Accelerated Degradation Models for Failure Based on Geometric Brownian Motion and Gamma Processes

Based on a generalized cumulative damage approach with a stochastic process describing degradation, new accelerated life test models are presented in which both observed failures and degradation measures can be considered for parametric inference of system lifetime. Incorporating an accelerated test variable, we provide several new accelerated degradation models for failure based on the geometric Brownian motion or gamma process. It is shown that in most cases, our models for failure can be approximated closely by accelerated test versions of Birnbaum–Saunders and inverse Gaussian distributions. Estimation of model parameters and a model selection procedure are discussed, and two illustrative examples using real data for carbon-film resistors and fatigue crack size are presented.     

Educating Social Workers for Health Care’s Brave New World

A transforming health care system challenges educators to formulate curriculum that is relevant and anticipates evolving expectations and demands. This article reviews key features of the changing health care landscape, describes a Centers for Disease Control funded prototypical social work practice model designed to fit the contours of that landscape, and suggests five fundamental principles to guide successful adaptation of social work health care practice and educational preparation. Curricular implications of these principles are discussed.     

Nonparametric density estimation from censored data

Nonparametric estimation of the probability density function f° of a lifetime distribution based on arbitrarily right-censor-ed observations from f° has been studied extensively in recent years. In this paper the density estimators from censored data that have been obtained to date are outlined. Histogram, kernel-type, maximum likelihood, series-type, and Bayesian nonparametric estimators are included. Since estimation of the hazard rate function can be considered as giving a density estimate, all known results concerning nonparametric hazard rate estimation from censored samples are also briefly mentioned.     

Inference from Accelerated Degradation and Failure Data Based on Gaussian Process Models

An important problem in reliability and survival analysis is that of modeling degradation together with any observed failures in a life test. Here, based on a continuous cumulative damage approach with a Gaussian process describing degradation, a general accelerated test model is presented in which failure times and degradation measures can be combined for inference about system lifetime. Some specific models when the drift of the Gaussian process depends on the acceleration variable are discussed in detail. Illustrative examples using simulated data as well as degradation data observed in carbon-film resistors are presented.     

Accelerated Test Models for System Strength Based on Birnbaum-Saunders Distributions

Recent research in cumulative damage models for strengths of systems has yielded various statistical distributions that incorporate a system size variable and follow a generalized Birnbaum-Saunders form. These models can be unified as a three-parameter Birnbaum-Saunders-type family of distributions, where the third parameter arises from the size variable through the cumulative damage approach. In this paper, the generalized three-parameter Birnbaum-Saunders distribution is characterized, and examples of cumulative damage models for system strength that fit this form are given. Also, estimation and asymptotic theory are developed for the generalized distribution, and illustrations are presented for experimental strength data for carbon composite materials.     

Nonparametric function estimation from inversely sampled record-breaking data

Often, in industrial stress testing, meteorological data analysis, and other similar situations, measurements may be made sequentially and only values smaller than all previous ones are recorded. When the number of records is fixed in advance, the data are referred to as inversely sampled record-breaking data. This paper is concerned with nonparametric estimation of the distribution and density functions from such data (successive minima). For a single record-breaking sample, consistent estimation is not possible except in the extreme left tail of the distribution. Hence, replication is required, and for m such independent record-breaking samples, the estimators are shown to be strongly consistent and asymptotically normal as m ∞ →. Computer simulations are used to investigate the effect of the bandwidth on the mean squared errors and biases of the smooth estimators, and are also used to provide a comparison of their performance with the analogous estimators obtained under random sampling for record values.     

Maximum likelihood estimation of un1modal and decreasing densities based on arbitrarily right-censored data

Nonparametric maximum likelihood estimation of decreasing and unimodal density functions based on observations subject to arbitrary right censorship is considered. The maximum likelihood estimator of both types of densities is shown to exist and is a step function. The estimators may be computed for small samples by maximizing nonlinear equations subject to linear constraints, and the SUMT algorithm for constrained nonlinear optimization is used for the necessary calculations in an example.     

Parameter estimation for a new distribution for the strength of brittle fibers: a simulation study

Parameter estimates of a new distribution for the strength of brittle fibers and composite materials are considered. An algorithm for generating random numbers from the distribution is suggested. Two parameter estimation methods, one based on a simple least squares procedure and the other based on the maximum likelihood principle, are studied using Monte Carlo simulation. In most cases, the maximum likelihood estimators were found to have somewhat smaller root mean squared error and bias than the least squares estimators. However, the least squares estimates are generally good and provide useful initial values for the numerical iteration used to find the maximum likelihood estimates.     

The Writer's Guild: A Model of Support for Social Work Faculty

The retention and promotion of social work faculty is partially dependent upon their success in publishing. Because of a perception among junior faculty at one Midwestern university that writing barriers posed a threat to their career development, they developed a Writer's Guild. The Guild model represents a collaborative, non-hierarchical approach to supporting scholarship. In this article, the authors describe the model, discuss some of the challenges involved in its formation, and offer recommendations for transplanting the model to other schools.