Victor Chan

A Three-Outcome Design for Phase II Clinical Trials

The goal of a phase II trial is to make a preliminary determination regarding the activity and tolerability of a new treatment and thus to determine whether the treatment warrants further study in the phase III setting. Phase II clinical trials are typically designed in the hypothesis testing framework with two possible outcomes, either reject the null hypothesis H(0) or reject the alternative hypothesis H(a), based on the observed activity level. However, in cases where the observed activity is borderline, the decision regarding the future of the agent is not as clear as the prespecified hypothesis test would indicate. In this paper we propose an alternative design that allows for three outcomes: reject H(0), reject H(a), or reject neither. We describe the theoretical properties of this design and illustrate it with several examples. We focus on the clinical implications of the three-outcome design. Control Clin Trials 2001;22:117-125

A failure-time model for infant-mortality and wearout failure modes

Some populations of electronic devices or other system components are subject to both infant-mortality and wearout failure modes. Typically, interest is in the estimation of reliability metrics such as distribution-quantiles or fraction-failing at a point in time for the population of units. This involves: (1) modeling the failure time; and (2) estimating the parameters of the failure-time distributions, for the different failure modes, as well as the proportion of defective units. This paper: (1) proposes GLFP (general limited failure population) for this purpose; (2) uses the ML (maximum likelihood) method of to estimate the unknown model parameters-the formulae for the likelihood contribution corresponding to different types of censoring are provided; (3) describes a likelihood-based method to construct statistical-confidence intervals and simultaneous statistical-confidence bands for quantities of interest; and (4) fits the model to a set of censored data to illustrate the estimation technique and some of the models characteristics. The model-fitting indicates that identification of the failure mode of at least a few failed units is necessary to estimate model-parameters. Based on the fitting of the data from the lifetime of circuit boards, the GLFP model provides a useful description of the failure-time distribution for components that have both wearout and some infant mortality behavior. However, the data must include the cause of failure for at least a few observations in order to avoid complications in the ML estimation. The more-failed units whose failure mode has been identified, the better model estimates are in terms of model-fitting.

Time Series Modeling of Degradation Due to Outdoor Weathering

Environmental variables have an important effect on the reliability of many products such as coatings and polymeric composites. Long-term prediction of the performance or service life of such products must take into account the probabilistic/stochastic nature of the outdoor weather. In this article, we propose a time series modeling procedure to model the time series data of daily accumulated degradation. Daily accumulated degradation is the total amount of degradation accrued within one day and can be obtained by using a degradation rate model for the product and the weather data. The fitted model of the time series can then be used to estimate the future distribution of cumulative degradation over a period of time, and to compute reliability measures such as the probability of failure. The modeling technique and estimation method are illustrated using the degradation of a solar reflector material. We also provide a method to construct approximate confidence intervals for the probability of failure.

Block Bootstrap Estimation of the Distribution of Cumulative Outdoor Degradation

An interesting prediction problem involving degradation of materials exposed to outdoor environments (weathering) is estimating the distribution of future cumulative degradation using small- to moderate-sized degradation datasets. This distribution, which is assumed to arise as a result of the uncertainty/variability in the weather, can be expressed mathematically as the distribution of the sum of a periodic dependent time series and is approximately normal by the central limit theorem. The estimation of this distribution is thus equivalent to estimating the mean and the variance of the distribution. In this article, we propose a block bootstrap-based approach for the estimation and a novel technique to estimate the variance of the distribution. We provide an example involving the degradation of a solar reflector material, as well as the results of a simulation study to show the efficacy of the proposed estimators. We also give a procedure for constructing an approximate confidence interval for the probability of failure.

A methodology for predicting probability of detection for ultrasonic testing

Theoretical models of physical processes have been utilized to predict expected flaw response and probability of detection (POD). The models have as inputs the most important inspection-related variables and also account for some sources of variability (e.g., material noise and scan plan). These models, however, do not adequately describe all sources of variability (e.g., human factors deliberate or unavoidable changes in inspection system properties, or complex changes in flaw morphology). This paper describes a new methodology that combines the use of physical modeling of factors that can be modeled adequately and statistical modeling of limited NDE inspection data (e.g. a-hat versus a data) to account for other important factors that are not included in the physical model. The resulting physical/statistical model provides predictions of POD or other inspection-evaluation metrics as a function of specified inspection plans and flaw characteristics that extend the range of predictions that could be made empirically, based on the available data. We illustrate the methodology with example data from experiments on synthetic hard-alpha flaws.

Ultrasonic and statistical analyses of hard-alpha defects in titanium alloys

This paper describes a research effort to model the geometry and ultrasonic responses of naturally occurring titanium hard-alpha defects. The hard-alpha defects were first geometrically reconstructed based on metallographs obtained from destructive sectioning. Using the reconstruction data, ultrasonic models were then developed to predict the defects’ responses in specific experimental configurations. The predicted responses were subsequently compared with the experimental observations, and error analyses were performed on the predictions to examine their accuracy, consistency as well as other underlying inter-relationships.