An Analysis of the New Reliability Model Based on Bathtub-Shaped Failure Rate Distribution with Application to Failure Data

Tabassum Naz Sindhu, Sadia Anwar, Marwa K. H. Hassan, Showkat Ahmad Lone, Tahani A. Abushal () and Anum Shafiq ()
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Tabassum Naz Sindhu: Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
Sadia Anwar: Department of Mathematics, College of Arts and Sciences, Wadi Ad Dawasir, Prince Sattam Bin Abdul Aziz University, Al-Kharj 11991, Saudi Arabia
Marwa K. H. Hassan: Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, Egypt
Showkat Ahmad Lone: Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia
Tahani A. Abushal: Department of Mathematical Science, Faculty of Applied Science, Umm Al-Qura University, Mecca 24382, Saudi Arabia
Anum Shafiq: School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Mathematics, 2023, vol. 11, issue 4, 1-18

Abstract: The reliability of software has a tremendous influence on the reliability of systems. Software dependability models are frequently utilized to statistically analyze the reliability of software. Numerous reliability models are based on the nonhomogeneous Poisson method (NHPP). In this respect, in the current study, a novel NHPP model established on the basis of the new power function distribution is suggested. The mathematical formulas for its reliability measurements were found and are visually illustrated. The parameters of the suggested model are assessed utilizing the weighted nonlinear least-squares, maximum-likelihood, and nonlinear least-squares estimation techniques. The model is subsequently verified using a variety of reliability datasets. Four separate criteria were used to assess and compare the estimating techniques. Additionally, the effectiveness of the novel model is assessed and evaluated with two foundation models both objectively and subjectively. The implementation results reveal that our novel model performed well in the failure data that we examined.

Keywords: mean value function; reliability function; maximum-likelihood estimation; intensity function; mean time between failures (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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