Stochastic degradation models with several accelerating variables

Many products & systems age, wear, or degrade over time before they fail or break down. Thus, in many engineering reliability experiments, measures of degradation or wear toward failure can often be observed over a period of time before failure occurs. Because the degradation values provide additional information beyond that provided by the failure observations, both sets of observations need to be considered when doing inference on the statistical parameters of the product or system lifetime distributions. For highly-reliable modern products, it often takes much more time to obtain lifetime & degradation data under usual use conditions, and this requires one to use accelerated tests. Accelerated tests expose the products to greater environmental stress levels so that we can obtain lifetime & degradation measurements in a more timely fashion. In addition, many products are exposed to several environmental variables in some manufacturing processes, or under some operating conditions. This motivates the need for developing general accelerated test models with several accelerating variables for inference based on both observed failure values, and degradation measurements. In this paper, new accelerated test models are developed based on a generalized cumulative damage approach with a stochastic process characterizing a degradation phenomenon.     

The first passage time distribution of brownian motion and its applications

This paper traces the development of the first passage time distribution of Brownian motion (inverse Gaussian) together with its various applications in inventory problems, usage and storage times, detection theory, labor turnover, money supply, purchasing models, hospital inpatient stay times, strikes duration, biology, … etc. Besides, since the inverse Gaussian distribution arises as the distribution of first passage time of Brownian motion, its applicability to lifetime modeling is a natural consequence. The general characteristics of the inverse Gaussian model which make it attractive for various applications are also identified.     

A multiplicative damage model for strength of fibrous compositematerials

Knowledge of the tensile strength properties of a fibrous composite material is essential in the design of reliable structures from that material. Determination of statistical models for the tensile strength of a composite material which provide good fits to experimental data from tensile tests on material specimens is therefore important for engineering design. Perhaps the most commonly used statistical model is the Weibull distribution, based on `weakest link of a chain' arguments. However, in many cases the usual Weibull distribution does not adequately fit experimental data on tensile strength for composite materials made from brittle fibers such as carbon. Here, an alternative model is developed for tensile strength of carbon composites, which is based on a multiplicative cumulative-damage approach. This approach results in a 3-parameter extension of the Birnbaum-Saunders fatigue model and incorporates the material specimen size (size effect) as a known variable. This new distribution can also be written as an inverse Gaussian-type distribution, which can be interpreted as the first passage of the accumulated damage past a damage threshold, resulting in material failure. The new model fits experimental tensile-strength data, for carbon micro-composites better than existing models, providing more accurate estimates of material strength     

Mutual Information for Stochastic Signals and Fractional Brownian Motion

The mutual information between a stochastic signal and this signal plus a fractional Brownian motion (described as an additive fractional Gaussian noise channel) is expressed as the error of an estimation problem that can be naturally associated with this model. If the stochastic signal with the additive fractional Brownian motion occurs multiplied by a scalar parameter, then the rate of change of the mutual information with respect to this parameter is described by the error of another related estimation problem. These results generalize some results for a model where the fractional Brownian motion is a Brownian motion to a model with an arbitrary fractional Brownian motion.      

Product Reliability Due to Random Load Variations at Elevated Temperatures

The survival capability of mechanical equipment often depends upon creep life at elevated temperature due to irregular load variations in a random service environment. The product reliability is related to the probability distribution of the creep damage, which depends, in turn, upon the statistical behavior of the stress waveform. The general stochastic connection between them is derived in this presentation for linear damage accumulation in a material with a power law of failure. The creep damage is related to the damage rate by a stochastic integral, while the damage rate is a stochastic function of the stress intensity. The statistical behavior of the damage rate depends upon the standard deviation of a stationary, Gaussian stress variation about a zero mean stress level. This paper illustrates the specific analysis of a time-invariant, linear system for a broadband, stationary, Gaussian excitation with a zero mean value and a uniform spectral density.     

An Exponential Damage Model for Strength of Fibrous Composite Materials

When modeling experimental data observed from carefully performed tensile strength tests, statistical distributions are typically used to describe the strength of composite specimens. Recently, cumulative damage models derived for predicting tensile strength have been shown to be superior to other models when used to fit composite strength data. Here, an alternative model is developed which is based on an exponential cumulative damage approach. The model is shown to exhibit a similar structural form to the other models in the literature so that previous theory for cumulative damage models can be utilized to find parameter estimates.     

A generalized SSI reliability model considering stochastic loading and strength aging degradation

A generalized stress-strength interference (SSI) reliability model to consider stochastic loading and strength aging degradation is presented in this paper. This model conforms to previous models for special cases, but also demonstrates the weakness of those models when multiple stochastic elements exist. It can be used for any nonhomogeneous Poisson loading process, and any kind of strength aging degradation model. To solve the SSI reliability equation, a numerical recurrence formula is presented based on the Gauss-Legendre quadrature formula to calculate multiple integrations of a random variable vector. Numerical analysis of three examples shows this SSI reliability model provides accurate results for both homogeneous & nonhomogeneous Poisson loading processes.     

Modeling and analysis of stochastic differential equations driven by point processes

The modeling and analysis of nonlinear systems described by differential equations driven by point process noise are considered. The stochastic calculus of McShane is generalized to include such differential equations, and a more general canonical extension is defined. It is proved that this canonical extension possesses the same desirable properties for point process noise that it does for the noise processes, such as Brownian motion, considered by McShane. In addition, a new stochastic integral with respect to a point process is defined; this alternative integral obeys the rules of ordinary calculus. As a special case of the analysis of such systems, linear systems with multiplicative point process noise are investigated. The consistency of the canonical extension is studied by means of the product integral. Finally, moment equations and criteria for the stochastic stability of linear systems with multiplicative Poisson noise are derived.     

Direct-Detection Optical Communication Receivers

A model that is sufficiently general to describe the predominant statistical characteristics of the output of many real optical detectors is formulated. This model is used to study the optimum receiver processing for direct-detection optical communication systems. In particular, the structures of detectors and estimators for randomly filtered doubly stochastic Poisson processes observed in additive white Gaussian noise are considered. Representations for the posterior statistics of a vector-valued Markov process that modulates the intensity of the doubly stochastic Poisson process are obtained. Quasi-optimum estimators and detectors are specified in general terms and specialized for several important applications. These include a demodulator for subcarrier angle modulation, a detector structure for binary signaling with known intensities, and a detector structure for binary signaling in the turbulent atmosphere.     

Coupling damage and reliability modeling for creep and fatigue of solder joint

Solder joint often plays a crucial role in the normal operation of electronic equipment due to its unique material properties and harsh working condition, making it very important to carry out the accurate reliability analysis of solder joint. The low-cycle fatigue due to temperature cycling and the creep brought by continuous high temperature are two dominant failure modes of the solder joint. Current modeling methods for these two mechanisms mainly focus on failure process of each mechanism separately, with little consideration of the coupling relationship in the material properties. This paper introduces a coupling damage model considering both low-cycle fatigue and creep. The coupling relationship between these two failure mechanisms is investigated with the effects of creep strain rate on the ductility and the effects of damage on mechanical properties of solder joint. The analysis of the former mechanism concerns the fatigue parameter of Coffin-Manson model, while the latter one focuses on the applied stress increasing with the accumulation of damage. Further, considering that creep degradation rate would increase once the cumulative damage reaches a trigger threshold, a generalized cumulative damage model is developed. Based on this assumption, a reliability model for solder joint considering the uncertainty of model parameters is then proposed. Finally, a case study of a lead-free solder joint is given to validate this method.     

干涉图幅度统计分布模型族及其参数估计

提出了新的干涉图幅度分布模型族及对应的参数估计器.首先,在乘积模型框架下,以复Wishart分布为基础,通过引入场景环境分类的思想,利用具备真实地物RCS分量精确建模能力的逆方根Gamma分布和广义逆Gauss方根分布,推导建立了理论完善的新的干涉图幅度分布模型族:E-Gamma分布、E-G0分布和E-G分布,解决了均匀度变化下的广泛区域对应的干涉图幅度数据的精确建模问题,实现了单通道SAR图像建模理论到多通道SAR干涉图幅度建模的拓展与统一;其次,基于Mellin变换导出了各新分布模型的参数估计器:E-Gamma_MoLC、E-G0_MoLC和E-G_MoLC,新估计器能够快速、准确地迭代出各分布参数的估计值.以KL度量、MSE度量和K-S检验作为定量评估准则,对星载多通道SAR实测数据对应的干涉图进行实验,结果证明了所提模型族及对应参数估计器的有效性.     

An extended Suzuki model for land mobile satellite channels and itsstatistical properties

This paper deals with the statistical characterization of a stochastic process which is a product of a Rice and lognormal process. Thereby, we consider the more general case where the two Gaussian noise processes describing the Rice process are correlated. The resulting process are named as extended Suzuki process, which can be used as a suitable statistical model for describing the fading behavior of large classes of frequency nonselective land mobile satellite channels. In particular, the statistical properties (e.g., probability density function (pdf) of amplitude and phase, level-crossing rate, and average duration of fades) of the Rice process with cross-correlated components as well as of the proposed extended Suzuki process are investigated. Moreover, all statistical model parameters are optimized numerically to fit the cumulative distribution function and the level-crossing rate of the underlying analytical model to measured data collected in different environments. Finally, an efficient simulation model is presented which is in excellent conformity with the proposed analytical model     

Graphical Analysis of Accelerated Life Test Data with the Inverse Power Law Model

In this paper, graphical methods are presented for analyzing accelerated life test data with the inverse power law model, when all test units are run to failure. The inverse power law model is described, and graphical methods for estimating its parameters from such complete data are given. These methods are illustrated with accelerated test data on time to breakdown of an insulating fluid. While the methods are presented with the inverse power law model, they can be used for analyzing many other accelerated life test situations. These methods are presented so that they can be used by individuals with a limited statistical background.     

Object-based estimation of dense motion fields

Motion estimation belongs to key techniques in image sequence processing. Segmentation of the motion fields such that, ideally, each independently moving object uniquely corresponds to one region, is one of the essential elements in object-based image processing. This paper is concerned with unsupervised simultaneous estimation of dense motion fields and their segmentations. It is based on a stochastic model relating image intensities to motion information. Based on the analysis of natural images, a region-based model of motion-compensated prediction error is proposed. In each region the error is modeled by a white stationary generalized Gaussian random process. The motion field and its segmentation are themselves modeled by a compound Gibbs/Markov random field accounting for statistical bindings in spatial direction and along the direction of motion trajectories. The a posteriori distribution of the motion field for a given image sequence is formulated as an objective function, such that its maximization results in the MAP estimate. A deterministic multiscale relaxation technique with regular structure is employed for optimization of the objective function. Simulation results are in a good agreement with human perception for both the motion fields and their segmentations.     

Fatigue Failure Models?Birnbaum-Saunders vs. Inverse Gaussian

The assumption of a common underlying failure process leads to both the inverse Gaussian distribution and the fatigue life distribution of Birnbaum & Saunders. The first is obtained by an exact derivation while the second involves certain approximations. Although both of these distributions fit many failure data well, the inverse Gaussian distribution enjoys a distinct advantage in regard to the availability of procedures for a sound statistical analysis and tractability of the sampling distributions.     

Statistical characterization of the Jones matrix of long fibers affected by polarization mode dispersion (PMD)

The unitary transfer matrix of a fiber affected by polarization mode dispersion (PMD) is analyzed using the Stokes representation of its eigenmodes and its retardation angle, or equivalently through its Pauli coordinates. We develop a statistical theory applied to these parameters and relate it to the extensive existing literature on the statistics of the PMD vector Dynamical equations are established for the Pauli coordinates. Assuming a standard "white Gaussian" model for the local birefringence, and using the tools of stochastic calculus, we derive the distributions of the eigenmodes, the retardation angle, the Pauli coordinates, and of the frequency derivatives of all these parameters. The evolution in space of the Pauli coordinates is also characterized as a standard Brownian motion on the unit sphere in /spl Rfr//sup 4/. An expression for the frequency autocorrelation function of the Pauli coordinates, the eigenmodes and the retardation angle is derived and their coherence bandwidth is compared to that of the PMD vector. All theoretical results are supported by simulation over an ensemble of 10000 fibers, using the standard retarder plate model.     

Characterization of interfacial adhesion damage induced byaccelerated life testing

The purpose of this effort was to characterize statistically and experimentally the interfacial adhesion damage of generic dual in-line packages (DIP's) exposed to accelerated stress conditions. DIP's, consisting of three parallel gold conductors in a meander pattern on a 24 pin Al₂O₃ ceramic substrate spin-coated with Pyralin PI-2555 polyimide with and without an adhesion promoter (APS), were chosen as the test vehicles. Leakage current measurements and optical microscopy were employed to monitor the degradation process at the interface between the polyimide and the substrate. In order to characterize the damage adequately, the entire surface of each DIP was analyzed. A two-parameter Frechet cumulative distribution function (cdf) was found to be excellent for characterizing the statistical scatter in the geometrical features, such as, the cross-sectional area of the damage located over the interface. It was observed that the adhesion damage tends to be larger and clustered for more severe testing conditions. It was demonstrated that APS statistically improves long-term reliability. Furthermore, interfacial adhesion damage was not initiated solely by contamination at the interface     

Limiting forms of the discrete-time estimator- correlator detector (Corresp.)

Starting with the canonical discrete-time detection formula for random signals in Gaussian noise, we demonstrate how different noise models lead to different limiting forms Of the detector. A Brownian motion model leads to the well-known estimator-correlator formula. With a band-limited white noise model, the limiting form contains an additional term: the posterior conditional variance. This second form, which is the Radon-Nikodym derivative of two finitely additive Gaussian measures, was derived by Balakrishnan using a different formulation [10]. We thus provide an alternative development and interpretation of this second detector, and illustrate the effect of model assumptions on going from discrete-time to continuous-time problems.     

Some properties of confidence bounds on reliability estimation for parts under varying stresses

Reliability estimation is usually performed on a part under a constant stress level. However, a part could experience several different stress levels, or profiled stress, during its lifetime. One such example is when the part is subject to step-stress accelerated life testing. Studying the reliability estimation & its confidence bounds for a part under varying stresses will generalize the existing estimation methods for accelerated life testing. In this paper, we derive the reliability function of a part under varying stresses based on a Weibull failure time distribution, and cumulative damage model. The reliability confidence bounds, based on a s-normal approximation, are given explicitly, and their limiting properties are discussed. A step-stress accelerated life testing example is used to illustrate these interesting properties, which provides the insights of the limitation of the current test plan, and how to design a better one.     

Statistical Models for Fading and Shadowed Fading Channels in Wireless Systems: A Pedagogical Perspective

A unified analysis of statistical models for describing fading, shadowing, and shadowed fading channels is presented from a pedagogical viewpoint. The different probability density functions such the Rayleigh, Nakagami, gamma, generalized gamma, Weibull, lognormal, Nakagami-lognormal, K distribution, generalized K distribution, and Nakagami inverse Gaussian distribution are presented and the relationships among them are detailed. These density functions are compared in terms of two quantitative measures, namely the amount of fading and outage probability. A general approach to fading and shadowed fading channels using a cluster based approach is also presented to link several of the distributions. It is expected that this overview will be very helpful to students and educators who are engaged in the study of wireless systems and the adverse impact of fading and shadowing in wireless data transmission.