{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,9]],"date-time":"2026-04-09T17:53:28Z","timestamp":1775757208137,"version":"3.50.1"},"reference-count":53,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T00:00:00Z","timestamp":1761004800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T00:00:00Z","timestamp":1761004800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Syst Assur Eng Manag"],"published-print":{"date-parts":[[2026,2]]},"DOI":"10.1007\/s13198-025-02988-x","type":"journal-article","created":{"date-parts":[[2025,10,21]],"date-time":"2025-10-21T09:52:00Z","timestamp":1761040320000},"page":"608-621","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Revisiting software reliability growth model under general setup"],"prefix":"10.1007","volume":"17","author":[{"given":"Vijay","family":"Kumar","sequence":"first","affiliation":[]},{"given":"Sujit Kumar","family":"Pradhan","sequence":"additional","affiliation":[]},{"given":"Anil","family":"Kumar","sequence":"additional","affiliation":[]},{"given":"P. K.","family":"Kapur","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,10,21]]},"reference":[{"issue":"1","key":"2988_CR1","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1108\/02656711011009335","volume":"27","author":"N Ahmad","year":"2010","unstructured":"Ahmad N, Khan MGM, Rafi LS (2010) A study of testing-effort dependent inflection s-shaped software reliability growth models with imperfect debugging. Int J Qual Reliab Manag 27(1):89\u2013110","journal-title":"Int J Qual Reliab Manag"},{"issue":"3","key":"2988_CR2","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1081\/SAC-100105083","volume":"30","author":"Y-P Chang","year":"2001","unstructured":"Chang Y-P (2001) Estimation of parameters for nonhomogeneous poisson process: software reliability with change-point model. Commun Stat-Simul Comput 30(3):623\u2013635","journal-title":"Commun Stat-Simul Comput"},{"issue":"1","key":"2988_CR3","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1007\/s10479-021-04258-y","volume":"312","author":"S Chatterjee","year":"2022","unstructured":"Chatterjee S, Saha D, Sharma A, Verma Y (2022) Reliability and optimal release time analysis for multi up-gradation software with imperfect debugging and varied testing coverage under the effect of random field environments. Annals Operations Res 312(1):65\u201385","journal-title":"Annals Operations Res"},{"issue":"12","key":"2988_CR4","doi-asserted-by":"publisher","first-page":"5009","DOI":"10.1007\/s13369-016-2189-0","volume":"41","author":"S Chatterjee","year":"2016","unstructured":"Chatterjee S, Shukla A (2016) Modeling and analysis of software fault detection and correction process through weibull-type fault reduction factor, change point and imperfect debugging. Arab J Sci Eng 41(12):5009\u20135025","journal-title":"Arab J Sci Eng"},{"key":"2988_CR5","doi-asserted-by":"crossref","unstructured":"Dhaka R, Pachauri B, Jain A (2021) SRGM using testing-effort function with uncertainty in operating environment. In: IOP conference series: materials science and engineering, vol 1099, pp 012020. IOP Publishing","DOI":"10.1088\/1757-899X\/1099\/1\/012020"},{"issue":"3","key":"2988_CR6","doi-asserted-by":"publisher","first-page":"206","DOI":"10.1109\/TR.1979.5220566","volume":"28","author":"AL Goel","year":"1979","unstructured":"Goel AL, Okumoto K (1979) Time-dependent error-detection rate model for software reliability and other performance measures. IEEE Trans Reliab 28(3):206\u2013211","journal-title":"IEEE Trans Reliab"},{"issue":"2","key":"2988_CR7","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/j.jss.2004.10.014","volume":"77","author":"C-Y Huang","year":"2005","unstructured":"Huang C-Y (2005) Cost-reliability-optimal release policy for software reliability models incorporating improvements in testing efficiency. J Syst Softw 77(2):139\u2013155","journal-title":"J Syst Softw"},{"issue":"3","key":"2988_CR8","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1109\/TR.2002.801847","volume":"51","author":"C-Y Huang","year":"2002","unstructured":"Huang C-Y, Kuo S-Y (2002) Analysis of incorporating logistic testing-effort function into software reliability modeling. IEEE Trans Reliab 51(3):261\u2013270","journal-title":"IEEE Trans Reliab"},{"key":"2988_CR9","unstructured":"Huang C-Y, Kuo S-Y, Chen Y (1997) Analysis of a software reliability growth model with logistic testing-effort function. In: Proceedings the eighth international symposium on software reliability engineering, pp 378\u2013388. IEEE"},{"key":"2988_CR10","unstructured":"Huang C-Y, Lin C-T, Kuo S-Y, Lyu MR, Sue C-C (2004) Software reliability growth models incorporating fault dependency with various debugging time lags. In: Proceedings of the 28th annual international computer software and applications conference, 2004. COMPSAC 2004, 186\u2013191. IEEE"},{"key":"2988_CR11","doi-asserted-by":"publisher","first-page":"111267","DOI":"10.1016\/j.jss.2022.111267","volume":"188","author":"Y-S Huang","year":"2022","unstructured":"Huang Y-S, Chiu K-C, Chen W-M (2022) A software reliability growth model for imperfect debugging. J Syst Softw 188:111267","journal-title":"J Syst Softw"},{"issue":"3","key":"2988_CR12","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1016\/j.jss.2009.09.042","volume":"83","author":"A Israeli","year":"2010","unstructured":"Israeli A, Feitelson DG (2010) The linux kernel as a case study in software evolution. J Syst Softw 83(3):485\u2013501","journal-title":"J Syst Softw"},{"issue":"7","key":"2988_CR13","doi-asserted-by":"publisher","first-page":"1298","DOI":"10.1016\/j.apm.2007.04.002","volume":"32","author":"PK Kapur","year":"2008","unstructured":"Kapur PK, Goswami DN, Bardhan A, Singh O (2008) Flexible software reliability growth model with testing effort dependent learning process. Appl Math Model 32(7):1298\u20131307","journal-title":"Appl Math Model"},{"issue":"04","key":"2988_CR14","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1142\/S0218539304001579","volume":"11","author":"PK Kapur","year":"2004","unstructured":"Kapur PK, Goswami DN, Gupta A (2004) A software reliability growth model with testing effort dependent learning function for distributed systems. Int J Reliab Qual Saf Eng 11(04):365\u2013377","journal-title":"Int J Reliab Qual Saf Eng"},{"issue":"3","key":"2988_CR15","first-page":"245","volume":"2","author":"PK Kapur","year":"2006","unstructured":"Kapur PK, Gupta A, Shatnawi O, Yadavalli VSS (2006) Testing effort control using flexible software reliability growth model with change point. Int J Perform Eng 2(3):245\u2013262","journal-title":"Int J Perform Eng"},{"issue":"9","key":"2988_CR16","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.1080\/00207721.2012.669861","volume":"44","author":"PK Kapur","year":"2013","unstructured":"Kapur PK, Pham H, Chanda U, Kumar V (2013) Optimal allocation of testing effort during testing and debugging phases: a control theoretic approach. Int J Syst Sci 44(9):1639\u20131650","journal-title":"Int J Syst Sci"},{"key":"2988_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-85729-204-9","volume-title":"Software reliability assessment with OR applications","author":"PK Kapur","year":"2011","unstructured":"Kapur PK, Pham H, Gupta A, Jha PC et al (2011) Software reliability assessment with OR applications, vol 364. Springer, London"},{"issue":"3","key":"2988_CR18","doi-asserted-by":"publisher","first-page":"771","DOI":"10.1080\/00207540600926113","volume":"46","author":"PK Kapur","year":"2008","unstructured":"Kapur PK, Singh VB, Anand S, Yadavalli VSS (2008) Software reliability growth model with change-point and effort control using a power function of the testing time. Int J Prod Res 46(3):771\u2013787","journal-title":"Int J Prod Res"},{"key":"2988_CR19","first-page":"331","volume":"13","author":"S Khurshid","year":"2021","unstructured":"Khurshid S, Shrivastava AK, Iqbal J (2021) Effort based software reliability model with fault reduction factor, change point and imperfect debugging. Int J Inf Technol 13:331\u2013340","journal-title":"Int J Inf Technol"},{"issue":"6\/7","key":"2988_CR20","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.1108\/IJQRM-09-2019-0296","volume":"37","author":"V Kumar","year":"2020","unstructured":"Kumar V, Sahni R (2020) Dynamic testing resource allocation modeling for multi-release software using optimal control theory and genetic algorithm. Int J Qual Reliab Manag 37(6\/7):1049\u20131069","journal-title":"Int J Qual Reliab Manag"},{"key":"2988_CR21","doi-asserted-by":"publisher","first-page":"68","DOI":"10.1016\/j.apm.2017.06.034","volume":"51","author":"Q Li","year":"2017","unstructured":"Li Q, Pham H (2017) Nhpp software reliability model considering the uncertainty of operating environments with imperfect debugging and testing coverage. Appl Math Model 51:68\u201385","journal-title":"Appl Math Model"},{"issue":"6","key":"2988_CR22","doi-asserted-by":"publisher","first-page":"1025","DOI":"10.1016\/j.jss.2007.10.002","volume":"81","author":"C-T Lin","year":"2008","unstructured":"Lin C-T, Huang C-Y (2008) Enhancing and measuring the predictive capabilities of testing-effort dependent software reliability models. J Syst Softw 81(6):1025\u20131038","journal-title":"J Syst Softw"},{"issue":"9","key":"2988_CR23","doi-asserted-by":"publisher","first-page":"1312","DOI":"10.1016\/j.jss.2005.12.006","volume":"79","author":"J-H Lo","year":"2006","unstructured":"Lo J-H, Huang C-Y (2006) An integration of fault detection and correction processes in software reliability analysis. J Syst Softw 79(9):1312\u20131323","journal-title":"J Syst Softw"},{"issue":"9","key":"2988_CR24","doi-asserted-by":"publisher","first-page":"1131","DOI":"10.1109\/PROC.1980.11812","volume":"68","author":"JD Musa","year":"1980","unstructured":"Musa JD (1980) The measurement and management of software reliability. Proc IEEE 68(9):1131\u20131143","journal-title":"Proc IEEE"},{"key":"2988_CR25","volume-title":"Software Reliability: Measurement, Prediction","author":"JD Musa","year":"1987","unstructured":"Musa JD, Iannino A, Okumoto K (1987) Software Reliability: Measurement, Prediction. McGraw-Hill Inc, Application"},{"key":"2988_CR26","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/S0065-2458(08)60299-5","volume":"30","author":"JD Musa","year":"1990","unstructured":"Musa JD, Iannino A, Okumoto K (1990) Software reliability. Adv Comput 30:85\u2013170","journal-title":"Adv Comput"},{"key":"2988_CR27","first-page":"430","volume-title":"International Colloquium on Reliability and Maintainability, 4th","author":"M Ohba","year":"1984","unstructured":"Ohba M, Yamada S (1984) S-shaped software reliability growth models. International colloquium on reliability and maintainability, 4th, Tregastel, France, pp 430\u2013436"},{"key":"2988_CR28","doi-asserted-by":"crossref","unstructured":"Ohba M (1984a) Inflection S-shaped software reliability growth model. In Stochastic models in reliability theory, pp 144\u2013162. Springer","DOI":"10.1007\/978-3-642-45587-2_10"},{"issue":"4","key":"2988_CR29","doi-asserted-by":"publisher","first-page":"428","DOI":"10.1147\/rd.284.0428","volume":"28","author":"M Ohba","year":"1984","unstructured":"Ohba M (1984) Software reliability analysis models. IBM J Res Dev 28(4):428\u2013443","journal-title":"IBM J Res Dev"},{"key":"2988_CR30","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.ress.2014.01.004","volume":"126","author":"R Peng","year":"2014","unstructured":"Peng R, Li YF, Zhang WJ, Hu QP (2014) Testing effort dependent software reliability model for imperfect debugging process considering both detection and correction. Reliab Eng Syst Saf 126:37\u201343","journal-title":"Reliab Eng Syst Saf"},{"issue":"5","key":"2988_CR31","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1080\/00207729608929237","volume":"27","author":"H Pham","year":"1996","unstructured":"Pham H (1996) A software cost model with imperfect debugging, random life cycle and penalty cost. Int J Syst Sci 27(5):455\u2013463","journal-title":"Int J Syst Sci"},{"issue":"4","key":"2988_CR32","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1007\/s11633-007-0325-8","volume":"4","author":"H Pham","year":"2007","unstructured":"Pham H (2007) An imperfect-debugging fault-detection dependent-parameter software. Int J Autom Comput 4(4):325","journal-title":"Int J Autom Comput"},{"issue":"10","key":"2988_CR33","doi-asserted-by":"publisher","first-page":"1481","DOI":"10.1080\/02331934.2013.854787","volume":"63","author":"H Pham","year":"2014","unstructured":"Pham H (2014) A new software reliability model with vtub-shaped fault-detection rate and the uncertainty of operating environments. Optimization 63(10):1481\u20131490","journal-title":"Optimization"},{"issue":"8","key":"2988_CR34","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1109\/32.624305","volume":"23","author":"K Pillai","year":"1997","unstructured":"Pillai K, Nair VS (1997) A model for software development effort and cost estimation. IEEE Trans Softw Eng 23(8):485\u2013497","journal-title":"IEEE Trans Softw Eng"},{"issue":"64","key":"2988_CR35","first-page":"241","volume":"16","author":"SK Pradhan","year":"2021","unstructured":"Pradhan SK, Kumar A, Kumar V (2021) An optimal resource allocation model considering two-phase software reliability growth model with testing effort and imperfect debugging. Reliability Theory Appl 16(64):241\u2013255","journal-title":"Reliability Theory Appl"},{"issue":"9","key":"2988_CR36","doi-asserted-by":"publisher","first-page":"2333","DOI":"10.1108\/IJQRM-08-2022-0240","volume":"41","author":"SK Pradhan","year":"2024","unstructured":"Pradhan SK, Kumar A, Kumar V (2024) An optimal software enhancement and customer growth model: a control-theoretic approach. Int J Qual Reliab Manag 41(9):2333\u20132350","journal-title":"Int J Qual Reliab Manag"},{"key":"2988_CR37","doi-asserted-by":"crossref","unstructured":"Pradhan SK, Kumar A, Kumar V (2023) An effort allocation model for a three stage software reliability growth model. In Predictive analytics in system reliability, pp 263\u2013282. Springer","DOI":"10.1007\/978-3-031-05347-4_17"},{"issue":"02","key":"2988_CR38","doi-asserted-by":"publisher","first-page":"2440002","DOI":"10.1142\/S0218539324400023","volume":"32","author":"SK Pradhan","year":"2024","unstructured":"Pradhan SK, Kumar A, Kumar V (2024) Modelling reliability driven software release strategy considering testing effort with fault detection and correction processes: a control theoretic approach. Int J Reliab Qual Saf Eng 32(02):2440002","journal-title":"Int J Reliab Qual Saf Eng"},{"issue":"1","key":"2988_CR39","doi-asserted-by":"publisher","first-page":"23145","DOI":"10.1038\/s41598-025-04102-4","volume":"15","author":"SK Pradhan","year":"2025","unstructured":"Pradhan SK, Kumar A, Kumar V (2025) Multi release software reliability modelling incorporating fault generation in detection process and fault dependency with change point in correction process. Sci Rep 15(1):23145","journal-title":"Sci Rep"},{"key":"2988_CR40","unstructured":"Pradhan V, Dhar J, Kumar A (2022) Testing-effort based NHPP software reliability growth model with change-point approach. J Inf Sci Eng 38 (2)"},{"issue":"3","key":"2988_CR41","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1080\/08982112.2023.2241067","volume":"36","author":"Umashankar Samal","year":"2023","unstructured":"Samal Umashankar, Kumar Ajay (2023) Redefining software reliability modeling: embracing fault-dependency, imperfect removal, and maximum fault considerations. Qual Eng 36(3):500\u2013509","journal-title":"Qual Eng"},{"key":"2988_CR42","doi-asserted-by":"crossref","unstructured":"Samal U, Kumar A (2024a) Incorporating human dynamics into software reliability analysis: learning, fatigue, and efficiency considerations. Int J Syst Assur Eng Management pp 1\u201310","DOI":"10.1007\/s13198-024-02368-x"},{"issue":"11\u201312","key":"2988_CR43","doi-asserted-by":"publisher","first-page":"1274","DOI":"10.1080\/14783363.2024.2366510","volume":"35","author":"U Samal","year":"2024","unstructured":"Samal U, Kumar A (2024) Metrics and trends: a bibliometric approach to software reliability growth models. Total Qual Manag Bus Excell 35(11\u201312):1274\u20131295","journal-title":"Total Qual Manag Bus Excell"},{"issue":"7","key":"2988_CR44","doi-asserted-by":"publisher","first-page":"2358","DOI":"10.1002\/qre.2516","volume":"35","author":"I Saraf","year":"2019","unstructured":"Saraf I, Iqbal J (2019) Generalized multi-release modelling of software reliability growth models from the perspective of two types of imperfect debugging and change point. Qual Reliab Eng Int 35(7):2358\u20132370","journal-title":"Qual Reliab Eng Int"},{"issue":"4","key":"2988_CR45","first-page":"751","volume":"11","author":"I Saraf","year":"2019","unstructured":"Saraf I, Iqbal J (2019) Generalized software fault detection and correction modeling framework through imperfect debugging, error generation and change point. Int J Inf Technol 11(4):751\u2013757","journal-title":"Int J Inf Technol"},{"key":"2988_CR46","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1007\/s13198-020-00988-7","volume":"11","author":"AK Shrivastava","year":"2020","unstructured":"Shrivastava AK, Kumar V, Kapur PK, Singh O (2020) Software release and testing stop time decision with change point. Int J Syst Assur Eng Manag 11:196\u2013207","journal-title":"Int J Syst Assur Eng Manag"},{"issue":"2","key":"2988_CR47","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1016\/S0164-1212(02)00071-7","volume":"66","author":"H-J Shyur","year":"2003","unstructured":"Shyur H-J (2003) A stochastic software reliability model with imperfect-debugging and change-point. J Syst Softw 66(2):135\u2013141","journal-title":"J Syst Softw"},{"key":"2988_CR48","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/s13198-014-0246-1","volume":"6","author":"O Singh","year":"2015","unstructured":"Singh O, Kapur PK, Shrivastava AK, Kumar V (2015) Release time problem with multiple constraints. Int J Syst Assur Eng Manag 6:83\u201391","journal-title":"Int J Syst Assur Eng Manag"},{"issue":"1","key":"2988_CR49","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1007\/s13198-014-0242-5","volume":"6","author":"VB Singh","year":"2015","unstructured":"Singh VB, Chaturvedi KK, Khatri SK, Kumar V (2015) Bug prediction modeling using complexity of code changes. Int J Syst Assur Eng Manag 6(1):44\u201360","journal-title":"Int J Syst Assur Eng Manag"},{"key":"2988_CR50","doi-asserted-by":"crossref","unstructured":"Tohma Y, Jacoby R, Murata Y, Yamamoto M (1989) Hyper-geometric distribution model to estimate the number of residual software faults. In: Proceedings of the thirteenth annual international computer software & applications conference, pp 610\u2013617. IEEE","DOI":"10.1109\/CMPSAC.1989.65155"},{"issue":"1","key":"2988_CR51","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1109\/TR.1986.4335332","volume":"35","author":"S Yamada","year":"1986","unstructured":"Yamada S, Ohtera H, Narihisa H (1986) Software reliability growth models with testing-effort. IEEE Trans Reliab 35(1):19\u201323","journal-title":"IEEE Trans Reliab"},{"issue":"12","key":"2988_CR52","doi-asserted-by":"publisher","first-page":"2241","DOI":"10.1080\/00207729208949452","volume":"23","author":"S Yamada","year":"1992","unstructured":"Yamada S, Tokuno K, Osaki S (1992) Imperfect debugging models with fault introduction rate for software reliability assessment. Int J Syst Sci 23(12):2241\u20132252","journal-title":"Int J Syst Sci"},{"key":"2988_CR53","first-page":"27","volume":"53","author":"M Zhu","year":"2018","unstructured":"Zhu M, Pham H (2018) A two-phase software reliability modeling involving with software fault dependency and imperfect fault removal. Comput Lang Syst Struct 53:27\u201342","journal-title":"Comput Lang Syst Struct"}],"container-title":["International Journal of System Assurance Engineering and Management"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13198-025-02988-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13198-025-02988-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13198-025-02988-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T09:04:20Z","timestamp":1772010260000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13198-025-02988-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,21]]},"references-count":53,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,2]]}},"alternative-id":["2988"],"URL":"https:\/\/doi.org\/10.1007\/s13198-025-02988-x","relation":{},"ISSN":["0975-6809","0976-4348"],"issn-type":[{"value":"0975-6809","type":"print"},{"value":"0976-4348","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,21]]},"assertion":[{"value":"29 January 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 September 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 October 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that there are no Conflict of interest regarding the publication of this paper.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}