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A new statistical methodology using the sine function: Control chart with an application to survival times data

Author

Listed:
  • Mustafa Kamal
  • Gadde Srinivasa Rao
  • Meshayil M Alsolmi
  • Zubair Ahmad
  • Ramy Aldallal
  • Md Mahabubur Rahman

Abstract

Statistical methodologies have a wider range of practical applications in every applied sector including education, reliability, management, hydrology, and healthcare sciences. Among the mentioned sectors, the implementation of statistical models in health sectors is very crucial. In the recent era, researchers have shown a deep interest in using the trigonometric function to develop new statistical methodologies. In this article, we propose a new statistical methodology using the trigonometric function, namely, a new trigonometric sine-G family of distribution. A subcase (special member) of the new trigonometric sine-G method called a new trigonometric sine-Weibull distribution is studied. The estimators of the new trigonometric sine-Weibull distribution are derived. A simulation study of the new trigonometric sine-Weibull distribution is also provided. The applicability of the new trigonometric sine-Weibull distribution is shown by considering a data set taken from the biomedical sector. Furthermore, we introduce an attribute control chart for the lifetime of an entity that follows the new trigonometric sine-Weibull distribution in terms of the number of failure items before a fixed time period is investigated. The performance of the suggested chart is investigated using the average run length. A comparative study and real example are given for the proposed control chart. Based on our study of the existing literature, we did not find any published work on the development of a control chart using new probability distributions that are developed based on the trigonometric function. This surprising gap is a key and interesting motivation of this research.

Suggested Citation

  • Mustafa Kamal & Gadde Srinivasa Rao & Meshayil M Alsolmi & Zubair Ahmad & Ramy Aldallal & Md Mahabubur Rahman, 2023. "A new statistical methodology using the sine function: Control chart with an application to survival times data," PLOS ONE, Public Library of Science, vol. 18(8), pages 1-29, August.
    • Handle: RePEc:plo:pone00:0285914
    DOI: 10.1371/journal.pone.0285914
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    References listed on IDEAS

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    1. Starling, James K. & Mastrangelo, Christina & Choe, Youngjun, 2021. "Improving Weibull distribution estimation for generalized Type I censored data using modified SMOTE," Reliability Engineering and System Safety, Elsevier, vol. 211(C).
    2. Farrukh Jamal & Christophe Chesneau & Dalal Lala Bouali & Mahmood Ul Hassan, 2021. "Beyond the Sin-G family: The transformed Sin-G family," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-22, May.
    3. Tien Thanh Thach & Radim Bris, 2020. "Improved new modified Weibull distribution: A Bayes study using Hamiltonian Monte Carlo simulation," Journal of Risk and Reliability, , vol. 234(3), pages 496-511, June.
    4. Srinivasa Rao Gadde & Amer Ibrahim Al-Omari & Kenan Yildirim, 2022. "Attribute Control Charts Based on TLT for Length-Biased Weighted Lomax Distribution," Journal of Mathematics, Hindawi, vol. 2022, pages 1-15, April.
    5. David E. Giles, 2021. "Improved Maximum Likelihood Estimation for the Weibull Distribution Under Length-Biased Sampling," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 59-77, December.
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