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Yamada's two stage fault removal modeling framework has been extensively worked in the past; wherein last decade has also seen the impact and importance of modeling related to imperfect debugging phenomenon. But, a major limitation of Yamada's two stage modeling framework has been its limitation to capture the time dependent nature of faults in the software. In the present proposition, an attempt has been made to reach to this requirement by making use of the approximation method as a solution methodology. The employment of this alternative solution methodology yields solutions to all the three possible situations; that is, pure error generation, exponential form and linear form of error generation. In order to facilitate the analysis, proposed cases have been verified on real life data sets and results obtained are quiet encouraging.<\/jats:p>","DOI":"10.1002\/qre.70021","type":"journal-article","created":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T06:23:33Z","timestamp":1752560613000},"page":"3244-3257","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Utility of Approximation Methods for Analyzing Software Error Detection Phenomenon"],"prefix":"10.1002","volume":"41","author":[{"given":"Adarsh","family":"Anand","sequence":"first","affiliation":[{"name":"Department of Operational Research University of Delhi  Delhi India"}]},{"given":"Shigeru","family":"Yamada","sequence":"additional","affiliation":[{"name":"Tottori University  Tottori Japan"}]},{"given":"Yoshinobu","family":"Tamura","sequence":"additional","affiliation":[{"name":"Graduate School of Sciences and Technology for Innovation Yamaguchi University  Yamaguchi Japan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9772-0490","authenticated-orcid":false,"given":"Asha","family":"Yadav","sequence":"additional","affiliation":[{"name":"Department of Operational Research University of Delhi  Delhi India"}]}],"member":"311","published-online":{"date-parts":[[2025,7,14]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.33889\/IJMEMS.2020.5.2.017"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.1997"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.2754"},{"key":"e_1_2_9_5_1","unstructured":"https:\/\/archive.nytimes.com\/dealbook.nytimes.com\/2012\/08\/02\/knight\u2010capital\u2010says\u2010trading\u2010mishap\u2010cost\u2010it\u2010440\u2010million\/."},{"key":"e_1_2_9_6_1","unstructured":"https:\/\/www.seattletimes.com\/business\/boeing\u2010aerospace\/what\u2010led\u2010to\u2010boeings\u2010737\u2010max\u2010crisis\u2010a\u2010qa\/."},{"key":"e_1_2_9_7_1","unstructured":"https:\/\/www.csoonline.com\/article\/563017\/wannacry\u2010explained\u2010a\u2010perfect\u2010ransomware\u2010storm.html."},{"key":"e_1_2_9_8_1","unstructured":"https:\/\/www.nytimes.com\/2018\/03\/19\/technology\/uber\u2010driverless\u2010fatality.html#:~:text=How%20a%20Self%2DDriving%20Uber offers%20clues%20about%20what%20happened."},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.33889\/IJMEMS.2021.6.4.061"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.33889\/IJMEMS.2017.2.3-012"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-85729-204-9"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1109\/TR.1979.5220566"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/TR.1983.5221735"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1109\/TSE.1985.232177"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0034288"},{"key":"e_1_2_9_16_1","doi-asserted-by":"publisher","DOI":"10.1049\/sej.1992.0030"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610929308831053"},{"key":"e_1_2_9_18_1","doi-asserted-by":"crossref","unstructured":"Y. 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