Accurate Reliability Estimation Research Articles

Direct Methods for Sparse Matrices

<p>The mathematical models of many practical problems lead to systems of linear algebraic equations where the coefficient matrix is large and sparse. Typical examples are the solutions of partial differential equations by finite difference or finite element methods but many other applications could be mentioned.</p><p>When there is a large proportion of zeros in the coefficient matrix then it is fairly obvious that we do not want to store all those zeros in the computer, but it might not be quite so obvious how to get around it. We first describe storage techniques which are convenient to use with direct solution methods, and we then show how a very efficient computational scheme can be based on Gaussian elimination and iterative refinement.</p><p>A serious problem in the storage and handling of sparse matrices is the appearance of fill-ins, i.e. new elements which are created in the process of generating zeros below the diagonal. Many of these new elements tend to be smaller than the original matrix elements, and if they are smaller than a quantity which we shall call the drop tolerance we simply ignore them. In this way we may preserve the sparsity quite well but we probably introduce rather large errors in the LU decomposition to the effect that the solution becomes unacceptable. In order to retrieve the accuracy we use iterative refinement and we show theoreticaly and with practical experiments that it is ideal for the purpose.</p><p>Altogether, the combination of Gaussian elimination, a large drop tolerance, and iterative refinement gives a very efficient and competitive computational scheme for sparse problems. For dense matrices iterative refinement will always require more storage and computation time, and the extra accuracy it yields may not be enough to justify it. For sparse problems, however, iterative refinement combined with a large drop tolerance will in most cases give very accurate results and reliable error estimates with less storage and computation time.</p>

Reliability and validity of self-report and observers' estimates of relative weight

Two studies were done to assess the reliability and validity of observers' ratings and self-reports of relative weight in order to establish procedures for naturalistic studies of obesity. In Study I, observers rated relative weight of college students on a five point rating scale. Self-reports of height and weight of each subject were also obtained. Both the observers' ratings and the self-reports were highly correlated with the measured height and weight data, but self-report data allowed for a more accurate classification of subjects into relative weight categories. Reliability and validity of the observer estimates and the self-reports were calculated using both correlational and percent agreement procedures. Percent agreement provided a more stringent measure of reliability than did the correlational procedures. Study II confirmed the results of Study I for an older, heavier population. Self-report was again superior to observational procedures for weight determination, and percent agreement provided more accurate estimates of reliability and validity than did the correlational techniques.

Refined hypocenters and accurate reliability estimates

Abstract A new method of correcting station arrival times for systematic source and station effects has been developed. The method yields source-region/station time (SRST) corrections which have a simple spatial variation and which are valid, in terms of yielding accurate focal depths and relative epicenters, over large areas. The method has been applied to over 200 earthquakes ranging in depth from about 10 to 650 km in the Kurile-Kamchatka-Okhotsk region. Resulting corrections are uniformly valid throughout an area of approximately one million square kilometers. Full utilization of the SRST corrections for the 25 close-in and 149 teleseismic stations was achieved by weighting each station's contribution to the computed hypocenters. The 95 per cent limits on the depth uncertainty cover the pP depth the appropriate percentage of the time regardless of the number or geometry of the stations in the observing network. The SRTS's for the close-in stations describe their arrival-time variations over the entire are structure and thus may be used in model studies to determine the structure and the epicenter bias.

Problems in Sensitivity Testing of "One Shot" Electro-Explosive Devices

Accurate estimates of aerospace electro-explosive device reliability can be made only by properly employed techniques of sensitivity testing. Improperly applied, sensitivity testing can produce misleading data which may compromise mission success or result in rejection of reliable units. This paper analyzes techniques used to estimate the reliability of "one shot" electro-explosive devices, discusses current practices which can produce suspect data, and suggests remedial action which will lead to accurate and dependable methods of reliability estimation.