{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,22]],"date-time":"2026-05-22T14:08:41Z","timestamp":1779458921285,"version":"3.53.1"},"reference-count":43,"publisher":"SAGE Publications","issue":"9","license":[{"start":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T00:00:00Z","timestamp":1757376000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Transactions of the Institute of Measurement and Control"],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:p>\n                    This paper explores a statistical approach to propose a new monitoring framework (control chart) for the Modified Weibull model\u2019s (\n                    <jats:italic toggle=\"yes\">MWM<\/jats:italic>\n                    ) failure rate function (\n                    <jats:italic toggle=\"yes\">FRF<\/jats:italic>\n                    ), based on type I-censored data under Step-Stress accelerated life test (\n                    <jats:italic toggle=\"yes\">SSALT<\/jats:italic>\n                    ) (MISS will be used hereafter). Specifically, we focus on\n                    <jats:italic toggle=\"yes\">SSALT<\/jats:italic>\n                    model under type I censoring, where testing stress increases in steps. This scheme utilizes\n                    <jats:italic toggle=\"yes\">FRF<\/jats:italic>\n                    of the\n                    <jats:italic toggle=\"yes\">MWM<\/jats:italic>\n                    and a Shewhart-type control chart approach. Special cases of the proposed scheme can be obtained for other specific distributions, including Weibull, generalized exponential, Rayleigh, and exponential, under type I censoring. To develop the Shewhart-type scheme, the article first derives the maximum likelihood estimators (\n                    <jats:italic toggle=\"yes\">MLE<\/jats:italic>\n                    ) for the\n                    <jats:italic toggle=\"yes\">MWM<\/jats:italic>\n                    under type I censoring. It then discusses the asymptotic properties of these estimators. An in-depth simulation study evaluates the in-control (\n                    <jats:italic toggle=\"yes\">IC<\/jats:italic>\n                    ) performance of the scheme. The study analyzes average run length (\n                    <jats:italic toggle=\"yes\">ARL<\/jats:italic>\n                    ) for various combinations of model parameters. The study also investigates the out-of-control (\n                    <jats:italic toggle=\"yes\">OOC<\/jats:italic>\n                    ) performance for different parameter shifts in the chosen density function. Finally, we illustrate the application of the proposed monitoring scheme with a real-world data example from industrial sector, demonstrating how the obtained results can be used in practice. The comparison reveals that the proposed schemes effectively detect\n                    <jats:italic toggle=\"yes\">OOC<\/jats:italic>\n                    signals, both in terms of frequency and speed.\n                  <\/jats:p>","DOI":"10.1177\/01423312251352878","type":"journal-article","created":{"date-parts":[[2025,9,9]],"date-time":"2025-09-09T16:36:38Z","timestamp":1757435798000},"page":"1977-1991","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Efficient failure detection in industrial applications: Enhanced monitoring framework for modified Weibull model"],"prefix":"10.1177","volume":"48","author":[{"given":"Muhammad","family":"Ikram","sequence":"first","affiliation":[{"name":"Department of Statistics, Government Graduate College Jamia Muhammadi Sharif, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Muhammad","family":"Wasim Amir","sequence":"additional","affiliation":[{"name":"Department of Statistics, Government Associate College, Miani, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hafiz Zafar","family":"Nazir","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Sargodha, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Noureen","family":"Akhtar","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of Sargodha, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4203-7798","authenticated-orcid":false,"given":"Qasim","family":"Ramzan","sequence":"additional","affiliation":[{"name":"Department of Statistics, Government Graduate College, Jauharabad, Pakistan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2025,9,9]]},"reference":[{"key":"e_1_3_2_2_1","doi-asserted-by":"publisher","DOI":"10.1109\/TR.1987.5222310"},{"key":"e_1_3_2_3_1","doi-asserted-by":"publisher","DOI":"10.3390\/math10162901"},{"key":"e_1_3_2_4_1","doi-asserted-by":"publisher","DOI":"10.6339\/JDS.202010_18(4).0009"},{"key":"e_1_3_2_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/qre.2790"},{"key":"e_1_3_2_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/24.159807"},{"key":"e_1_3_2_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1334-5"},{"key":"e_1_3_2_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-7152(01)00104-3"},{"key":"e_1_3_2_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2012.03.025"},{"key":"e_1_3_2_10_1","doi-asserted-by":"publisher","DOI":"10.1080\/00031305.1995.10476150"},{"key":"e_1_3_2_11_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610920902866966"},{"key":"e_1_3_2_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.measurement.2024.114191"},{"key":"e_1_3_2_13_1","unstructured":"Cheng Y Elsayed E (2013) Accelerated life testing model for a generalized Birnbaum-Saunders distribution. 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