arXiv subjects

Yili Hong

Publications and source records attributed to Yili Hong.

51 records · Page 3Linked to original sources

arXiv2019

Statistical Analysis of Modern Reliability Data

Traditional reliability analysis has been using time to event data, degradation data, and recurrent event data, while the associated covariates tend to be simple and constant over time. Over the past years, we have witnessed the rapid development of sensor and wireless technology, which enables us to track how the product has been used and under which environmental conditions it has been used. Nowadays, we are able to collect richer information on covariates which provides opportunities for better reliability predictions. In this chapter, we first review recent development on statistical methods for reliability analysis. We then focus on introducing several specific methods that were developed for different types of reliability data with covariate information. Illustrations of those methods are also provided using examples from industry. Test planning is also an important part of reliability analysis. In addition to data analysis, we also provide a briefly review on recent developments of test planning and then focus on illustrating the sequential Bayesian design with an example of fatigue testing for polymer composites. The paper is concluded with some discussions and remarks.

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arXiv2018

Bayesian Sequential Design Based on Dual Objectives for Accelerated Life Tests

Traditional accelerated life test plans are typically based on optimizing the C-optimality for minimizing the variance of an interested quantile of the lifetime distribution. The traditional methods rely on some specified planning values for the model parameters, which are usually unknown prior to the actual tests. The ambiguity of the specified parameters can lead to suboptimal designs for optimizing the intended reliability performance. In this paper, we propose a sequential design strategy for life test plans based on considering dual objectives. In the early stage of the sequential experiment, we suggest to allocate more design locations based on optimizing the D-optimality to quickly gain precision in the estimated model parameters. In the later stage of the experiment, we can allocate more samples based on optimizing the C-optimality to maximize the precision of the estimated quantile of the lifetime distribution. We compare the proposed sequential design strategy with existing test plans considering only a single criterion and illustrate the new method with an example on fatigue testing of polymer composites.

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arXiv2018

Spatial Variable Selection and An Application to Virginia Lyme Disease Emergence

Lyme disease is an infectious disease that is caused by a bacterium called Borrelia burgdorferi sensu stricto. In the United States, Lyme disease is one of the most common infectious diseases. The major endemic areas of the disease are New England, Mid-Atlantic, East-North Central, South Atlantic, and West North-Central. Virginia is on the front-line of the disease's diffusion from the northeast to the south. One of the research objectives for the infectious disease community is to identify environmental and economic variables that are associated with the emergence of Lyme disease. In this paper, we use a spatial Poisson regression model to link the spatial disease counts and environmental and economic variables, and develop a spatial variable selection procedure to effectively identify important factors by using an adaptive elastic net penalty. The proposed methods can automatically select important covariates, while adjusting for possible spatial correlations of disease counts. The performance of the proposed method is studied and compared with existing methods via a comprehensive simulation study. We apply the developed variable selection methods to the Virginia Lyme disease data and identify important variables that are new to the literature. Supplementary materials for this paper are available online.

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arXiv2018

Applications of the Fractional-Random-Weight Bootstrap

The bootstrap, based on resampling, has, for several decades, been a widely used method for computing confidence intervals for applications where no exact method is available and when sample sizes are not large enough to be able to rely on easy-to-compute large-sample approximate methods, such a Wald (normal-approximation) confidence intervals. Simulation based bootstrap intervals have been proven useful in that their actual coverage probabilities are close to the nominal confidence level in small samples. Small samples analytical approximations such as the Wald method, however, tend to have coverage probabilities that greatly exceed the nominal confidence level. There are, however, many applications where the resampling bootstrap method cannot be used. These include situations where the data are heavily censored, logistic regression when the success response is a rare event or where there is insufficient mixing of successes and failures across the explanatory variable(s), and designed experiments where the number of parameters is close to the number of observations. The thing that these three situations have in common is that there may be a substantial proportion of the resamples where is not possible to estimate all of the parameters in the model. This paper reviews the fractional-random-weight bootstrap method and demonstrates how it can be used to avoid these problems and construct confidence intervals. For the examples, it is seen that the fractional-random-weight bootstrap method is easy to use and has advantages over the resampling method in many challenging applications.

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arXiv2018

Disentangling and Assessing Uncertainties in Multiperiod Corporate Default Risk Predictions

Measuring the corporate default risk is broadly important in economics and finance. Quantitative methods have been developed to predictively assess future corporate default probabilities. However, as a more difficult yet crucial problem, evaluating the uncertainties associated with the default predictions remains little explored. In this paper, we attempt to fill this blank by developing a procedure for quantifying the level of associated uncertainties upon carefully disentangling multiple contributing sources. Our framework effectively incorporates broad information from historical default data, corporates' financial records, and macroeconomic conditions by a) characterizing the default mechanism, and b) capturing the future dynamics of various features contributing to the default mechanism. Our procedure overcomes the major challenges in this large scale statistical inference problem and makes it practically feasible by using parsimonious models, innovative methods, and modern computational facilities. By predicting the marketwide total number of defaults and assessing the associated uncertainties, our method can also be applied for evaluating the aggregated market credit risk level. Upon analyzing a US market data set, we demonstrate that the level of uncertainties associated with default risk assessments is indeed substantial. More informatively, we also find that the level of uncertainties associated with the default risk predictions is correlated with the level of default risks, indicating potential for new scopes in practical applications including improving the accuracy of default risk assessments.

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arXiv2018

Reliability Analysis of Polymeric Materials

Polymeric materials are widely used in many applications and are especially useful when combined with other polymers to make polymer composites. The appealing features of these materials come from their having comparable levels of strength and endurance to what one would find in metal alloys while being more lightweight and economical. However, these materials are still susceptible to degradation over time and so it is of great importance to manufacturers to assess their product's lifetime. Because these materials are meant to last over a span of several years or even decades, accelerated testing is often the method of choice in assessing product lifetimes in a more feasible time frame. In this article, a brief introduction is given to the methods of accelerated testing and analysis used with polymer materials. Special attention is given to degradation testing and modeling due to the growing popularity of these techniques along with a brief discussion of fatigue testing. References are provided for further reading in each of these areas.

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arXiv2018

Big Data and Reliability Applications: The Complexity Dimension

Big data features not only large volumes of data but also data with complicated structures. Complexity imposes unique challenges in big data analytics. Meeker and Hong (2014, Quality Engineering, pp. 102-116) provided an extensive discussion of the opportunities and challenges in big data and reliability, and described engineering systems that can generate big data that can be used in reliability analysis. Meeker and Hong (2014) focused on large scale system operating and environment data (i.e., high-frequency multivariate time series data), and provided examples on how to link such data as covariates to traditional reliability responses such as time to failure, time to recurrence of events, and degradation measurements. This paper intends to extend that discussion by focusing on how to use data with complicated structures to do reliability analysis. Such data types include high-dimensional sensor data, functional curve data, and image streams. We first provide a review of recent development in those directions, and then we provide a discussion on how analytical methods can be developed to tackle the challenging aspects that arise from the complexity feature of big data in reliability applications. The use of modern statistical methods such as variable selection, functional data analysis, scalar-on-image regression, spatio-temporal data models, and machine learning techniques will also be discussed.

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arXiv2017

Development of an Accelerated Test Methodology to the Predict Service Life of Polymeric Materials Subject to Outdoor Weathering

Service life prediction is of great importance to manufacturers of coatings and other polymeric materials. Photodegradation, driven primarily by ultraviolet (UV) radiation, is the primary cause of failure for organic paints and coatings, as well as many other products made from polymeric materials exposed to sunlight. Traditional methods of service life prediction involve the use of outdoor exposure in harsh UV environments (e.g., Florida and Arizona). Such tests, however, require too much time (generally many years) to do an evaluation. Non-scientific attempts to simply "speed up the clock" result in incorrect predictions. This paper describes the statistical methods that were developed for a scientifically-based approach to using laboratory accelerated tests to produce timely predictions of outdoor service life. The approach involves careful experimentation and identifying a physics/chemistry-motivated model that will adequately describe photodegradation paths of polymeric materials. The model incorporates the effects of explanatory variables UV spectrum, UV intensity, temperature, and humidity. We use a nonlinear mixed-effects model to describe the sample paths. The methods are illustrated with accelerated laboratory test data for a model epoxy coating. The validity of the methodology is checked by extending our model to allow for dynamic covariates and comparing predictions with specimens that were exposed in an outdoor environment where the explanatory variables are uncontrolled but recorded.

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arXiv2017

An Algorithm for Computing the Distribution Function of the Generalized Poisson-Binomial Distribution

The Poisson-binomial distribution is useful in many applied problems in engineering, actuarial science, and data mining. The Poisson-binomial distribution models the distribution of the sum of independent but not identically distributed Bernoulli random variables whose success probabilities vary. In this paper, we extend the Poisson-binomial distribution to the generalized Poisson-binomial (GPB) distribution. The GPB distribution is defined in cases where the Bernoulli variables can take any two arbitrary values instead of 0 and~1. The GPB distribution is useful in many areas such as voting theory, actuarial science, warranty prediction, and probability theory. With few previous works studying the GPB distribution, we derive the probability distribution via the discrete Fourier transform of the characteristic function of the distribution. We develop an efficient algorithm for computing the distribution function, which uses the fast Fourier transform. We test the accuracy of the developed algorithm upon comparing it with enumeration-based exact method and the results from the binomial distribution. We also study the computational time of the algorithm in various parameter settings. Finally, we discus the factors affecting the computational efficiency of this algorithm, and illustrate the use of the software package.

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arXiv2016

Statistical Methods for Thermal Index Estimation Based on Accelerated Destructive Degradation Test Data

Accelerated destructive degradation test (ADDT) is a technique that is commonly used by industries to access material's long-term properties. In many applications, the accelerating variable is usually the temperature. In such cases, a thermal index (TI) is used to indicate the strength of the material. For example, a TI of 200C may be interpreted as the material can be expected to maintain a specific property at a temperature of 200C for 100,000 hours. A material with a higher TI possesses a stronger resistance to thermal damage. In literature, there are three methods available to estimate the TI based on ADDT data, which are the traditional method based on the least-squares approach, the parametric method, and the semiparametric method. In this chapter, we provide a comprehensive review of the three methods and illustrate how the TI can be estimated based on different models. We also conduct comprehensive simulation studies to show the properties of different methods. We provide thorough discussions on the pros and cons of each method. The comparisons and discussion in this chapter can be useful for practitioners and future industrial standards.

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arXiv2016

ADDT: An R Package for Analysis of Accelerated Destructive Degradation Test Data

Accelerated destructive degradation tests (ADDT) are often used to collect necessary data for assessing the long-term properties of polymeric materials. Based on the data, a thermal index (TI) is estimated. The TI can be useful for material rating and comparisons. The R package ADDT provides the functionalities of performing the traditional method based on the least-squares method, the parametric method based on maximum likelihood estimation, and the semiparametric method based on spline methods for analyzing ADDT data, and then estimating the TI for polymeric materials. In this chapter, we provide a detailed introduction to the ADDT package. We provide a step-by-step illustration for the use of functions in the package. Publicly available datasets are used for illustrations.

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arXiv2015

Semi-parametric Models for Accelerated Destructive Degradation Test Data Analysis

Accelerated destructive degradation tests (ADDT) are widely used in industry to evaluate materials' long term properties. Even though there has been tremendous statistical research in nonparametric methods, the current industrial practice is still to use application-specific parametric models to describe ADDT data. The challenge of using a nonparametric approach comes from the need to retain the physical meaning of degradation mechanisms and also perform extrapolation for predictions at the use condition. Motivated by this challenge, we propose a semi-parametric model to describe ADDT data. We use monotonic B-splines to model the degradation path, which not only provides flexible models with few assumptions, but also retains the physical meaning of degradation mechanisms (e.g., the degradation path is monotonically decreasing). Parametric models, such as the Arrhenius model, are used for modeling the relationship between the degradation and accelerating variable, allowing for extrapolation to the use conditions. We develop an efficient procedure to estimate model parameters. We also use simulation to validate the developed procedures and demonstrate the robustness of the semi-parametric model under model misspecification. Finally, the proposed method is illustrated by multiple industrial applications.

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arXiv2015

Survival and lifetime data analysis with a flexible class of distributions

We introduce a general class of continuous univariate distributions with positive support obtained by transforming the class of two-piece distributions. We show that this class of distributions is very flexible, easy to implement, and contains members that can capture different tail behaviours and shapes, producing also a variety of hazard functions. The proposed distributions represent a flexible alternative to the classical choices such as the log-normal, Gamma, and Weibull distributions. We investigate empirically the inferential properties of the proposed models through an extensive simulation study. We present some applications using real data in the contexts of time-to-event and accelerated failure time models. In the second kind of applications, we explore the use of these models in the estimation of the distribution of the individual remaining life.

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arXiv2014

How do heterogeneities in operating environments affect field failure predictions and test planning?

The main objective of accelerated life tests (ALTs) is to predict fraction failings of products in the field. However, there are often discrepancies between the predicted fraction failing from the lab testing data and that from the field failure data, due to the yet unobserved heterogeneities in usage and operating conditions. Most previous research on ALT planning and data analysis ignores the discrepancies, resulting in inferior test plans and biased predictions. In this paper we model the heterogeneous environments together with their effects on the product failures as a frailty term to link the lab failure time distribution and field failure time distribution of a product. We show that in the presence of the heterogeneous operating conditions, the hazard rate function of the field failure time distribution exhibits a range of shapes. Statistical inference procedure for the frailty models is developed when both the ALT data and the field failure data are available. Based on the frailty models, optimal ALT plans aimed at predicting the field failure time distribution are obtained. The developed methods are demonstrated through a real life example.

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arXiv2009

Prediction of remaining life of power transformers based on left truncated and right censored lifetime data

Prediction of the remaining life of high-voltage power transformers is an important issue for energy companies because of the need for planning maintenance and capital expenditures. Lifetime data for such transformers are complicated because transformer lifetimes can extend over many decades and transformer designs and manufacturing practices have evolved. We were asked to develop statistically-based predictions for the lifetimes of an energy company's fleet of high-voltage transmission and distribution transformers. The company's data records begin in 1980, providing information on installation and failure dates of transformers. Although the dataset contains many units that were installed before 1980, there is no information about units that were installed and failed before 1980. Thus, the data are left truncated and right censored. We use a parametric lifetime model to describe the lifetime distribution of individual transformers. We develop a statistical procedure, based on age-adjusted life distributions, for computing a prediction interval for remaining life for individual transformers now in service. We then extend these ideas to provide predictions and prediction intervals for the cumulative number of failures, over a range of time, for the overall fleet of transformers.

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