Multi release software reliability modelling incorporating fault generation in detection process and fault dependency with change point in correction process Sujit Kumar Pradhan, Anil Kumar, Vijay Kumar Scientific Reports, 2025 Many software reliability growth models (SRGMs) have been proposed in the literature to evaluate the remaining faults and software reliability. The probability of getting failure-free software within a specified period and environment is known as software reliability and is recognized as one of the essential aspects. In this paper, we present a new SRGM of the fault detection process (FDP) and fault correction process (FCP) and study the dependency between the FDP and FCP as the amount of fault dependency, not time dependency. The FDP is modeled by considering a multi-release concept where the leftover faults from the previous release and newly added faults after enhancing the existing features in the software are considered. Further, the FCP model is proposed by introducing the change point concept in the fault dependency function. These models are validated on two actual medium-sized software system data sets. The results show that the proposed models fit the data set more accurately than the existing SRGMs. We have also discussed the optimal release time through a cost model where setup, testing, and debugging costs are introduced in both the testing and operational phases in the cost model.
Asymptotic Behavior of the Semidiscrete FE Approximations to Weakly Damped Wave Equations With Minimal Smoothness on Initial Data P. Danumjaya, Anil Kumar, Amiya K. Pani Mathematical Methods in the Applied Sciences, 2025 Exponential decay estimates of a general linear weakly damped wave equation are studied with decay rate lying in a range. Based on the ‐conforming finite element method to discretize spatial variables while keeping temporal variable continuous, a semidiscrete system is analyzed, and uniform decay estimates are derived with precisely the same decay rate as in the continuous case. Optimal error estimates with minimal smoothness assumptions on the initial data are established, which preserve the exponential decay rate, and for a 2D problem, the maximum error bound is also proved. The present analysis is then generalized to include the problems with nonhomogeneous forcing function, space‐dependent damping, and problems with compensator. It is observed that decay rates are improved with large viscous damping and compensator. Finally, some numerical experiments are performed to confirm our theoretical findings.
Modeling Reliability-Driven Software Release Strategy Considering Testing Effort with Fault Detection and Correction Processes: A Control Theoretic Approach Sujit Kumar Pradhan, Anil Kumar, Vijay Kumar International Journal of Reliability Quality and Safety Engineering, 2025 In this paper, we have introduced a software reliability growth model (SRGM) that integrates a Weibull testing effort function (TEF) within the software fault detection process (FDP) and fault correction process (FCP), effectively capturing the intricacies of software testing. Leveraging the least squared estimation method, we estimated both model parameters and the TEF, leading to a notably improved fit with the dataset and enhancing our comprehension of software reliability dynamics. Our approach also involved employing a reliability-based method to identify the optimal time for software release, further reinforcing the robustness of our model. Subsequently, we devised an optimal control model to minimize testing efforts throughout the software development life cycle. This work provides a comprehensive methodological framework for computing the total cost while ensuring debugging costs follow a learning curve pattern. Through numerical simulations involving hypothetical values and the Weibull TEF, we observed that once the software achieves the desired reliability for release, subsequent costs gradually decline to zero. In essence, both testing and future costs converge to zero post-release, reducing instantaneous expenses.
An optimal software enhancement and customer growth model: a control-theoretic approach Sujit K. Pradhan, Anil Kumar, Vijay Kumar International Journal of Quality and Reliability Management, 2024 PurposeRecently, the popularity of software has grown significantly in the market. Enhancement of software is needed to decrease the burden of getting high-quality and reliable software. To achieve this, the software is upgraded by adding new features to the previous version. Therefore, adding new features in the last version to be consistent with the earlier version is challenging. This paper aims to discuss the optimal software enhancement and customer growth model.Design/methodology/approachThis paper discusses a model when new features are added to the software, and the customers' adoption of the software is presented as a customer growth model. An optimal control problem is introduced to maximize the profit obtained from the software system over the system's lifetime period. Total gain is calculated by the value generated from selling the software over the total expenditure during the software development process. The closed-form solution and some theoretical results are presented using the optimal control-theoretic approach. The theoretical results are supported by a numerical example.FindingsThis paper gives several substantive insights during sensitivity analysis and provides essential results. The results discussed here are compatible with the actual scenario and useful in software enhancement.Originality/valueThe authors have proposed a new feature growth and customer growth model to maximize the total profit using optimal control theory.
Revisiting software reliability growth model under general setup V Kumar, SK Pradhan, A Kumar, PK Kapur International Journal of System Assurance Engineering and Management , 2025 2025 Citations: 6
Multi release software reliability modelling incorporating fault generation in detection process and fault dependency with change point in correction process SK Pradhan, K Anil, V Kumar Scientific Reports 15, 23145 , 2025 2025 Citations: 10
Asymptotic Behavior of the Semidiscrete FE Approximations to Weakly Damped Wave Equations With Minimal Smoothness on Initial Data P Danumjaya, A Kumar, AK Pani Mathematical Methods in the Applied Sciences , 2025 2025 Citations: 2
Error analysis with exponential decay estimates for a fully discrete approximation of a class of strongly damped wave equations K Kumar, D Palla, A Kumar, AK Pani 10.13140/RG.2.2.29344.24323 , 2025 2025
Modelling Reliability-Driven Software Release Strategy Considering Testing Effort with Fault Detection and Correction Processes: A Control Theoretic Approach SK Pradhan, K Anil, V Kumar International Journal of Reliability, Quality and Safety Engineering 32 (2 … , 2025 2025 Citations: 9
Imperfect Debugging, Testing Coverage, and Compiler Error-Based SRGM with Two Types of Faults Under the Uncertainty of the Operating Environment SK Pradhan, A Kumar, V Kumar, PK Kapur Reliability Engineering for Industrial Processes. Springer Series in … , 2024 2024 Citations: 4
Approximate Controllability of Linear Parabolic Equation with Memory A Kumar, AK Pani, MC Joshi Authorea Preprints , 2024 2024
Virtual Element Method for Control Constrained Dirichlet Boundary Control Problem Governed by the Diffusion Problem J Tushar, RC Sau, A Kumar Journal of Scientific Computing 98 (21), 26 , 2024 2024 Citations: 1
A new software reliability growth model with testing coverage and uncertainty of operating environments SK Pradhan, A Kumar, V Kumar Proceedings of the 1st International Online Conference on Mathematics and … , 2023 2023 Citations: 4
Mixed Virtual Element Methods for optimal control of Darcy flow J Tushar, A Kumar, S Kumar Computers and Mathematics with Applications 140 (2023), 134-153 , 2023 2023 Citations: 5
An optimal software enhancement and customer growth model: a control-theoretic approach SK Pradhan, A Kumar, V Kumar International Journal of Quality & Reliability Management , 2023 2023 Citations: 11
Virtual Element Methods for Optimal Control Problems Governed by Elliptic Interface Problems J Tushar, A Kumar, S Kumar FIAM 2021: Frontiers in Industrial and Applied Mathematics 410, 521-533 , 2023 2023
Asymptotic behaviour of the semidiscrete FE approximations to weakly damped wave equations with minimal smoothness on initial data P Danumjaya, A Kumar, AK Pani https://doi.org/10.48550/arXiv.2302.12476 , 2023 2023
Approximate Controllability of linear parabolic equation with memory A Kumar, AK Pani, MC Joshi Computers & Mathematics with Applications 128 (320-330) , 2022 2022 Citations: 4
An effort allocation model for a three stage software reliability growth model SK Pradhan, A Kumar, V Kumar Predictive analytics in system reliability, 263-282 , 2022 2022 Citations: 9
Virtual element methods for general linear elliptic interface problems on polygonal meshes with small edges JaiTushar, A Kumar, S Kumar Computers & Mathematics with Applications 122, 61-75 , 2022 2022 Citations: 22
Variational and Virtual Discretizations of Optimal Control Problems Governed by Diffusion Problems J Tushar, A Kumar, S Kumar Applied Mathematics & Optimization 85 (2), 36 , 2022 2022 Citations: 8
Controllability of a space-time fractional order parabolic equation A Kumar, SG Latpate, RB Sonawane Discussiones Mathematicae: Differential Inclusions, Control and Optimization … , 2022 2022
Approximations of quasi-linear elliptic optimal control problems on polygonal meshes under variational and virtual discretizations J Tushar, A Kumar, S Kumar International Journal of Applied and Computational Mathematics 8 , 2022 2022 Citations: 2
An optimal resource allocation model considering two-phase software reliability growth model with testing effort and imperfect debugging SK Pradhan, A Kumar, V Kumar Reliability: Theory & Applications 16 (SI 2 (64)), 241–255 , 2021 2021 Citations: 14
MOST CITED SCHOLAR PUBLICATIONS
Virtual element methods for general linear elliptic interface problems on polygonal meshes with small edges JaiTushar, A Kumar, S Kumar Computers & Mathematics with Applications 122, 61-75 , 2022 2022 Citations: 22
Approximation theorems for controllability problem governed by fractional differential equation D Rajesh, M Malik, S Abbas, A Kumar, S Rathinasamy Evolution Equations and Control Theory , 2020 2020 Citations: 16
An optimal resource allocation model considering two-phase software reliability growth model with testing effort and imperfect debugging SK Pradhan, A Kumar, V Kumar Reliability: Theory & Applications 16 (SI 2 (64)), 241–255 , 2021 2021 Citations: 14
An optimal software enhancement and customer growth model: a control-theoretic approach SK Pradhan, A Kumar, V Kumar International Journal of Quality & Reliability Management , 2023 2023 Citations: 11
On approximation theorems for controllability of non-linear parabolic problems A Kumar, MC Joshi, AK Pani IMA Journal of Mathematical Control and Information 24 (1), 115-136 , 2007 2007 Citations: 11
Multi release software reliability modelling incorporating fault generation in detection process and fault dependency with change point in correction process SK Pradhan, K Anil, V Kumar Scientific Reports 15, 23145 , 2025 2025 Citations: 10
Modelling Reliability-Driven Software Release Strategy Considering Testing Effort with Fault Detection and Correction Processes: A Control Theoretic Approach SK Pradhan, K Anil, V Kumar International Journal of Reliability, Quality and Safety Engineering 32 (2 … , 2025 2025 Citations: 9
An effort allocation model for a three stage software reliability growth model SK Pradhan, A Kumar, V Kumar Predictive analytics in system reliability, 263-282 , 2022 2022 Citations: 9
Variational and Virtual Discretizations of Optimal Control Problems Governed by Diffusion Problems J Tushar, A Kumar, S Kumar Applied Mathematics & Optimization 85 (2), 36 , 2022 2022 Citations: 8
Ordinary differential equations: modern perspective MC Joshi (No Title) , 2006 2006 Citations: 8
Revisiting software reliability growth model under general setup V Kumar, SK Pradhan, A Kumar, PK Kapur International Journal of System Assurance Engineering and Management , 2025 2025 Citations: 6
Approximation of exact controllability problem involving parabolic differential equations MC Joshi, A Kumar IMA Journal of Mathematical Control and Information 22 (3), 350-363 , 2005 2005 Citations: 6
Mixed Virtual Element Methods for optimal control of Darcy flow J Tushar, A Kumar, S Kumar Computers and Mathematics with Applications 140 (2023), 134-153 , 2023 2023 Citations: 5
Imperfect Debugging, Testing Coverage, and Compiler Error-Based SRGM with Two Types of Faults Under the Uncertainty of the Operating Environment SK Pradhan, A Kumar, V Kumar, PK Kapur Reliability Engineering for Industrial Processes. Springer Series in … , 2024 2024 Citations: 4
A new software reliability growth model with testing coverage and uncertainty of operating environments SK Pradhan, A Kumar, V Kumar Proceedings of the 1st International Online Conference on Mathematics and … , 2023 2023 Citations: 4
Approximate Controllability of linear parabolic equation with memory A Kumar, AK Pani, MC Joshi Computers & Mathematics with Applications 128 (320-330) , 2022 2022 Citations: 4
A fourth-order orthogonal spline collocation method to fourth-order boundary value problems SK Bhal, P Danumjaya, A Kumar International Journal for Computational Methods in Engineering Science and … , 2019 2019 Citations: 3
Approximate controllability of a class of partial integro-differential equations of parabolic type A Kumar, AK Pani, MC Joshi arXiv preprint arXiv:1606.03673 , 2016 2016 Citations: 3
Optimal control for a vibrating string with variable axial load and damping gain RB Sonawane, A Kumar, SB Nimse IFAC Proceedings Volumes 47 (1), 75-81 , 2014 2014 Citations: 3
Asymptotic Behavior of the Semidiscrete FE Approximations to Weakly Damped Wave Equations With Minimal Smoothness on Initial Data P Danumjaya, A Kumar, AK Pani Mathematical Methods in the Applied Sciences , 2025 2025 Citations: 2
