Software Reliability Growth Model Combining Testing Effort Function and Burr-Type Fault Detection Rate

Yixin Qiao, Qiang Han (), Sheng Han, Zhichao Shi and Kehan Xue
Additional contact information
Yixin Qiao: School of Computer Science and Engineering, North Minzu University, Yinchuan 750021, China
Qiang Han: School of Computer Science and Engineering, North Minzu University, Yinchuan 750021, China
Sheng Han: School of Computer Science and Engineering, North Minzu University, Yinchuan 750021, China
Zhichao Shi: School of Computer Science and Engineering, North Minzu University, Yinchuan 750021, China
Kehan Xue: School of Computer Science and Engineering, North Minzu University, Yinchuan 750021, China

Mathematics, 2025, vol. 13, issue 22, 1-22

Abstract: Software reliability growth models (SRGMs) often assume a linear relationship between the fault detection rate (FDR) and testing effort function (TEF), which fails to capture their dynamic and nonlinear characteristics. To address this limitation, this paper proposes a novel SRGM framework that employs Burr-III and Burr-XII distributions to characterize the FDR, integrated with S-shaped TEFs. To tackle the parameter estimation challenge for such complex models, we designed a hybrid GRU-HMM deep learning framework. Experiments on multiple real-world datasets demonstrate that the proposed models (particularly III-is and XII-is) significantly outperform traditional baseline models in both goodness-of-fit and prediction accuracy. Quantitatively, on the DS1 dataset, the III-is model reduced the MSE from 110.7 to 102.9 and improved the AIC from 108.3 to 91.7 compared to the best baseline. On the DS2 dataset, the XII-is model notably decreased the MSE from 64.2 to 48.9. These results not only validate the theoretical advantage of combining Burr distributions with S-shaped TEFs in modeling nonlinear, multi-phase testing dynamics but also provide a practical solution for high-precision reliability assessment and resource planning in complex software testing environments.

Keywords: software reliability growth models; testing effort function; Burr-III/Burr-XII distributions; GRU-HMM (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/22/3633/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/22/3633/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:22:p:3633-:d:1793535

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().