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The reliability assessment of the project duration is essential for successful project management; this has prompted the development of various methods to assess whether a project will be completed within the target duration. In this study, an efficient and effective method for assessing the reliability of project duration based on the method of moments is proposed, which utilizes bivariate-dimension reduction technology and the third-moment reliability index. The proposed method can avoid the extensive calculations of various factors in the commonly used methods: the correlation coefficients between each pair of paths and the joint failure probability of each pair of representative paths. From two numerical examples, it can be concluded that the proposed method can obtain almost the same results as Monte Carlo simulations with less calculation. [ABSTRACT FROM AUTHOR]

The Hannuoba basalt, located in the northern margin of the North China Craton, is a typical intra-continental basalt with ocean island basalt-like geochemical features and has been extensively studied. However, its origin and deep processes, such as magma mixing and crystallization conditions, are still unclear. To further understand the mechanisms leading to the compositional heterogeneity and magmatic processes of Hannuoba basalt at crustal and/or mantle depth, in situ major element, trace element, and 87Sr/86Sr compositional heterogeneity of four representative plagioclase crystals in three Hannuoba tholeiite samples, as well as whole-rock major and trace element data, are reported. According to the petrographic characteristics, the basalts are divided into fine-grained and coarse-grained groups. The anorthite content in plagioclase of samples varies in a small range (56–64%), but the content of trace elements in plagioclase from the coarse-grained samples is generally higher than that of the fine-grained samples. Clinopyroxene-melt equilibrium thermobarometer and plagioclase-clinopyroxene magnesium and rare earth element exchange thermometers show that the magma for the two types of basalt was stored and crystallized at a similar depth, and crystallized within a 20 °C (fine-grained basalt) and 50 °C (coarse-grained basalt) temperature window, which may be a reason for the grain size diferences between the two types of basalts. We found that 87Sr/86Sr of all the studied plagioclase crystals varied from 0.70333 ± 0.00018 (2SE) to 0.70556 ± 0.00031 (2SE), a much large range than the whole rock of Hannuoba basalts reported previously and consistent with that of Cenozoic basalts in North China. Therefore, at least two kinds of melts with significant differences in isotope and minor heterogeneity in major and trace elements are injected into each magma plumbing system. The content of trace elements in the Hanuoba tholeiite is between the Hanuoba alkaline basalt and the lower crust, which may be explained by the mixing of the alkaline basalt and the lower crust, but the low 87Sr/86Sr (<0.704) characteristics of plagioclase cannot be derived from alkaline basalts, because trace element abundances in the plagioclase are not in equilibrium with the alkaline basalt. Therefore, we believe that the compositional heterogeneity of Hannuoba tholeiitic basalt is caused by the mixing of heterogeneous lower crust rather than different mantle-derived melts. In turn this indicates that the contribution of the continental lower crust to the continental basalt is more complicated than previously recognized. [ABSTRACT FROM AUTHOR]