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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1981

Software models: A Bayesian approach to parameter estimation in the Jelenski-Moranda software reliability model

Maximum likelihood estimation procedures for the Jelinski-Moranda software reliability model often give misleading answers. A reparameterization and a Bayesian analysis eliminate some of the problems incurred by MLE methods and often give better predictions on sets of real and simulated data. Practical difficulties in estimating the initial number of errors N and the failure rate of each error phi by the method of maximum likelihood are: N, the MLE of N, is occasionally infinite (i.e., the routines for calculating N and phi do not converge). It is shown that N is finite sub i only if the regression line of the interevent times t sub i vs. i has positive slope. A serious problem is that often N approximates n, the sample size, and sometimes N = n. Thus the MLE predicts that the program is perfect even when it is far from being so. Only when almost all failures have been removed can N and phi be trusted near the end of debugging.

Littlewood, B.↗

NASA NTRS1983

A Bayesian modification to the Jelinski-Moranda software reliability growth model

The Jelinski-Moranda (JM) model for software reliability was examined. It is suggested that a major reason for the poor results given by this model is the poor performance of the maximum likelihood method (ML) of parameter estimation. A reparameterization and Bayesian analysis, involving a slight modelling change, are proposed. It is shown that this new Bayesian-Jelinski-Moranda model (BJM) is mathematically quite tractable, and several metrics of interest to practitioners are obtained. The BJM and JM models are compared by using several sets of real software failure data collected and in all cases the BJM model gives superior reliability predictions. A change in the assumption which underlay both models to present the debugging process more accurately is discussed.

Littlewood, B.↗

NASA NTRS1983

Formulation of a practical algorithm for parameter estimation with process and measurement noise

A new formulation is proposed for the problem of parameter estimation in dynamic systems with both process and measurement noise. The formulation applies to continuous-time state space system models with discrete-time measurements. Previous formulations of this problem encountered several theoretical and practical difficulties which are overcome by the new formulation. The most important element of the new formulation is a reparameterization of the unknown noise covariances. A computer program that implements the new formulation is available.

Maine, R. E.↗

NASA NTRS1986

Transformation of two and three-dimensional regions by elliptic systems

A natural grid is defined on any parameterized curve or surface by selecting an equi-spaced set of parameter values. Redistributing the grid points can be accomplished by defining a new parameterization. Reparameterization techniques are introduced and applied in the construction of computational grids.

Mastin, C. W.↗

NASA NTRS1987

Gauge invariant quantum cosmology

The study of boundary conditions, the Hamiltonian constraint, reparameterization-invariance, and quantum dynamics, is presently approached by means of the path-integral quantization of minisuperspace models. The separation of the wave functions for expansion and contraction by the Feynman boundary conditions is such that there can be no interference between them. This is implemented by the choice of a contour in the complex plane, in order to define the phase of the square-root Arnowitt, Deser, and Misner (1960) Hamiltonian for expansion, collapse, and the classically forbidden region.

Berger, Beverly K.↗

NASA NTRS1994

Approximate analysis for repeated eigenvalue problems with applications to controls-structure integrated design

A method for eigenvalue and eigenvector approximate analysis for the case of repeated eigenvalues with distinct first derivatives is presented. The approximate analysis method developed involves a reparameterization of the multivariable structural eigenvalue problem in terms of a single positive-valued parameter. The resulting equations yield first-order approximations to changes in the eigenvalues and the eigenvectors associated with the repeated eigenvalue problem. This work also presents a numerical technique that facilitates the definition of an eigenvector derivative for the case of repeated eigenvalues with repeated eigenvalue derivatives (of all orders). Examples are given which demonstrate the application of such equations for sensitivity and approximate analysis. Emphasis is placed on the application of sensitivity analysis to large-scale structural and controls-structures optimization problems.

Kenny, Sean P.↗

NASA NTRS1995

Pseudoclassical description of the Dirac Oscillator

In this paper we discuss the Dirac Oscillator wave equation in terms of pseudoclassical language, using Grassmann variables to describe the internal degrees of freedom of the oscillator. Regarding the original wave equation as a classical constraint, we use the theory of constrained systems, to develop a reparameterization invariant lagrangian, which is the pseudoclassical equivalent of the quantum case. The consistency of the Hamiltonian formalism and the quantization procedure are also analyzed.

Delsolmesa, Antonio↗