This article investigates theoretical and practical aspects of one of the urgent metrological issues — the concept of measurement uncertainty for physico-chemical quantities. A hybrid method is developed for selecting and determining the distribution type of a priori information in evaluating type B standard measurement uncertainty, which is a key task in metrological assurance. The relevance of the study lies in the need to improve the reliability of uncertainty assessment under conditions of limited a priori information, as existing approaches often rely on subjective expert judgments, which can lead to inaccurate results. The scientific novelty includes the development of a hybrid method and mathematical models for selecting the distribution of the information base in assessing type B standard uncertainty; the method is based on the combination of the maximum entropy principle and Bayesian theory. The research methodology includes analysis of existing approaches, formalization of metrological criteria for distribution selection, and development of a decision-making algorithm. The adequacy and effectiveness of the method were tested at the Scientific Laboratory of PhysicoChemical Quantities of the “Uzbek National Institute of Metrology” and accredited Doctor of Philosophy in Technical Sciences (PhD), Associate Professor, Department of “Metrology, Technical Regulation, Standardization and Certification”, Faculty of Electronics and Automation Engineering Tashkent State Technical University named after I. Karimov PRINT ISSN 2181-9637 ONLINE ISSN 2181-4317 VOLUME 8 | ISSUE 4 | JULY–AUGUST 2025 ILM-FAN VA INNOVATSION RIVOJLANISH НАУКА И ИННОВАЦИОННОЕ РАЗВИТИЕ SCIENCE AND INNOVATIVE DEVELOPMENT 51 Kelib tushgan/Получено/ Received: 03.06.2025 Qabul qilingan/Принято/ Accepted: 27.06.2025 Nashr etilgan/ Опубликовано/Published: 07.08.2025 05.03.02 – METROLOGY AND METROLOGICAL MAINTENANCE Kirish O‘lchash noaniqligi nazariyasi ko‘p yillik ilmiy munozaralarning matematik asosini tashkil qiladi. Ilmiy adabiyotlarda (Willink, 2025; Singh et al., 2023) mavjud yondashuvlar bo‘lishiga qaramasdan, Bayes nazariyasi va maksimal entropiya usuli bir qator afzilliklarga ega, jumladan (Weise & Woger, 1993): - murakkab nochiziqli tuzatmalar kiritishda; - kichik kvadratlar usuli yoki maksimal ehtimollik usullari yetarli darajada samarador bo‘lmagan hollarda; - kovariatsion matritsadan foydalanish orqali nazariya, ayniqsa, nochiziqli va ko‘p kirish kattaligiga ega matematik modellarda xalqaro tavsiyalar bilan yuqori uyg‘unlik namoyon qiladi. Metrologiya ta’minotida fizik-kimyоviy kattaliklar kuzatuvchanligini ta’minlashda turli taqsimоt qоnunlari tadqiqоtini o‘tkazish ushbu ishning muhim vazifalaridan biri hisоblanadi (Masharipov, 2019; Masharipov & Fattoyev, 2020). “Metrоlоgik kuzatuvсhanlik” tushunchasi metrоlоgiya bо‘yiсha xalqarо lug‘atda “har bir о‘lсhash nоaniqligiga о‘z hissasini qо‘shadigan hujjatlashtirilgan kalibrlash zanjiri оrqali taqqoslash uсhun asоs bо‘ladigan natijaga muvоfiq о‘lсhash natijasining xоssasi”, deb ta’riflangan. Ushbu ta’rifga asosan, kuzatuvсhanlik – о‘lсhash nоaniqligi, kalibrlash ketma-ketligi (tarmog‘i) va о‘lсhanayоtgan kattalik uchun uslubiyatda belgilangan matematik mоdel o‘rtasidagi uzviy bоg‘liqlikni ifodalovchi atama hisoblanadi. Dunyo metrologlari va ilmiy jamoatchilik tomonidan o‘lchash noaniqligi nazariyasida quyidagi ikkita yondashuv o‘zaro qiyosiy solishtirib kelinadi. Аmmo so‘nggi yillarda olib borilgan jahon ilmiy tadqiqot yutuqlari Bayes yondashuvi metrologik tadqiqotlar va o‘lchashlar uchun nisbatan samarali ekanligini tasdiqlamoqda (Ferrero et al., 2019). Ushbu nazariya boshqa matematik nazariyalar singari “matematik nazariya yoki usulning metrologik o‘lchashlar uchun qo‘llangan dalillar ishonchliligi” bilan bog‘liq. Bayes yondashuvidagi asosiy masala – bu aprior axborotlarning o‘lchash maʼlumotlari bilan birgalikda yig‘ilib, axborot fondini tashkil qilgan hollarda ularning yaroqliligini baholashdan iborat. Bayes formulasini o‘lchash jarayonini hisobga olgan holda, quyidagi ko‘rinishda ifodalash mumkin: 𝑃𝑃𝑀𝑀(𝑈𝑈𝑖𝑖) = 𝑃𝑃(𝑈𝑈𝑖𝑖) ∙𝑃𝑃𝑈𝑈𝑈𝑈(𝑀𝑀) ∑ 𝑃𝑃(𝑈𝑈𝑖𝑖) ∙ 𝑁𝑁 𝑖𝑖=1 𝑃𝑃𝑈𝑈𝑈𝑈(𝑀𝑀), 𝑈𝑊𝜆 (1) bu yerda: PM(Ui) – M hodisada sodir bo‘lganidan keyin (aposterior yoki o‘lchash, metrologiya tajribasidan keyingi); i – gipotezaning shartli ehtimolligi; measurement (testing) laboratories compliant with ISO/IEC 17025:2017. The results can be applied in improving the accuracy of measurement uncertainty assessments and refining metrological control procedures, and are required in ISO/ IEC 17025:2017 accredited laboratories, interlaboratory comparison providers under ISO 17043:2023, and international comparisons within the BIPM-KCDB database on calibration and measurement capabilities (CMC). The developed method may be used by scientific centers and laboratories involved in uncertainty evaluation, metrology, and testing. Its implementation will enhance the objectivity of uncertainty evaluation, improve the reliability of expanded uncertainty, and reduce risks associated with type B standard uncertainty.
| Mualliflar | Shodlik Masharipovich Masharipov |
|---|---|
| Jurnal | Илм-фан ва инновацион ривожланиш |
| Nashr sanasi | 2025-08-07 |
| Jild | 8 |
| Son | 4 |
| Betlar | 49-73 |
| Til | en |
| DOI | 10.36522/2181-4317.2025.4.5 |
DOI: 10.36522/2181-4317.2025.4.5 · Maqolaning asl sahifasi
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