Unit-Weibull distribution with innovative applications in engineering and management

V. Mariappan (), Milind Sakhardande (), Mahesh Dhawalikar (), P. K. Srividya () and S. Raikar ()
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V. Mariappan: Agnel Institute of Technology and Design
Milind Sakhardande: Goa College of Engineering
Mahesh Dhawalikar: Goa College of Engineering
P. K. Srividya: Periyar Maniammai University
S. Raikar: Agnel Institute of Technology and Design

International Journal of System Assurance Engineering and Management, 2025, vol. 16, issue 10, No 4, 3272-3283

Abstract: Abstract The Unit-Weibull distribution has applications in the study of reliability engineering, risk analysis, and survival modeling. While the traditional Weibull distribution provides a framework for modeling the failure times of systems and components, the Unit-Weibull distribution is very flexible. It is highly competitive with many classical distributions on the unit interval. This paper begins by presenting the development and mathematical formulation of the Unit-Weibull distribution, describing its probability density function and cumulative distribution function, and hence describing various reliability measures that are generally required for the reliability assessment of any system and maintenance policy decision. Bathtub-shaped hazard and reversed hazard rates are discussed at length in this paper. A sensitivity analysis of parameters is carried out to get the bathtub-shaped hazard rate with appropriate visuals. Through a rigorous examination of its properties, this study aims to comprehensively understand the distribution’s behavior and characteristics, including its shape, scale, and reliability parameters. For the investigation of the nature of various reliability measures, appropriate spreadsheets are also used to support the claim when the functions are transcendental. Two real-life cases were applied and analyzed to draw appropriate managerial decisions regarding warranty and maintenance policy.

Keywords: Weibull distribution; Unit-Weibull distribution; Reliability measures; Hazard rate; Reversed hazard rate (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13198-025-02832-2

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