G. A. Whitmore

Estimating degradation by a wiener diffusion process subject to measurement error

Most materials and components degrade physically before they fail. Engineering degradation tests are designed to measure these degradation processes. Measurements in the tests reflect the inherent randomness of degradation itself as well as measurement errors created by imperfect instruments, procedures and environments. This paper describes a statistical model for measured degradation data that takes both sources of variation into account. The degradation process in the model is taken to be a Wiener diffusion process. The measurement errors are assumed to be independent normal random outcomes that are independent of the degradation process. The paper describes inference procedures for the model and discusses some practical issues that must be considered in dealing with the statistical problem. A case study is presented.

Failure Inference From a Marker Process Based on a Bivariate Wiener Model

Many models have been proposed that relate failure times and stochastic time-varying covariates. In some of these models, failure occurs when a particular observable marker crosses a threshold level. We are interested in the more difficult, and often more realistic, situation where failure is not related deterministically to an observable marker. In this case, joint models for marker evolution and failure tend to lead to complicated calculations for characteristics such as the marginal distribution of failure time or the joint distribution of failure time and marker value at failure. This paper presents a model based on a bivariate Wiener process in which one component represents the marker and the second, which is latent (unobservable), determines the failure time. In particular, failure occurs when the latent component crosses a threshold level. The model yields reasonably simple expressions for the characteristics mentioned above and is easy to fit to commonly occurring data that involve the marker value at the censoring time for surviving cases and the marker value and failure time for failing cases. Parametric and predictive inference are discussed, as well as model checking. An extension of the model permits the construction of a composite marker from several candidate markers that may be available. The methodology is demonstrated by a simulated example and a case application.

Models for microarray gene expression data

This paper describes a general methodology for the analysis of differential gene expression based on microarray data. First, we characterize the data by a linear statistical model that accounts for relevant sources of variation in the data and then we consider estimation of the model parameters. Because microarray studies typically involve thousands of genes, we propose a two-stage method for parameter estimation. The interaction terms for genes and experimental conditions in this model capture all relevant information about differential gene expression in the microarray data. We propose a mixture distribution model for a summary statistic of differential expression that consists of null and alternative component distributions. The mixture model suggests two methods for identifying genes exhibiting differential expression. One is a frequentist method that identifies distinguished genes and the other an empirical Bayes procedure that yields estimated posterior probabilities of differential expression, conditional on observed microarray readings. An extensive case application involving juvenile cystic kidney disease in mice is used to illustrate the methodology. The application controls for variation arising from array, color channel, experimental condition (tissue type), and gene, with the analysis of variance (ANOVA) model including both main effects to normalize the expression data and all interaction terms involving genes. The gene expression profile is found to vary by tissue type as expected, but also by color channel, which was less expected. A concluding section discusses some outstanding research questions related to the analysis of microarray data.

Comparative Performance of Chinese Commercial Banks: Analysis, Findings and Policy Implications

This paper investigates the financial performance of Chinesebanks by using financial ratio analysis. The analysis shows that the lowprofitability of state-owned commercial banks results from their higherratio for non-interest expenses and lower interest margin thanjoint-equity banks. The much lower profit margin in state-owned banksdraws down their levels of ROE and ROA, even with the offsetting effectsof more efficient utilization of their assets and higher financialleverage. Although data limitations prevent us from studying the riskprofiles of the banks in detail, it is clear that these Chinese banksgenerated lower returns with higher financial risks than their Westerncounterparts. The paper concludes with a discussion of major issuesaffecting Chinese bank performance. Significant difficulties encounteredin assessing bank performance are also identified anddiscussed.

Accounting for Individual Over-Dispersion in a Bonus-Malus Automobile Insurance System

Individual automobile insurance claims are characterized by over-dispersion relative to the Poisson model. In addition, claim propensities vary among individuals in any insurance portfolio. This paper presents a model which takes account of both characteristics. The model employs the negative-binomial distribution as the distribution for individual-level claims and a Pareto distribution as the distribution for claim propensities within the portfolio. The paper shows that the resulting model is tractable and has a number of attractive properties which make it suitable for this application. The fit of the model to actual claim numbers for automobile third party liability insurance is examined and found acceptable. Bayes theorem is then applied to this model to calculate illustrative optimal premiums under the Bonus-Malus System (BMS).

Two-Stage Reliability Tests with Technological Evolution: A Bayesian Analysis

The reliability of equipment is of interest to manufacturers. Frequently minor modifications are made to devices and there is insufficient time to test these modified devices fully before they must enter service. The problem of interest here is how we can use the information already obtained from the testing of a device before modification to help us to evaluate the reliability of the modified device. A Bayesian analysis allows the flexibility to use any available prior information in the analysis. In this paper we consider two different types of prior information that may be available and the resulting analyses

Stochastic Dominance for the Class of Completely Monotonic Utility Functions

According to the expected utility axioms, a decision maker with utility function u(x) for wealth x assigns the following subjective value to an uncertain prospect with cumulative distribution function F(x).

Reliability analysis of a multipath switching network

E(u;F) = \smallint _0^\infty u(x)dF(x)