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Trigonometric function transformation and its application in software reliability modeling.

Dai-Nghia Vy1, Van-Thuan Nguyen1, Quyet-Thang Huynh2

  • 1Faculty of Engineering Technology, Hung Vuong University, Phu Tho, Vietnam.

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Summary

This study mathematically evaluates four S-shaped functions for software reliability, transforming a trigonometric function to offer new advantages and potential for novel reliability models.

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Area of Science:

  • Software Engineering
  • Reliability Engineering
  • Mathematical Modeling

Background:

  • S-shaped functions are vital for non-homogeneous Poisson process software reliability modeling.
  • Existing models often use three common S-shaped functions without thorough mathematical assessment.
  • There is a need to explore additional S-shaped functions for enhanced reliability analysis.

Purpose of the Study:

  • To mathematically transform the sine function, preserving its S-shape across different domains and co-domains.
  • To conduct a rigorous mathematical evaluation of four S-shaped functions, including three established types and a novel trigonometric transformation.
  • To assess the applicability and advantages of the transformed trigonometric function in software reliability.

Main Methods:

  • A four-step transformation process (horizontal/vertical shifts and scaling) was applied to the sine function.
  • Numerical analysis techniques were employed to evaluate functions based on special cases, domain, range, and limitations.
  • Mathematical assessment focused on maintaining the characteristic S-shape for reliability modeling.

Main Results:

  • Provided a detailed mathematical analysis of three widely used S-shaped functions.
  • Successfully transformed a trigonometric function to satisfy real-world assumptions for reliability modeling.
  • Demonstrated the advantages and practical applicability of the transformed trigonometric function in software reliability contexts.

Conclusions:

  • The transformed trigonometric function offers distinct advantages over commonly used S-shaped functions.
  • This research highlights the potential for developing new software reliability models based on trigonometric functions.
  • The study contributes a novel mathematical approach to S-shaped function selection in reliability engineering.