{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T12:12:28Z","timestamp":1773922348441,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2019,4,10]],"date-time":"2019-04-10T00:00:00Z","timestamp":1554854400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2018R1D1A1B07045734"],"award-info":[{"award-number":["2018R1D1A1B07045734"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2018R1A6A3A03011833"],"award-info":[{"award-number":["2018R1A6A3A03011833"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The non-homogeneous Poisson process (NHPP) software has a crucial role in computer systems. Furthermore, the software is used in various environments. It was developed and tested in a controlled environment, while real-world operating environments may be different. Accordingly, the uncertainty of the operating environment must be considered. Moreover, predicting software failures is commonly an important part of study, not only for software developers, but also for companies and research institutes. Software reliability model can measure and predict the number of software failures, software failure intervals, software reliability, and failure rates. In this paper, we propose a new model with an inflection factor of the fault detection rate function, considering the uncertainty of operating environments and analyzing how the predicted value of the proposed new model is different than the other models. We compare the proposed model with several existing NHPP software reliability models using real software failure datasets based on ten criteria. The results show that the proposed new model has significantly better goodness-of-fit and predictability than the other models.<\/jats:p>","DOI":"10.3390\/sym11040521","type":"journal-article","created":{"date-parts":[[2019,4,10]],"date-time":"2019-04-10T11:25:08Z","timestamp":1554895508000},"page":"521","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["NHPP Software Reliability Model with Inflection Factor of the Fault Detection Rate Considering the Uncertainty of Software Operating Environments and Predictive Analysis"],"prefix":"10.3390","volume":"11","author":[{"given":"Kwang Yoon","family":"Song","sequence":"first","affiliation":[{"name":"Department of Industrial and Systems Engineering, Rutgers University, 96 Frelinghuysen Road, Piscataway, NJ 08855-8018, USA"}]},{"given":"In Hong","family":"Chang","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Statistics, Chosun University, 309 Pilmun-daero Dong-gu, Gwangju 61452, Korea"}]},{"given":"Hoang","family":"Pham","sequence":"additional","affiliation":[{"name":"Department of Industrial and Systems Engineering, Rutgers University, 96 Frelinghuysen Road, Piscataway, NJ 08855-8018, USA"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1109\/TR.1979.5220566","article-title":"Time-dependent error-detection rate model for software reliability and other performance measures","volume":"28","author":"Goel","year":"1979","journal-title":"IEEE Trans. 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