LED Lighting System Reliability Modeling and Inference via Random Effects Gamma Process and Copula Function

Light emitting diode (LED) lamp has attracted increasing interest in the field of lighting systems due to its low energy and long lifetime. For different functions (i.e., illumination and color), it may have two or more performance characteristics. When the multiple performance characteristics are dependent, it creates a challenging problem to accurately analyze the system reliability. In this paper, we assume that the system has two performance characteristics, and each performance characteristic is governed by a random effects Gamma process where the random effects can capture the unit to unit differences. The dependency of performance characteristics is described by a Frank copula function. Via the copula function, the reliability assessment model is proposed. Considering the model is so complicated and analytically intractable, the Markov chain Monte Carlo (MCMC) method is used to estimate the unknown parameters. A numerical example about actual LED lamps data is given to demonstrate the usefulness and validity of the proposed model and method

Models for Data Analysis in Accelerated Reliability Growth

This work develops new methodologies for analyzing accelerated testing data in the context of a reliability growth program for a complex multi-component system. Each component has multiple failure modes and the growth program consists of multiple test-fix stages with corrective actions applied at the end of each stage. The first group of methods considers time-to-failure data and test covariates for predicting the final reliability of the system. The time-to-failure of each failure mode is assumed to follow a Weibull distribution with rate parameter proportional to an acceleration factor. Acceleration factors are specific to each failure mode and test covariates. We develop a Bayesian methodology to analyze the data by assigning a prior distribution to each model parameter, developing a sequential Metropolis-Hastings procedure to sample the posterior distribution of the model parameters, and deriving closed form expressions to aggregate component reliability information to assess the reliability of the system. The second group of methods considers degradation data for predicting the final reliability of a system. First, we provide a non-parametric methodology for a single degradation process. The methodology utilizes functional data analysis to predict the mean time-to-degradation function and Gaussian processes to capture unit-specific deviations from the mean function. Second, we develop parametric model for a component with multiple dependent monotone degradation processes. The model considers random effects on the degradation parameters and a parametric life-stress relationship. The assumptions are that degradation increments follow an Inverse Gaussian process and a Copula function captures the dependency between them. We develop a Bayesian and a maximum likelihood procedure for estimating the model parameters using a two-stage process: (1) estimate the parameters of the degradation processes as if they were independent and (2) estimate the parameters of the Copula function using the estimated cumulative distribution function of the observed degradation increments as observed data. Simulation studies show the efficacy of the proposed methodologies for analyzing multi-stage reliability growth data

Reliability Analysis By Considering Steel Physical Properties

Most customers today are pursuing engineering materials (e.g., steel) that not only can achieve their expected functions but also are highly reliable. As a result, reliability analysis of materials has been receiving increasing attention over the past few decades. Most existing studies in the reliability engineering field focus on developing model-based and data-driven approaches to analyze material reliability based on material failure data such as lifetime data and degradation data, without considering effects of material physical properties. Ignoring such effects may result in a biased estimation of material reliability, which in turn could incur higher operation or maintenance costs. Recently, with the advancement of sensor technology more information/data concerning various physical properties of materials are accessible to reliability researchers. In this dissertation, considering the significant impacts of steel physical properties on steel failures, we propose systematic methodologies for steel reliability analysis by integrating a set of steel physical properties. Specifically, three steel properties of various scales are considered: 1) a macro-scale property called overload retardation; 2) a local-scale property called dynamic local deformation; and 3) a micro-scale property called microstructure effect. For incorporating property 1), a novel physical-statistical model is proposed based on a modification of the current Paris law. To incorporate property 2), a novel statistical model named multivariate general path model is proposed, which is a generalization of an existing univariate general path model. For the integration of property 3), a novel statistical model named distribution-based functional linear model is proposed, which is a generalization of an existing functional linear model. Theoretical property analyses and statistical inferences of these three models are intensively developed. Various simulation studies are implemented to verify and illustrate the proposed methodologies. Multiple physical experiments are designed and conducted to demonstrate the proposed models. The results show that, through the integration of the aforementioned three steel physical properties, a significant improvement of steel reliability assessment is achieved in terms of failure prediction accuracy compared to traditional reliability studies

Accelerated degradation modeling considering long-range dependence and unit-to-unit variability

Accelerated degradation testing (ADT) is an effective way to evaluate the reliability and lifetime of highly reliable products. Existing studies have shown that the degradation processes of some products are non-Markovian with long-range dependence due to the interaction with environments. Besides, the degradation processes of products from the same population generally vary from each other due to various uncertainties. These two aspects bring great difficulty for ADT modeling. In this paper, we propose an improved ADT model considering both long-range dependence and unit-to-unit variability. To be specific, fractional Brownian motion (FBM) is utilized to capture the long-range dependence in the degradation process. The unit-to-unit variability among multiple products is captured by a random variable in the degradation rate function. To ensure the accuracy of the parameter estimations, a novel statistical inference method based on expectation maximization (EM) algorithm is proposed, in which the maximization of the overall likelihood function is achieved. The effectiveness of the proposed method is fully verified by a simulation case and a microwave case. The results show that the proposed model is more suitable for ADT modeling and analysis than existing ADT models

Updated Operational Reliability from Degradation Indicators and Adaptive Maintenance Strategy

This chapter is dedicated to the reliability and maintenance of assets that are characterized by a degradation process. The item state is related to a degradation mechanism that represents the unit-to-unit variability and time-varying dynamics of systems. The maintenance scheduling has to be updated considering the degradation history of each item. The research method relies on the updating process of the reliability of a specific asset. Given a degradation process and costs for preventive/corrective maintenance actions, an optimal inspection time is obtained. At this time, the degradation level is measured and a prediction of the degradation is conducted to obtain the next inspection time. A decision criterion is established to decide whether the maintenance action should take place at the current time or postpone. Consequently, there is an optimal number of inspections that allows to extend the useful life of an asset before performing the preventive maintenance action. A numerical case study involving a non-stationary Wiener-based degradation process is proposed as an illustration of the methodology. The results showed that the expected cost per unit of time considering the adaptive maintenance strategy is lower than the expected cost per unit of time obtained for other maintenance policies

Practical reliability. Volume 3 - Testing

Application of testing to hardware program

A Generic Prognostic Framework for Remaining Useful Life Prediction of Complex Engineering Systems

Prognostics and Health Management (PHM) is a general term that encompasses methods used to evaluate system health, predict the onset of failure, and mitigate the risks associated with the degraded behavior. Multitudes of health monitoring techniques facilitating the detection and classification of the onset of failure have been developed for commercial and military applications. PHM system designers are currently focused on developing prognostic techniques and integrating diagnostic/prognostic approaches at the system level. This dissertation introduces a prognostic framework, which integrates several methodologies that are necessary for the general application of PHM to a variety of systems. A method is developed to represent the multidimensional system health status in the form of a scalar quantity called a health indicator. This method is able to indicate the effectiveness of the health indicator in terms of how well or how poorly the health indicator can distinguish healthy and faulty system exemplars. A usefulness criterion was developed which allows the practitioner to evaluate the practicability of using a particular prognostic model along with observed degradation evidence data. The criterion of usefulness is based on comparing the model uncertainty imposed primarily by imperfectness of degradation evidence data against the uncertainty associated with the time-to-failure prediction based on average reliability characteristics of the system. This dissertation identifies the major contributors to prognostic uncertainty and analyzes their effects. Further study of two important contributions resulted in the development of uncertainty management techniques to improve PHM performance. An analysis of uncertainty effects attributed to the random nature of the critical degradation threshold, , was performed. An analysis of uncertainty effects attributed to the presence of unobservable failure mechanisms affecting the system degradation process along with observable failure mechanisms was performed. A method was developed to reduce the effects of uncertainty on a prognostic model. This dissertation provides a method to incorporate prognostic information into optimization techniques aimed at finding an optimal control policy for equipment performing in an uncertain environment

Prognostics and health management of power electronics

Prognostics and health management (PHM) is a major tool enabling systems to evaluate their reliability in real-time operation. Despite ground-breaking advances in most engineering and scientific disciplines during the past decades, reliability engineering has not seen significant breakthroughs or noticeable advances. Therefore, self-awareness of the embedded system is also often required in the sense that the system should be able to assess its own health state and failure records, and those of its main components, and take action appropriately. This thesis presents a radically new prognostics approach to reliable system design that will revolutionise complex power electronic systems with robust prognostics capability enhanced Insulated Gate Bipolar Transistors (IGBT) in applications where reliability is significantly challenging and critical. The IGBT is considered as one of the components that is mainly damaged in converters and experiences a number of failure mechanisms, such as bond wire lift off, die attached solder crack, loose gate control voltage, etc. The resulting effects mentioned are complex. For instance, solder crack growth results in increasing the IGBT’s thermal junction which becomes a source of heat turns to wire bond lift off. As a result, the indication of this failure can be seen often in increasing on-state resistance relating to the voltage drop between on-state collector-emitter. On the other hand, hot carrier injection is increased due to electrical stress. Additionally, IGBTs are components that mainly work under high stress, temperature and power consumptions due to the higher range of load that these devices need to switch. This accelerates the degradation mechanism in the power switches in discrete fashion till reaches failure state which fail after several hundred cycles. To this end, exploiting failure mechanism knowledge of IGBTs and identifying failure parameter indication are background information of developing failure model and prognostics algorithm to calculate remaining useful life (RUL) along with ±10% confidence bounds. A number of various prognostics models have been developed for forecasting time to failure of IGBTs and the performance of the presented estimation models has been evaluated based on two different evaluation metrics. The results show significant improvement in health monitoring capability for power switches.Furthermore, the reliability of the power switch was calculated and conducted to fully describe health state of the converter and reconfigure the control parameter using adaptive algorithm under degradation and load mission limitation. As a result, the life expectancy of devices has been increased. These all allow condition-monitoring facilities to minimise stress levels and predict future failure which greatly reduces the likelihood of power switch failures in the first place

Stochastic Modeling of Deterioration in Nuclear Power Plant Components

The risk-based life-cycle management of engineering systems in a nuclear power plant is intended to ensure safe and economically efficient operation of energy generation infrastructure over its entire service life. An important element of life-cycle management is to understand, model and forecast the effect of various degradation mechanisms affecting the performance of engineering systems, structures and components. The modeling of degradation in nuclear plant components is confounded by large sampling and temporal uncertainties. The reason is that nuclear systems are not readily accessible for inspections due to high level of radiation and large costs associated with remote data collection methods. The models of degradation used by industry are largely derived from ordinary linear regression methods. The main objective of this thesis is to develop more advanced techniques based on stochastic process theory to model deterioration in engineering components with the purpose of providing more scientific basis to life-cycle management of aging nuclear power plants. This thesis proposes a stochastic gamma process (GP) model for deterioration and develops a suite of statistical techniques for calibrating the model parameters. The gamma process is a versatile and mathematically tractable stochastic model for a wide variety of degradation phenomena, and another desirable property is its nonnegative, monotonically increasing sample paths. In the thesis, the GP model is extended by including additional covariates and also modeling for random effects. The optimization of age-based replacement and condition-based maintenance strategies is also presented. The thesis also investigates improved regression techniques for modeling deterioration. A linear mixed-effects (LME) regression model is presented to resolve an inconsistency of the traditional regression models. The proposed LME model assumes that the randomness in deterioration is decomposed into two parts: the unobserved heterogeneity of individual units and additive measurement errors. Another common way to model deterioration in civil engineering is to treat the rate of deterioration as a random variable. In the context of condition-based maintenance, the thesis shows that the random variable rate (RV) model is inadequate to incorporate temporal variability, because the deterioration along a specific sample path becomes deterministic. This distinction between the RV and GP models has profound implications to the optimization of maintenance strategies. The thesis presents detailed practical applications of the proposed models to feeder pipe systems and fuel channels in CANDU nuclear reactors. In summary, a careful consideration of the nature of uncertainties associated with deterioration is important for credible life-cycle management of engineering systems. If the deterioration process is affected by temporal uncertainty, it is important to model it as a stochastic process