Statistical Degradation Models for Electronics

With increasing presence of electronics in modern systems and in every-day products, their reliability is inextricably dependent on that of their electronics. We develop reliability models for failure-time prediction under small failure-time samples and information on individual degradation history. The development of the model extends the work of Whitmore et al. 1998, to incorporate two new data-structures common to reliability testing. Reliability models traditionally use lifetime information to evaluate the reliability of a device or system. To analyze small failure-time samples within dynamic environments where failure mechanisms are unknown, there is a need for models that make use of auxiliary reliability information. In this thesis we present models suitable for reliability data, where degradation variables are latent and can be tracked by related observable variables we call markers. We provide an engineering justification for our model and develop parametric and predictive inference equations for a data-structure that includes terminal observations of the degradation variable and longitudinal marker measurements. We compare maximum likelihood estimation and prediction results obtained by Whitmore et. al. 1998 and show improvement in inference under small sample sizes. We introduce modeling of variable failure thresholds within the framework of bivariate degradation models and discuss ways of incorporating covariates. In the second part of the thesis we investigate anomaly detection through a Bayesian support vector machine and discuss its place in degradation modeling. We compute posterior class probabilities for time-indexed covariate observations, which we use as measures of degradation. Lastly, we present a multistate model used to model a recurrent event process and failure-times. We compute the expected time to failure using counting process theory and investigate the effect of the event process on the expected failure-time estimates

A Data-Driven Predictive Model of Reliability Estimation Using State-Space Stochastic Degradation Model

The concept of the Industrial Internet of Things (IIoT) provides the foundation to apply data-driven methodologies. The data-driven predictive models of reliability estimation can become a major tool in increasing the life of assets, lowering capital cost, and reducing operating and maintenance costs. Classical models of reliability assessment mainly rely on lifetime data. Failure data may not be easily obtainable for highly reliable assets. Furthermore, the collected historical lifetime data may not be able to accurately describe the behavior of the asset in a unique application or environment. Therefore, it is not an optimal approach anymore to conduct a reliability estimation based on classical models. Fortunately, most of the industrial assets have performance characteristics whose degradation or decay over the operating time can be related to their reliability estimates. The application of the degradation methods has been recently increasing due to their ability to keep track of the dynamic conditions of the system over time. The main purpose of this study is to develop a data-driven predictive model of reliability assessment based on real-time data using a state-space stochastic degradation model to predict the critical time for initiating maintenance actions in order to enhance the value and prolonging the life of assets. The new degradation model developed in this thesis is introducing a new mapping function for the General Path Model based on series of Gamma Processes degradation models in the state-space environment by considering Poisson distributed weights for each of the Gamma processes. The application of the developed algorithm is illustrated for the distributed electrical systems as a generic use case. A data-driven algorithm is developed in order to estimate the parameters of the new degradation model. Once the estimates of the parameters are available, distribution of the failure time, time-dependent distribution of the degradation, and reliability based on the current estimate of the degradation can be obtained

Reliability Analysis of Hafnium Oxide Dielectric Based Nanoelectronics

With the physical dimensions ever scaling down, the increasing level of sophistication in nano-electronics requires a comprehensive and multidisciplinary reliability investigation. A kind of nano-devices, HfO2-based high-k dielectric films, are studied in the statistical aspect of reliability as well as electrical and physical aspects of reliability characterization, including charge trapping and degradation mechanisms, breakdown modes and bathtub failure rate estimation. This research characterizes charge trapping and investigates degradation mechanisms in high-k dielectrics. Positive charges trapped in both bulk and interface contribute to the interface state generation and flat band voltage shift when electrons are injected from the gate under a negative gate bias condition.A negligible number of defects are generated until the stress voltage increases to a certain level. As results of hot electrons and positive charges trapped in the interface region, the difference in the breakdown sequence is attributed to the physical thickness of the bulk high-k layer and the structure of the interface layer. Time-to-breakdown data collected in the accelerated life tests are modeled with a bathtub failure rate curve by a 3-step Bayesian approach. Rather than individually considering each stress level in accelerating life tests (ALT), this approach derives the change point and the priors for Bayesian analysis from the time-to-failure data under neighborhood stresses, based on the relationship between the lifetime and stress voltage. This method can provide a fast and reliable estimation of failure rate for burn-in optimization when only a small sample of data is available

Reliability assessment of permanent magnet brake based on accelerated bivariate Wiener degradation process

Permanent magnet brake (PMB) is a safe and effective braking mechanism used to stop and hold the load in place. Due to its complex structure and high reliability, assessing the reliability of PMB remains a challenge. The main difficulty lies in that there are several performance indicators reflecting the health state of PMB, and they are correlated with each other. In order to assess the reliability of PMB more accurately, a constant stress accelerated degradation test (ADT) is carried out to collect degradation data of two main performance indicators in PMB. An accelerated bivariate Wiener degradation model is proposed to analyse the ADT data. In the proposed model, the relationship between degradation rate and stress levels is described by Arrhenius model, and a common random effect is introduced to describe the unit-to-unit variation and correlation between the two performance indicators. The Markov Chain Monte Carlo (MCMC) algorithm is performed to obtain the point and interval estimates of the model parameters. Finally, the proposed model and method are applied to analyse the accelerated degradation data of PMB, and the results show that the reliability of PMB at the used condition can be quantified quite well

Knowledge Discovery from Complex Event Time Data with Covariates

In particular engineering applications, such as reliability engineering, complex types of data are encountered which require novel methods of statistical analysis. Handling covariates properly while managing the missing values is a challenging task. These type of issues happen frequently in reliability data analysis. Specifically, accelerated life testing (ALT) data are usually conducted by exposing test units of a product to severer-than-normal conditions to expedite the failure process. The resulting lifetime and/or censoring data are often modeled by a probability distribution along with a life-stress relationship. However, if the probability distribution and life-stress relationship selected cannot adequately describe the underlying failure process, the resulting reliability prediction will be misleading. To seek new mathematical and statistical tools to facilitate the modeling of such data, a critical question to be asked is: Can we find a family of versatile probability distributions along with a general life-stress relationship to model complex lifetime data with covariates? In this dissertation, a more general method is proposed for modeling lifetime data with covariates. Reliability estimation based on complete failure-time data or failure-time data with certain types of censoring has been extensively studied in statistics and engineering. However, the actual failure times of individual components are usually unavailable in many applications. Instead, only aggregate failure-time data are collected by actual users due to technical and/or economic reasons. When dealing with such data for reliability estimation, practitioners often face challenges of selecting the underlying failure-time distributions and the corresponding statistical inference methods. So far, only the Exponential, Normal, Gamma and Inverse Gaussian (IG) distributions have been used in analyzing aggregate failure-time data because these distributions have closed-form expressions for such data. However, the limited choices of probability distributions cannot satisfy extensive needs in a variety of engineering applications. Phase-type (PH) distributions are robust and flexible in modeling failure-time data as they can mimic a large collection of probability distributions of nonnegative random variables arbitrarily closely by adjusting the model structures. In this paper, PH distributions are utilized, for the first time, in reliability estimation based on aggregate failure-time data. To this end, a maximum likelihood estimation (MLE) method and a Bayesian alternative are developed. For the MLE method, an expectation-maximization (EM) algorithm is developed to estimate the model parameters, and the corresponding Fisher information is used to construct the confidence intervals for the quantities of interest. For the Bayesian method, a procedure for performing point and interval estimation is also introduced. Several numerical examples show that the proposed PH-based reliability estimation methods are quite flexible and alleviate the burden of selecting a probability distribution when the underlying failure-time distribution is general or even unknown

Imprecise Statistical Methods for Accelerated Life Testing

Accelerated Life Testing (ALT) is frequently used to obtain information on the lifespan of devices. Testing items under normal conditions can require a great deal of time and expense. To determine the reliability of devices in a shorter period of time, and with lower costs, ALT can often be used. In ALT, a unit is tested under levels of physical stress (e.g. temperature, voltage, or pressure) greater than the unit will experience under normal operating conditions. Using this method, units tend to fail more quickly, requiring statistical inference about the lifetime of the units under normal conditions via extrapolation based on an ALT model. This thesis presents a novel method for statistical inference based on ALT data. The method quantifies uncertainty using imprecise probabilities, in particular it uses Nonparametric Predictive Inference (NPI) at the normal stress level, combining data from tests at that level with data from higher stress levels which have been transformed to the normal stress level. This has been achieved by assuming an ALT model, with the relation between different stress levels modelled by a simple parametric link function. We derive an interval for the parameter of this link function, based on the application of classical hypothesis tests and the idea that, if data from a higher stress level are transformed to the normal stress level, then these transformed data and the original data from the normal stress level should not be distinguishable. In this thesis we consider two scenarios of the methods. First, we present this approach with the assumption of Weibull failure time distributions at each stress level using the likelihood ratio test to obtain the interval for the parameter of the link function. Secondly, we present this method without an assumed parametric distribution at each stress level, and using a nonparametric hypothesis test to obtain the interval. To illustrate the possible use of our new statistical method for ALT data, we present an application to support decisions on warranties. A warranty is a contractual commitment between consumer and producer, in which the latter provides post-sale services in case of product failure. We will consider pricing basic warranty contracts based on the information from ALT data and the use of our novel imprecise probabilistic statistical method