Exact Failure Frequency Calculations for Extended Systems

This paper shows how the steady-state availability and failure frequency can be calculated in a single pass for very large systems, when the availability is expressed as a product of matrices. We apply the general procedure to $k$-out-of-$n$:G and linear consecutive $k$-out-of-$n$:F systems, and to a simple ladder network in which each edge and node may fail. We also give the associated generating functions when the components have identical availabilities and failure rates. For large systems, the failure rate of the whole system is asymptotically proportional to its size. This paves the way to ready-to-use formulae for various architectures, as well as proof that the differential operator approach to failure frequency calculations is very useful and straightforward

Reliability and Failure Probability Functions of the m-Consecutive-k-out-of-n: F Linear and Circular Systems

في هذه الورقة ، تم دراسة الانواع الخطية والدائرية  للنظام m لعدد k التتابعي  من n من المكونات، حيث تم تصنيف عناصر فضاء عينة فشل مكونات النظام الى تجمعين من التصنيفات، الأول للحالات التي يكون فيها النظام في حالة العمل والآخر للحالات التي يكون فيها النظام وصل لمرحلة الفشل، ومن ثم  تم استخدام هذه التصنيفات لحساب دالة كثافة احتمال موثوقية النظام ودالة كثافة احتمال فشل النظام، وفي النهاية تم اقتراح خوارزمية رياضية لحساب ذلك، تتضمن عمليات التصنيفات هذه وكيفية حساب الدالتين المذكورين من خلال عملية التصنيف.The m-consecutive-k-out-of-n: F linear and circular system consists of n sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least m non-overlapping runs of consecutive-k failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly m-consecutive-k-out-of-n: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided

Marker effects and examination reliability: a comparative exploration from the perspectives of generalizability theory, Rasch modelling and multilevel modelling

This study looked at how three different analysis methods could help us to understand rater effects on exam reliability. The techniques we looked at were: generalizability theory (G-theory) item response theory (IRT): in particular the Many-Facets Partial Credit Rasch Model (MFRM) multilevel modelling (MLM) We used data from AS component papers in geography and psychology for 2009, 2010 and 2011 from Edexcel.</p

Influence of snow properties on directional surface reflectance in Antarctica

The significance of the polar regions for the Earth’s climate system and their observed amplified response to climate change indicate the necessity for high temporal and spatial coverage for the monitoring of the reflective properties of snow surfaces and their influencing factors. Therefore, the specific surface area (SSA, as a proxy for snow grain size) and the hemispherical directional reflectance factor (HDRF) of snow were measured for a 2-month period in central Antarctica (Kohnen research station) during austral summer 2013/14. The SSA data were retrieved on the basis of ground-based spectral surface albedo measurements collected by the COmpact RAdiation measurement System (CORAS) and airborne observations with the Spectral Modular Airborne Radiation measurement sysTem (SMART). The snow grain size and pollution amount (SGSP) algorithm, originally developed to analyze spaceborne reflectance measurements by the MODerate Resolution Imaging Spectroradiometer (MODIS), was modified in order to reduce the impact of the solar zenith angle on the retrieval results and to cover measurements in overcast conditions. Spectral ratios of surface albedo at 1280 and 1100 nm wavelength were used to reduce the retrieval uncertainty. The retrieval was applied to the ground-based and airborne observations and validated against optical in situ observations of SSA utilizing an IceCube device. The SSA retrieved from CORAS observations varied between 29 and 96 m2 kg-1. Snowfall events caused distinct relative maxima of the SSA which were followed by a gradual decrease in SSA due to snow metamorphism and wind-induced transport of freshly fallen ice crystals. The ability of the modified algorithm to include measurements in overcast conditions improved the data coverage, in particular at times when precipitation events occurred and the SSA changed quickly. SSA retrieved from measurements with CORAS and MODIS agree with the in situ observations within the ranges given by the measurement uncertainties. However, SSA retrieved from the airborne SMART data underestimated the ground-based results. The spatial variability of SSA in Dronning Maud Land ranged in the same order of magnitude as the temporal variability revealing differences between coastal areas and regions in interior Antarctica. The validation presented in this study provided an unique test bed for retrievals of SSA under Antarctic conditions where in situ data are scarce and can be used for testing prognostic snowpack models in Antarctic conditions. The HDRF of snow was derived from airborne measurements of a digital 180° fish-eye camera for a variety of conditions with different surface roughness, snow grain size, and solar zenith angle. The camera provides radiance measurements with high angular resolution utilizing detailed radiometric and geometric calibrations. The comparison between smooth and rough surfaces (sastrugi) showed significant differences in the HDRF of snow, which are superimposed on the diurnal cycle. By inverting a semi-empirical kernel-driven model for the bidirectional reflectance distribution function (BRDF), the snow HDRF was parameterized with respect to surface roughness, snow grain size, and solar zenith angle. This allows a direct comparison of the HDRF measurements with BRDF products from satellite remote sensing

Connected-X-out-of-(m; n):F システムの信頼度評価と最適設計に関する研究

首都大学東

Determinants of presidential longevity in higher education: estimating a structural model from a dataset derived from publicly available data

Long-term presidents are important to institutions of higher education, yet, studies on presidential tenure in higher education have reported declining tenures for several decades. The studies reporting these declines primarily used surveys of sitting presidents, computed tenure based on years completed to date, and none, to date, have employed structural equation modeling (SEM). This study used a convergent mixed methods design to create a dataset (n=202) on research university presidents from publicly available data and used SEM to test a structural model of presidential longevity. The findings suggest that publicly available data is a viable data source for studies on presidential longevity and that SEM can be applied to higher education research given a large sample and correctly specified models. The study also found that research university presidents’ tenure has remained stable over several decades, demonstrating the importance of using presidents’ full tenure, rather than completed tenure of sitting presidents as a measure of presidential longevity

The Gaussian graphical model in cross-sectional and time-series data

We discuss the Gaussian graphical model (GGM; an undirected network of partial correlation coefficients) and detail its utility as an exploratory data analysis tool. The GGM shows which variables predict one-another, allows for sparse modeling of covariance structures, and may highlight potential causal relationships between observed variables. We describe the utility in 3 kinds of psychological datasets: datasets in which consecutive cases are assumed independent (e.g., cross-sectional data), temporally ordered datasets (e.g., n = 1 time series), and a mixture of the 2 (e.g., n > 1 time series). In time-series analysis, the GGM can be used to model the residual structure of a vector-autoregression analysis (VAR), also termed graphical VAR. Two network models can then be obtained: a temporal network and a contemporaneous network. When analyzing data from multiple subjects, a GGM can also be formed on the covariance structure of stationary means---the between-subjects network. We discuss the interpretation of these models and propose estimation methods to obtain these networks, which we implement in the R packages graphicalVAR and mlVAR. The methods are showcased in two empirical examples, and simulation studies on these methods are included in the supplementary materials.Comment: Accepted pending revision in Multivariate Behavioral Researc