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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
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    References listed on IDEAS

    as
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