Estimation of system reliability using a semiparametric model

An important problem in reliability engineering is to predict the failure rate, that is, the frequency with which an engineered system or component fails. This paper presents a new method of estimating failure rate using a semiparametric model with Gaussian process smoothing. The method is able to provide accurate estimation based on historical data and it does not make strong a priori assumptions of failure rate pattern (e.g., constant or monotonic). Our experiments of applying this method in power system failure data compared with other models show its efficacy and accuracy. This method can be used in estimating reliability for many other systems, such as software systems or components

Estimation of System Reliability Using a Semiparametric Model

An important problem in reliability engineering is to predict the failure rate, that is, the frequency with which an engineered system or component fails. This paper presents a new method of estimating failure rate using a semiparametric model with Gaussian process smoothing. The method is able to provide accurate estimation based on historical data and it does not make strong a priori assumptions of failure rate pattern (e.g., constant or monotonic). Our experiments of applying this method in power system failure data compared with other models show its efficacy and accuracy. This method can be used in estimating reliability for many other systems, such as software systems or components

A Study to Determine if Economically Disadvantaged Adults Improved Their Reading and Math Scores after Utilizing Plato

The purpose of this study was to ascertain the following questions: 1. Did the clients of the Learning center increase their scores in reading and math after completion of the PLATO program? 2. What percentage of students who completed the PLATO program were placed into either employment training program or directly into employment? 3. What percentage of students dropped out of the program after their start with the PLATO system? 4. Were the grade equivalencies (4.0 to 5.9) too narrow to allow maximum participation in the PLATO program by the clients of JTPA

Continuous Methods for Elliptic Inverse Problems

Numerous mathematical models in applied and industrial mathematics take the form of a partial differential equation involving certain variable coefficients. These coefficients are known and they often describe some physical properties of the model. The direct problem in this context is to solve the partial differential equation. By contrast, an inverse problem asks for the identification of the variable coefficient when a certain measurement of a solution of the partial differential equation is available. A commonly used approach to inverse problems is to solve an optimization problem whose solution is an approximation of the sought coefficient. Such optimization problems are typically solved by discrete iterative schemes. It turns out that most known iterative schemes have their continuous counterparts given in terms of dynamical systems. However, such differential equations are usually solved by specific differential equation solvers. The primary objective of this thesis is to test the feasibility of differential equations based solvers for solving elliptic inverse problems. We will use differential equation solvers such as Euler\u27s Method, Trapezoidal Method, Runge-Kutta Method and Adams-Bashforth Method. In addition, these solvers will also be compared to built-in MATLAB ODE solvers. The performance and accuracy of these methods to solve inverse problems will be thoroughly discussed

Semiparametric Estimation of a Gaptime-Associated Hazard Function

This dissertation proposes a suite of novel Bayesian semiparametric estimators for a proportional hazard function associated with the gaptimes, or inter-arrival times, of a counting process in survival analysis. The Cox model is applied and extended in order to identify the subsequent effect of an event on future events in a system with renewal. The estimators may also be applied, without changes, to model the effect of a point treatment on subsequent events, as well as the effect of an event on subsequent events in neighboring subjects. These Bayesian semiparametric estimators are used to analyze the survival and reliability of the New York City electric grid. In particular, the phenomenon of "infant mortality," whereby electrical supply units are prone to immediate recurrence of failure, is flexibly quantified as a period of increased risk. In this setting, the Cox model removes the significant confounding effect of seasonality. Without this correction, infant mortality would be misestimated due to the exogenously increased failure rate during summer months and times of high demand. The structural assumptions of the Bayesian estimators allow the use and interpretation of sparse event data without the rigid constraints of standard parametric models used in reliability studies

Almost primes in almost all short intervals

Let E-k be the set of positive integers having exactly k prime factors. We show that almost all intervals [x, x + log(1+epsilon) x] contain E-3 numbers, and almost all intervals [x, x + log(3.51) x] contain E-2 numbers. By this we mean that there are only 0(X) integers 1 infinity

Exploring the literacy related behaviours and feelings of pupils eligible for free school meals in relation to their use of, and access to, school libraries

Although it has been argued that school libraries are important for supporting the reading engagement of pupils who receive free school meals, to date there has been little analysis of the extent to which use of school library spaces is related to these pupils' reading behaviors. We analyzed data from 6,264 UK children and young people entitled to FSM who completed the 2019 National Literacy Trust Annual Literacy Survey, to understand the extent to which these pupils' engagement with reading and writing is related to access to or use of their school library. We found their enjoyment of both reading and writing, their confidence in their own abilities, and the frequency with which they read or wrote for pleasure outside of school was significantly higher for those pupils eligible for FSM who used their school libraries relative to both those who did not, and those who had no school library. Consistent with this, children eligible for FSM who used their school library engaged with a greater diversity of reading material and writing than those who were not school library users. We argue that school library provision appears to be a significant resource in supporting low income children's engagement with self-motivated literacy practices