelligence, Modern University for Technology and Information, Cairo 12613, Egypt)

  • Mohamed S. Eliwa

    (Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia
    Department of Statistics and Computer Science, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Hana N. Alqifari

    (Department of Statistics and Operation Research, College of Science, Qassim University, Buraydah 51482, Saudi Arabia)

  • Mahmoud El-Morshedy

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Laila A. Al-Essa

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia)

  • Rashad M. EL-Sagheer

    (Mathematics Department, Faculty of Science, Al-Azhar University, Cairo 11884, Egypt
    High Institute of Computer and Management Information System, First Statement, New Cairo 11865, Egypt)

Abstract

The majority of approaches proposed in the past few decades to solve life test problems have differed markedly from those used for closely related, yet broader, issues. Due to the complexity of data that are generated each day in many practical domains, as a result of the development of scales for rating the success or failure of reliability, a new domain of reliability has been created. This domain is referred to as life classes, where specific probability distributions are presented. In this study, it is shown that the use of the quality-of-fit technique to solve problems involving life testing makes sense, and produces simpler processes that are roughly equivalent or superior to those used in traditional procedures. They may also behave better in limited samples. This work investigates a novel quality-of-fit test statistic; it is based on an exponential transform and is compared to the best renewal used Laplace test in increasing convex ordering (NBRULC). Evidence for approach normality is provided. The calculated variables include powers, Pitman asymptotic effectiveness, and critical points. Methods on how to handle censored data were also studied. Our experiments have real-world applications in the fields of medicine and engineering.

Suggested Citation

  • Walid B. H. Etman & Mohamed S. Eliwa & Hana N. Alqifari & Mahmoud El-Morshedy & Laila A. Al-Essa & Rashad M. EL-Sagheer, 2023. "The NBRULC Reliability Class: Mathematical Theory and Goodness-of-Fit Testing with Applications to Asymmetric Censored and Uncensored Data," Mathematics, MDPI, vol. 11(13), pages 1-22, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:2805-:d:1176581
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/13/2805/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/13/2805/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bhattacharyya, Dhrubasish & Khan, Ruhul Ali & Mitra, Murari, 2021. "Tests for Laplace order dominance with applications to insurance data," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 163-173.
    2. Priyanka Majumder & Murari Mitra, 2019. "A test for detecting Laplace order dominance and related Bahadur efficiency issues," Statistical Papers, Springer, vol. 60(6), pages 1921-1937, December.
    3. Navarro, Jorge, 2018. "Preservation of DMRL and IMRL aging classes under the formation of order statistics and coherent systems," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 264-268.
    4. Bengt Klefsjö, 1982. "The hnbue and hnwue classes of life distributions," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(2), pages 331-344, June.
    5. Priyanka Majumder & Murari Mitra, 2019. "A test of exponentiality against ℳ alternatives," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(3), pages 794-812, July.
    6. Bhattacharyya, Dhrubasish & Khan, Ruhul Ali & Mitra, Murari, 2020. "A test of exponentiality against DMTTF alternatives via L-statistics," Statistics & Probability Letters, Elsevier, vol. 165(C).
    7. Shyamal Ghosh & Murari Mitra, 2020. "A new test for exponentiality against HNBUE alternatives," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(1), pages 27-43, January.
    8. Bera, Smaranika & Bhattacharyya, Dhrubasish & Khan, Ruhul Ali & Mitra, Murari, 2023. "Test for harmonic mean residual life function: A goodness of fit approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 58-70.
    9. Ruhul Ali Khan & Dhrubasish Bhattacharyya & Murari Mitra, 2021. "Exact and asymptotic tests of exponentiality against nonmonotonic mean time to failure type alternatives," Statistical Papers, Springer, vol. 62(6), pages 3015-3045, December.
    10. Rashad M. EL-Sagheer & Mohamed S. Eliwa & Khaled M. Alqahtani & Mahmoud EL-Morshedy & Ali Sajid, 2022. "Asymmetric Randomly Censored Mortality Distribution: Bayesian Framework and Parametric Bootstrap with Application to COVID-19 Data," Journal of Mathematics, Hindawi, vol. 2022, pages 1-14, March.
    11. Ghosh, Shyamal & Mitra, Murari, 2017. "A weighted integral approach to testing against HNBUE alternatives," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 58-64.
    Full references (including those not matched with items on IDEAS)

    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. Bo H. Lindqvist & Francisco J. Samaniego, 2019. "Some new results on the preservation of the NBUE and NWUE aging classes under the formation of coherent systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(5), pages 430-438, August.
    2. Denuit, Michel & Trufin, Julien, 2022. "Tweedie dominance for autocalibrated predictors and Laplace transform order," LIDAM Discussion Papers ISBA 2022040, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Tommaso Lando, 2022. "Testing convexity of the generalised hazard function," Statistical Papers, Springer, vol. 63(4), pages 1271-1289, August.
    4. Chen Li & Xiaohu Li, 2020. "Weak aging properties for coherent systems with statistically dependent component lifetimes," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 559-572, October.
    5. Zubair Ahmad & Zahra Almaspoor & Faridoon Khan & Mahmoud El-Morshedy, 2022. "On Predictive Modeling Using a New Flexible Weibull Distribution and Machine Learning Approach: Analyzing the COVID-19 Data," Mathematics, MDPI, vol. 10(11), pages 1-26, May.
    6. Ibrahim Ahmad & A. Mugdadi, 2005. "Bounds of moment generating functions of some life distributions," Statistical Papers, Springer, vol. 46(4), pages 575-585, October.
    7. Lisa Parveen & Ruhul Ali Khan & Murari Mitra, 2024. "A two sample nonparametric test for variability via empirical likelihood methods," Statistical Papers, Springer, vol. 65(7), pages 4243-4265, September.
    8. Sengupta, Debasis & Das, Sudipta, 2016. "Sharp bounds on DMRL and IMRL classes of life distributions with specified mean," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 101-107.

    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:11:y:2023:i:13:p:2805-:d:1176581. 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.