20.500.12556/RUL-169327 Finite mixture models a key tool for reliability analyses As system complexity increases, accurately capturing true system reliability becomes increasingly challenging. Rather than relying on exact analytical solutions, it is often more practical to use approximations based on observed time-to-failure data. Finite mixture models provide a flexible framework for approximating arbitrary probability density functions and are well suited for reliability modelling. A critical factor in achieving accurate approximations is the choice of parameter estimation algorithm. The REBMIX&EM algorithm, implemented in the rebmix R package, generally performs well but struggles when components of the finite mixture model overlap. To address this issue, we revisit key steps of the REBMIX algorithm and propose improvements. With these improvements, we derive parameter estimators for finite mixture models based on three parametric families commonly applied in reliability analysis: lognormal, gamma, and Weibull. We conduct a comprehensive simulation study across four system configurations, using lognormal, gamma, and Weibull distributions with varying parameters as system component time-to-failure distributions. Performance is benchmarked against five widely used R packages for finite mixture modelling. The results confirm that our proposal improves both estimation accuracy and computational efficiency, consistently outperforming existing packages. We also demonstrate that finite mixture models can approximate analytical reliability solutions with fewer components than the actual number of system components. Our proposals are also validated using a practical example from Backblaze hard drive data. All improvements are included in the open-source rebmix R package, with complete source code provided to support the broader adoption of the R programming language in reliability analysis. system reliability mixture model numerical modelling density estimation parameter estimation EM algorithm REBIX algorithm zanesljivost sistema mešani model numerično modeliranje ocena gostote porazdelitve verjetnosti ocena parametrov EM algoritem REBMIX algoritem true false true Angleški jezik Slovenski jezik Članek v reviji 2025-05-23 10:21:31 2025-05-23 10:21:39 2025-12-22 14:31:27 0000-00-00 00:00:00 2025 0 0 24 str. issue 10, art. 1605 Vol. 13 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 621:51 2227-7390 10.3390/math13101605 236840707 RAZ_Nagode_Marko_2025.pdf RAZ_Nagode_Marko_2025.pdf 1 13253B61CC929020AA29BAC344DBEC5A 58de104b556092babef014378e21defd2e18e9cad2e42bf1c28d39a659885c95 e02146e5-37ad-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=210620 https://www.mdpi.com/2227-7390/13/10/1605 1 b27c3337-37ad-11f0-b232-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=210619 Fakulteta za strojništvo 0 0 0