{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:30:21Z","timestamp":1750307421468,"version":"3.41.0"},"reference-count":27,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2010,5,11]],"date-time":"2010-05-11T00:00:00Z","timestamp":1273536000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGSOFT Softw. Eng. Notes"],"published-print":{"date-parts":[[2010,5,11]]},"abstract":"<jats:p>The progress of software testing is influenced by various uncertainty factors like effort expenditure, skill of test personal, testing tool, defect density, irregular state of open source project, and irregular state of software fault-report phenomena on the bug tracking system. Hence, there is an irregular fluctuation in fault detection\/removal rate during testing phase. In software, the independence of failures can hardly be assumed and dependency of faults can also be considered as one of the factor for getting irregular fluctuation. In Literature, various software reliability growth models have been developed by considering fault dependency with various debugging time lag functions. But, none of the models have incorporated irregular fluctuation in their fault detection rate. Therefore, in this paper fault dependency based software reliability growth models have been developed by applying an It \u2227o type Stochastic Differential Equations in order to incorporate (i) the irregular fluctuation in the fault detection process due to various uncertainty factor during testing phase and (ii) irregular state of software fault-report phenomena on the bug tracking system. The proposed stochastic differential equation based fault dependency models have been validated using (i) open source software fault count data where software fault-report phenomena on the bug tracking system keep an irregular state and (ii) a fault counting data with minor, major and critical faults. The proposed models have been compared with the existing fault dependency models. Various comparison criteria results for goodness of fit have also been presented in the paper.<\/jats:p>","DOI":"10.1145\/1764810.1764831","type":"journal-article","created":{"date-parts":[[2010,5,18]],"date-time":"2010-05-18T13:46:22Z","timestamp":1274190382000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Measuring reliability growth of software by considering fault dependency, debugging time Lag functions and irregular fluctuation"],"prefix":"10.1145","volume":"35","author":[{"given":"V. B.","family":"Singh","sequence":"first","affiliation":[{"name":"University of Delhi"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P. K.","family":"Kapur","sequence":"additional","affiliation":[{"name":"University of Delhi"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abhishek","family":"Tandon","sequence":"additional","affiliation":[{"name":"University of Delhi"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2010,5,11]]},"reference":[{"key":"e_1_2_1_1_1","unstructured":"Fedora Project sponsored by Red Hat. Online available: http:\/\/fedora.redhat.com\/  Fedora Project sponsored by Red Hat. Online available: http:\/\/fedora.redhat.com\/"},{"key":"e_1_2_1_2_1","volume-title":"Stochastic Differential Equations-Theory and Applications","author":"Arnold","year":"1974","unstructured":"L. Arnold , Stochastic Differential Equations-Theory and Applications , John Wiley & Sons , New York , 1974 . L. Arnold, Stochastic Differential Equations-Theory and Applications, John Wiley & Sons, New York, 1974."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1080\/07408170490507792"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jss.2005.12.006"},{"key":"e_1_2_1_5_1","unstructured":"Oksendal B. \"Stochastic Differential Equations-An Introduction with Applications\" Springer 2003.   Oksendal B. \"Stochastic Differential Equations-An Introduction with Applications\" Springer 2003."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/32.624305"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1155\/2009\/581383"},{"key":"e_1_2_1_8_1","first-page":"850","volume-title":"in the proceedings of Advances in Performance and safety of complex systems (Eds A.K. Verma","author":"Kapur P.K.","year":"2008","unstructured":"Kapur P.K. , Jha P.C. , Gupta Deepali , and Yadav Kalpana \"Identification of Different Stages in the Testing Phase of a Software Reliability Growth Model\" , in the proceedings of Advances in Performance and safety of complex systems (Eds A.K. Verma , P.K. Kapur and S.G. Ghadge) MacMillan India Ltd , 2008 , pp. 850 -- 861 . Kapur P.K., Jha P.C., Gupta Deepali, and Yadav Kalpana \"Identification of Different Stages in the Testing Phase of a Software Reliability Growth Model\", in the proceedings of Advances in Performance and safety of complex systems (Eds A.K. Verma, P.K. Kapur and S.G. Ghadge) MacMillan India Ltd, 2008, pp. 850--861."},{"key":"e_1_2_1_9_1","unstructured":"P.K. Kapur V.B. Singh and Kalpana Yadav \"Software Reliability Growth Model Incorporating Fault Dependency Concept Using a Power Function of Testing Time\" Quality Reliability and Infocom Technology (Eds. P.K. Kapur and A.K. Verma) MacMillan India Ltd. pp. 587--595 2007.  P.K. Kapur V.B. Singh and Kalpana Yadav \"Software Reliability Growth Model Incorporating Fault Dependency Concept Using a Power Function of Testing Time\" Quality Reliability and Infocom Technology (Eds. P.K. Kapur and A.K. Verma) MacMillan India Ltd. pp. 587--595 2007."},{"issue":"3","key":"e_1_2_1_10_1","first-page":"46","article-title":"Fault Dependency Based Software Reliability Growth Modeling with Debugging Time Lag Functions","volume":"10","author":"Kapur V.B.","year":"2007","unstructured":"P.K. Kapur , V.B. Singh and Sameer Anand , \" Fault Dependency Based Software Reliability Growth Modeling with Debugging Time Lag Functions \", Communications in Dependability and Quality Management An International Journal, Serbia , Vol. 10 No. 3 , pp. 46 -- 68 , 2007 . P.K. Kapur, V.B. Singh and Sameer Anand, \"Fault Dependency Based Software Reliability Growth Modeling with Debugging Time Lag Functions\", Communications in Dependability and Quality Management An International Journal, Serbia, Vol. 10 No. 3, pp. 46--68, 2007.","journal-title":"Communications in Dependability and Quality Management An International Journal, Serbia"},{"key":"e_1_2_1_11_1","first-page":"82","article-title":"Anand Sameer Yadavalli V.S.S. and Beichelt Frank \"A Generalised Software Growth Model using Stochastic Differential Equation","author":"Kapur P.K","year":"2007","unstructured":"Kapur P.K . Anand Sameer Yadavalli V.S.S. and Beichelt Frank \"A Generalised Software Growth Model using Stochastic Differential Equation \" Communication in Dependability and Quality Management Belgrade, Serbia , pp. 82 -- 96 , 2007 . Kapur P.K. Anand Sameer Yadavalli V.S.S. and Beichelt Frank \"A Generalised Software Growth Model using Stochastic Differential Equation\" Communication in Dependability and Quality Management Belgrade, Serbia, pp. 82--96, 2007.","journal-title":"Communication in Dependability and Quality Management Belgrade, Serbia"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/TR.2006.879607"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/0026-2714(94)00054-R"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1049\/sej.1992.0030"},{"key":"e_1_2_1_15_1","volume-title":"IIT Mumbai, Dec. 26-28","author":"Kapur P.K.","year":"2001","unstructured":"Kapur , P.K. , Bardhan , A.K. and Shatnawi , O . \" Software Reliability Growth Model With Fault Dependency Using Lag Function\" International Conference on Quality, Reliability and Control , IIT Mumbai, Dec. 26-28 , pp R53-1-7, 2001 . Kapur, P.K., Bardhan, A.K. and Shatnawi, O. \"Software Reliability Growth Model With Fault Dependency Using Lag Function\" International Conference on Quality, Reliability and Control, IIT Mumbai, Dec. 26-28, pp R53-1-7, 2001."},{"key":"e_1_2_1_16_1","volume-title":"Lecture notes in Economics and Mathematical Systems Ed. S. Osaki and Y. Hotoyama","author":"Ohbha M.","year":"1984","unstructured":"Ohbha , M. ( 1984 ) \" Inflection S-shaped Software Reliability Growth Model \", Lecture notes in Economics and Mathematical Systems Ed. S. Osaki and Y. Hotoyama , Springer Verlag , 144--162. Ohbha, M. (1984) \"Inflection S-shaped Software Reliability Growth Model\", Lecture notes in Economics and Mathematical Systems Ed. S. Osaki and Y. Hotoyama, Springer Verlag, 144--162."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/390016.808456"},{"key":"e_1_2_1_18_1","first-page":"185","volume-title":"CA","author":"Schneidewind N.F.","year":"2001","unstructured":"Schneidewind , N.F. \" Modelling the Fault Correction Process \" in the proceedings of the 12thInternational Symposium on Software Reliability Engineering , IEEE Computer Society press: Loss Alarmitcs , CA , 2001 , pp. 185 -- 190 . Schneidewind, N.F. \"Modelling the Fault Correction Process \" in the proceedings of the 12thInternational Symposium on Software Reliability Engineering, IEEE Computer Society press: Loss Alarmitcs, CA, 2001, pp. 185--190."},{"key":"e_1_2_1_19_1","first-page":"186","volume-title":"the proceedings of Fifth International Conference on Quality and Reliability (ICQR 2007","author":"Tamura Y.","year":"2008","unstructured":"Tamura , Y. ; Yamada , S. , ( 2008 ), \" Optimal Version-Upgrade Problem Based on Stochastic Differential Equations for Open Source Software \", In the proceedings of Fifth International Conference on Quality and Reliability (ICQR 2007 ), Chiang Mai, Thailand , pp. 186 -- 191 , 2007. Tamura, Y.; Yamada, S., (2008), \"Optimal Version-Upgrade Problem Based on Stochastic Differential Equations for Open Source Software\", In the proceedings of Fifth International Conference on Quality and Reliability (ICQR 2007), Chiang Mai, Thailand, pp. 186--191, 2007."},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2004.04.034"},{"issue":"1","key":"e_1_2_1_21_1","first-page":"1","article-title":"A Stochastic Differential Equation Model for Software Reliability Assessment and its Goodness of Fit","volume":"4","author":"Yamada S.","year":"2003","unstructured":"Yamada , S. , Nishigaki , A. , Kimura , M. \" A Stochastic Differential Equation Model for Software Reliability Assessment and its Goodness of Fit \" International Journal of Reliability and Applications Vol. 4 , No. 1 , pp. 1 -- 11 , 2003 . Yamada, S., Nishigaki, A., Kimura, M. \"A Stochastic Differential Equation Model for Software Reliability Assessment and its Goodness of Fit\" International Journal of Reliability and Applications Vol. 4, No. 1, pp. 1--11, 2003.","journal-title":"International Journal of Reliability and Applications"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11633-007-0359-y"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1080\/00207720802556245"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.827"},{"key":"e_1_2_1_25_1","volume-title":"Measuring Reliability Growth of Open Source Software\", poster presented in IBM-Indian Research Laboratory Collaborative Academia Research Exchange, held during","author":"Singh V.B.","year":"2009","unstructured":"Singh , V.B. and Kapur , P.K . \" Measuring Reliability Growth of Open Source Software\", poster presented in IBM-Indian Research Laboratory Collaborative Academia Research Exchange, held during October 26, 2009 at IBM India Researchj, New Delhi , India . Singh, V.B. and Kapur, P.K. \"Measuring Reliability Growth of Open Source Software\", poster presented in IBM-Indian Research Laboratory Collaborative Academia Research Exchange, held during October 26, 2009 at IBM India Researchj, New Delhi, India."},{"key":"e_1_2_1_26_1","first-page":"399","article-title":"Instructions Executed Dependent Software Reliability Growth Modeling for Open Source Software by Considering Change-point Published in proceeding of 4th National Conference on Computing for Nation Development-INDIACOM-2010","author":"Singh V.B.","year":"2010","unstructured":"Singh , V.B. , Kapur , P.K and Mashaallah Basirzadeh \" Instructions Executed Dependent Software Reliability Growth Modeling for Open Source Software by Considering Change-point Published in proceeding of 4th National Conference on Computing for Nation Development-INDIACOM-2010 \" Bharatia Vidyapith , pp. 399 -- 404 , New Delhi, 25-26 February , 2010 . Singh, V.B., Kapur, P.K and Mashaallah Basirzadeh \"Instructions Executed Dependent Software Reliability Growth Modeling for Open Source Software by Considering Change-point Published in proceeding of 4th National Conference on Computing for Nation Development-INDIACOM-2010\" Bharatia Vidyapith, pp.399--404, New Delhi, 25-26 February, 2010.","journal-title":"Bharatia Vidyapith"},{"key":"e_1_2_1_27_1","volume-title":"Published in the proceedings of IASTED International Conference on Software Engineering held during","author":"Singh V.B.","year":"2010","unstructured":"Singh , V.B. , Kapur , P.K and Kumar Ravi \"Developing S-shaped Software Reliability Growth Model for Open Source Software\" Published in the proceedings of IASTED International Conference on Software Engineering held during February 16-18, 2010 . Innsbruck, Austria(track 677--103). Singh, V.B., Kapur, P.K and Kumar Ravi \"Developing S-shaped Software Reliability Growth Model for Open Source Software\" Published in the proceedings of IASTED International Conference on Software Engineering held during February 16-18, 2010. Innsbruck, Austria(track 677--103)."}],"container-title":["ACM SIGSOFT Software Engineering Notes"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1764810.1764831","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1764810.1764831","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T11:39:44Z","timestamp":1750246784000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1764810.1764831"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,5,11]]},"references-count":27,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,5,11]]}},"alternative-id":["10.1145\/1764810.1764831"],"URL":"https:\/\/doi.org\/10.1145\/1764810.1764831","relation":{},"ISSN":["0163-5948"],"issn-type":[{"type":"print","value":"0163-5948"}],"subject":[],"published":{"date-parts":[[2010,5,11]]},"assertion":[{"value":"2010-05-11","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}