Quantifying Cross-Release Vulnerability Discovery in Software: A Multi-Release Modeling Approach

Authors

  • Jyotish N. P. Singh NICMAR University, Pune, Maharashtra, India
  • Navneet Bhatt Anil Surendra Modi School of Commerce, SVKM’s Narsee Monjee Institute of Management Studies (NMIMS), Mumbai 400056, India
  • Adarsh Anand Department of Operational Research, University of Delhi, Delhi 110007, India
  • Divya Department of Operational Research, University of Delhi, Delhi 110007, India

DOI:

https://doi.org/10.13052/jgeu0975-1416.1416

Keywords:

Multi-release software, patch, security, vulnerability discovery models (VDMs)

Abstract

Software Vulnerability Discovery Models (VDMs) help understand how security flaws are identified in software after release. Traditionally, most models focus on a single release and assume vulnerabilities are discovered independently. However, modern software often exists in multiple versions that share a significant portion of code. This shared structure means that discovering a vulnerability in one version can also help identify similar issues in other versions: a phenomenon referred to as cross-discovery. In this paper, the author extends the traditional VDM framework to model multiple software releases simultaneously, enabling interaction between versions via cross-discovery. Unlike existing multi-release models that use constant values for shared-code influence, the author proposes a new model that introduces time-dependent cross-discovery coefficients. These functions reflect how the influence between software versions changes over time, making the model more realistic.

The author applies the proposed model to real-world data from two popular Windows operating system versions, Windows XP and Windows Vista. The proposed model accurately captures both within-release discoveries and those triggered by interaction with the other version. The author estimates parameters, validates results using statistical measures, and visualizes predicted and actual trends. The results show that the proposed approach provides deeper insights into how vulnerabilities are found across multiple software releases, supporting better software maintenance and security planning.

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Author Biographies

Jyotish N. P. Singh, NICMAR University, Pune, Maharashtra, India

Jyotish N. P. Singh is an Assistant Professor of Decision Sciences, an academic with expertise in Operational Research, Mathematics, and Software Reliability, known for his research, publications, and mentorship, associated with NICMAR Pune and Delhi University. He’s an author on software reliability and mathematical modeling, a public speaker, and passionate about India’s contributions to math, while also dabbling in poetry.

Navneet Bhatt, Anil Surendra Modi School of Commerce, SVKM’s Narsee Monjee Institute of Management Studies (NMIMS), Mumbai 400056, India

Navneet Bhatt is an Assistant Professor at SVKM’s NMIMS Anil Surendra Modi School of Commerce. He holds a PhD and MPhil in Operational Research and specializes in mathematical modeling, quantitative techniques, machine learning, and software vulnerability analytics, with several research publications and academic contributions.

Adarsh Anand, Department of Operational Research, University of Delhi, Delhi 110007, India

Adarsh Anand did his doctorate in the area of Innovation Diffusion Modeling in Marketing and Software Reliability Assessment. Presently he is working as an Associate Professor in the Department of Operational Research, University of Delhi (INDIA). He has been conferred with Young Promising Researcher in the field of Technology Management and Software Reliability by Society for Reliability Engineering, Quality and Operations Management (SREQOM) in 2012. He is a lifetime member of the Society for Reliability Engineering, Quality and Operations Management (SREQOM). He is also on the editorial board of International Journal of System Assurance and Engineering management (Springer). He has Guest edited several Special Issues for Journals of international repute. He has edited two books namely: “System Reliability Management (Solutions and Technologies)” and “Recent Advancements in Software Reliability Assurance” under the banner of Taylor and Francis (CRC – Press). He has publications in journals of national and international repute. His research interest includes modeling innovation adoption and successive generations in marketing, software reliability growth modelling and social media analysis.

Divya, Department of Operational Research, University of Delhi, Delhi 110007, India

Divya received a bachelor’s degree in Mathematics from University of Delhi in 2020 and a master’s degree in operational research from University of Delhi in 2022, and she is currently pursuing the philosophy of doctorate degree in operational research from University of Delhi.

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Published

2026-01-01

How to Cite

Singh, J. N. P., Bhatt, N., Anand, A., & Divya. (2026). Quantifying Cross-Release Vulnerability Discovery in Software: A Multi-Release Modeling Approach. Journal of Graphic Era University, 14(01), 183–204. https://doi.org/10.13052/jgeu0975-1416.1416

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Articles