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Survival analysis is a statistical method used to study time-to-event data, where the "event" might represent outcomes like death, disease relapse, system failure, or recovery. A unique feature of survival data is censoring, which occurs when the event of interest has not been observed for some individuals during the study period. This requires specialized techniques to handle incomplete data effectively.
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Survival curves are graphical representations that depict the survival experience of a population over time, offering an intuitive way to track the proportion of individuals who remain event-free at each time point. These curves are widely used in fields such as medicine, public health, and reliability engineering to visualize and compare survival probabilities across different groups or conditions.
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Survival analysis is a cornerstone of medical research, used to evaluate the time until an event of interest occurs, such as death, disease recurrence, or recovery. Unlike standard statistical methods, survival analysis is particularly adept at handling censored data—instances where the event has not occurred for some participants by the end of the study or remains unobserved. To address these unique challenges, specialized techniques like the Kaplan-Meier estimator, log-rank test, and...
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A new statistical methodology using the sine function: Control chart with an application to survival times data.

Mustafa Kamal1, Gadde Srinivasa Rao2, Meshayil M Alsolmi3

  • 1Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Dammam, Saudi Arabia.

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Researchers developed a new trigonometric sine-Weibull statistical distribution and control chart for healthcare applications. This novel method enhances reliability analysis and quality control in biomedical data, addressing a gap in trigonometric-based statistical tools.

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Area of Science:

  • Statistics
  • Reliability Engineering
  • Biomedical Science

Background:

  • Statistical models are crucial in healthcare, with growing interest in trigonometric functions for new methodologies.
  • Existing literature lacks control charts based on trigonometric function-derived probability distributions.

Purpose of the Study:

  • To propose a novel trigonometric sine-G family of distributions.
  • To introduce and analyze a trigonometric sine-Weibull distribution and its estimators.
  • To develop and evaluate a new attribute control chart for lifetime data using this distribution.

Main Methods:

  • Development of the trigonometric sine-G family of distributions.
  • Derivation of estimators for the trigonometric sine-Weibull distribution.
  • Simulation studies and application to biomedical data.
  • Introduction of an attribute control chart for time-to-failure analysis.
  • Performance evaluation of the control chart using average run length (ARL).

Main Results:

  • The trigonometric sine-Weibull distribution was successfully derived and its estimators obtained.
  • Simulation studies confirmed the distribution's properties.
  • The new distribution demonstrated applicability in a biomedical dataset.
  • The proposed attribute control chart showed effectiveness in monitoring lifetime data.
  • Comparative analysis validated the performance of the new control chart.

Conclusions:

  • The novel trigonometric sine-Weibull distribution and its associated control chart offer a valuable new tool for statistical analysis in healthcare and reliability.
  • This research fills a significant gap by introducing trigonometric function-based probability distributions and control charts.
  • The developed methods show practical utility in biomedical data analysis and quality control.