Review: likelihood method for fitting Weibull log-linear models toaccelerated life-test data

The analysis of data from accelerated life-test experiments via the method of maximum likelihood estimation must, for a Weibull log-linear model, be performed numerically. This paper promotes a particular log-likelihood as the basis for such inferences, and introduces notation and formulae to aid the implementation of various numerical methods. Two examples illustrate the performance of a widely-used maximization technique; these examples indicate that the performance of this technique compares favorably with that from commercially available software     

Fitting the Weibull log-linear model to accelerated life-test data

The Weibull log-linear model is a widely-used accelerated life-test model in reliability engineering. The standard deviation of log(life), s, was often assumed to be a constant or stress-independent. However, theoretical and experimental research results suggest that, in many cases, s is stress-dependent. The data analysis via the MLE method must be performed numerically, because of the complexity of the model and many unknown parameters being involved. The commonly-used methods often fail to converge when the starting point is not close to the solution, especially for censored data. Generally, no easy-to-use software is available for the Weibull log-linear model. To facilitate this process, an efficient algorithm is presented in this paper, to obtain the MLE of the model parameters from test data (with or without censoring) for both stress-independent and stress-dependent models. The validity and effectiveness of this procedure are illustrated with numerical examples. The method is numerically stable, and easy to implement and program     

Accelerated Life Testing?Step-Stress Models and Data Analyses

This paper presents statistical models and methods for analyzing accelerated life-test data from step-stress tests. Maximum likelihood methods provide estimates of the parameters of such models, the life distribution under constant stress, and other information. While the methods are applied to the Weibull distribution and inverse power law, they apply to many other accelerated life test models. These methods are illustrated with step-stress data on time to breakdown of an electrical insulation.     

Bayes parameter estimation for the bivariate Weibull model ofMarshall-Olkin for censored data [reliability theory]

Industrial applications frequently require statistical procedures to analyze life-test data from various sources, particularly in situations where observations are limited. The author develops a Bayes parameter estimation method for bivariate censored data collected from both system and component levels. The bivariate Weibull distribution of Marshall & Olkin (1967) is used to model lifetimes of components in a two-component system. Closed-form Bayes estimators of the model parameters are proposed along with their variances and high-probability density intervals     

Classes of Discrete Decreasing and Increasing Mean-Residual-Life Distributions

Discrete failure-time distributions can be appropriate to model lifetimes. This paper represents two well-known non-parametric families of discrete distributions: decreasing and increasing mean-residual-life. It provides two parametric families of discrete distributions which are suitable for fitting decreasing and increasing mean-residual-life models to discrete life-test data.     

Early-life reliability prediction methodology for integrated circuits

A methodology for predicting early failures due to random process flaws in integrated circuits is proposed. Early failures are not intrinsic failures, and therefore the current practice of extrapolating intrinsic life-test distributions to estimate early-life reliability is incorrect and yields optimistic results. Early failure mechanisms are classified into three categories based on the physical understanding and statistical data available for the mechanism. Subpopulations with defect-related failure distributions are characterized by a knowledge of the effects of defects in category one and using past field return data in category two. The third category, associated with failures due to applied overstress or misuse, iis characterized by field return, technology and design data. Modeling early failures at the ‘micro’ level (subsystem level) is an improvement over the existing practice of characterizing infant mortality based on field returns at the ‘macro’ level (chip level). Using the proposed methodology, process and design improvements can be incorporated in the early failure predictions. Examples showing the application of this methodology are included.     

User behavior modeling of voice communications: an empirical study

In this study, analysis and modeling of arrival and service processes are presented in a comprehensive fashion in order to determine statistical properties of voice traffic from end‐user perspective in accordance with the queueing theory. For the first time in the literature, we introduce a user centric approach and examine these services considering both flow directions of voice traffic, the uplink and the downlink as opposed to existing studies with the network centric approach. In our study, we use experimental data composed of actual phone calls collected from 2G/3G networks. To achieve this, we designed and implemented a data collection system for mobile users and compared the results by using data from an operational cellular network. In order to determine the time correlation of voice calls, Hurst parameter estimation methods are used. On the basis of the outcomes, independency of call arrivals is shown. Additionally, it is shown that calls acquired from user and network centric approaches are both Poisson distributed. Next, looking at the problem from service process perspective, thorough analyses are performed to determine mathematical models that can best characterize call holding times. Maximum likelihood estimation and expectation maximization algorithm are used, and it is shown that the optimum mathematical model for the characterization of call holding times is the lognormal distribution family. Copyright © 2014 John Wiley & Sons, Ltd.     

Estimation of Weibull Shape-Parameters for Two Independent Competing Risks

This paper presents a technique to estimate Weibull shape parameters of life distribution of two components in a series system. The data consist of lifetime of the system only, that is, it is not known which component caused the system failure. The relations among cumulative hazard functions of the system at virtual observation limit are used for estimation. This technique is useful for 1) analysing this common kind of life-test data, and 2) estimating parameters of the smallest extreme value distribution. A numerical example including the experimental data on electron tubes is discussed briefly.     

Reliability of an Electronic Assembly: A Case History

This article describes the work done in evaluating the reliability of a printed-circuit-card assembly. Some assemblies went through thermal shock, humidity, and power-temperature cycling. A model was developed for interpreting a long term, high temperature life-test. Two iterations of the life test took place as part of the evaluation. A short term, intermediate temperature life-test of a relatively large number of assemblies preceded release to manufacturing.     

Variational data assimilation of microwave radiobrightnessobservations for land surface hydrology applications

Our ability to accurately describe large-scale variations in soil moisture is severely restricted by process uncertainty and the limited availability of appropriate soil moisture data. Remotely sensed microwave radiobrightness observations can cover large scales but have limited resolution and are only indirectly related to the hydrologic variables of interest. The authors describe a four-dimensional (4D) variational assimilation algorithm that makes best use of available information while accounting for both measurement and model uncertainty. The representer method used is more efficient than a Kalman filter because it avoids explicit propagation of state error covariances. In a synthetic example, which is based on a field experiment, the authors demonstrate estimation performance by examining data residuals. Such tests provide a convenient way to check the statistical assumptions of the approach and to assess its operational feasibility. Internally computed covariances show that the estimation error decreases with increasing soil moisture. An adjoint analysis reveals that trends in model errors in the soil moisture equation can be estimated from daily L-band brightness measurements, whereas model errors in the soil and canopy temperature equations cannot be adequately retrieved from daily data alone. Nonetheless, state estimates obtained from the assimilation algorithm improve significantly on prior model predictions derived without assimilation of radiobrightness data     

Software reliability estimations for telecommunications products

Reliability of software used in telecommunications networks is a crucial determinant of network performance. Software reliability (SR) estimation is an important element of a network product's reliability management. In particular, SR estimation can guide the product's system testing process and releasability decisions. SR estimation is performed using an appropriate SR estimation model. However, the art of SR estimation is still evolving. There are many available SR estimation models to select from, with different models being appropriate for different applications. Although there is no “ultimate” and “universal” SR model on the horizon (and there may not be one in the foreseeable future), methods have been developed for selecting a trustworthy SR model for each application. The present authors have been analyzing and adapting these methods for applicability to network software. Their results indicate that there already exist methods for SR model selection which are practical to use for telecommunications software. If utilized, these methods can promote significant improvements in SR management. The paper presents the results to date     

基于GNSS的武汉区域电离层TEC建模

为研究适用于区域电离层总电子含量(total electron content, TEC)建模的方法和估计策略,对传统单层假设下的几种建模方法和估计策略进行了比较分析. 基于我国中纬度武汉地区17个连续运行参考站的数据进行TEC建模,建模方法分别采用4×3阶多项式模型、2阶多项式模型、4阶球谐级数模型,估计策略使用分段常数估计策略和分段线性估计策略. 在传统单层假设的基础上,本文还提出了三层电离层TEC模型,该模型可以分别给出底部电离层、峰高电离层和顶部电离层的TEC. 研究结果表明,几种模型的天顶方向总电子含量拟合效果和欧洲轨道确定中心公布的电离层格网地图均具有较好的一致性,其中4阶球谐级数模型和分段线性估计策略效果最佳. 通过三层电离层模型,可以得到TEC与电离层高度之间的关系,多层电离层模型对空间目标监视和低轨卫星航天测控具有重要应用价值.     

Failure rate prediction of optical semiconductor devices

The failure modes of optical semiconductor devices are classified into wear-out and random failures. The failure rate estimation methods are also presented for each mode using lognormal and exponential distributions. Moreover, based on the life-test data of InGaAsP/InP DH LDs and Ge-APDs as concrete examples, statistical analysis is carried out for the wear-out mode. This analysis suggests some problems underlying the high-reliability assurance of these devices. Finally, the testing scale and conditions are statistically investigated to confirm the random failure rates of 300 FITs for LDs and 3 FITs for Ge-APDs assuming the temperature dependency of the failure rate obeys the Arrhenius law.     

Estimation of threshold stress in accelerated life-testing

The author presents a method that uses accelerated life-test data to estimate the mean life at the service stress and the threshold stress below which a failure is unlikely to occur. The relation between stress and mean-life at that stress is assumed to follow an inverse power law that includes a threshold stress. The failure times at a given stress are assumed to follow a Weibull distribution in which the shape parameter varies with the stress. This model extends the well-known Weibull inverse power law model. If only the mean life but not a specific percentile point at a service stress is sought, the maximum likelihood method is useful for parameter estimation. This is a tradeoff in the parametric approach. For adoption of an appropriate probability model, the likelihood ratio test as well as the Akaike Information Criterion are used. Type I right censored data are considered. Extensions of the method are discussed     

Blind Channel Estimation in Multicode CDMA Using Multiantenna Receiver

In this paper blind channel estimation methods for long code CDMA system with multicode transmission are proposed. By allocating multiple codes, higher data rates may be provided to a user. Blind channel estimation allows reducing pilot signaling. Hence, higher effective data rates may be achieved and larger sample support may be obtained by using both the information symbols and known pilot symbols for channel estimation. Algorithms are extended to multi-antenna receiver which further improves the performance. The performance of the algorithms is studied in extensive simulations using WCDMA system model. The effects of code selection, interference and noise, number of antennas, antenna correlation are considered using frequency selective channel models. The proposed methods are more robust in the face of interference and code selection than the well-known subspace method in [7]. The computational complexity is lower as well.     

Early signatures for REDR-based laser degradations

The basic theory for Recombination Enhanced Defect Reaction (REDR) as responsible for sudden failures in 980 nm SL SQW InGaAs pump laser diodes is here tested on experimental constant-current life-test data. A link between the occurrence of long term sudden failures and early detectable signatures has been looked for. For a specific case, where the reacting defects may display saturation effects on their recombination efficiency, a possible screening method may be proposed, able to individuate the great majority of sudden failures at about 1000 hours by inspecting data at 20 hours.     

Robust least-squares estimation with a relative entropy constraint

Given a nominal statistical model, we consider the minimax estimation problem consisting of finding the best least-squares estimator for the least favorable statistical model within a neighborhood of the nominal model. The neighborhood is formed by placing a bound on the Kullback-Leibler (KL) divergence between the actual and nominal models. For a Gaussian nominal model and a finite observations interval, or for a stationary Gaussian process over an infinite interval, the usual noncausal Wiener filter remains optimal. However, the worst case performance of the filter is affected by the size of the neighborhood representing the model uncertainty. On the other hand, standard causal least-squares estimators are not optimal, and a characterization is provided for the causal estimator and the corresponding least favorable model. The causal estimator takes the form of a risk-sensitive estimator with an appropriately selected risk sensitivity coefficient.     

Comparison of residence time estimation methods for radioimmunotherapy dosimetry and treatment planning--Monte Carlo simulation studies

Estimating the residence times in tumor and normal organs is an essential part of treatment planning for radioimmunotherapy (RIT). This estimation is usually done using a conjugate view whole body scan time series and planar processing. This method has logistical and cost advantages compared to 3-D imaging methods such as Single photon emission computed tomography (SPECT), but, because it does not provide information about the 3-D distribution of activity, it is difficult to fully compensate for effects such as attenuation and background and overlapping activity. Incomplete compensation for these effects reduces the accuracy of the residence time estimates. In this work we compare residence times estimates obtained using planar methods to those from methods based on quantitative SPECT (QSPECT) reconstructions. We have previously developed QSPECT methods that provide compensation for attenuation, scatter, collimator-detector response, and partial volume effects. In this study we compared the use of residence time estimation methods using QSPECT to planar methods. The evaluation was done using the realistic NCAT phantom with organ time activities that model (111)In ibritumomab tiuxetan. Projection data were obtained using Monte Carlo simulations (MCS) that realistically model the image formation process including penetration and scatter in the collimator-detector system. These projection data were used to evaluate the accuracy of residence time estimation using a time series of QSPECT studies, a single QSPECT study combined with planar scans and the planar scans alone. The errors in the residence time estimates were 3.8%, 15%, and 2%-107% for the QSPECT, hybrid planar/QSPECT, and planar methods, respectively. The quantitative accuracy was worst for pure planar processing and best for pure QSPECT processing. Hybrid planar/QSPECT methods, where a single QSPECT study was combined with a series of planar scans, provided a large and statistically significant improvement in quantitative accuracy for most organs compared to the planar scans alone, even without sophisticated attention to background subtraction or thickness corrections in planar processing. These results indicate that hybrid planar/QSPECT methods are generally superior to pure planar methods and may be an acceptable alternative to performing a time series of QSPECT studies.     

ML parameter estimation for Markov random fields with applicationsto Bayesian tomography

Markov random fields (MRFs) have been widely used to model images in Bayesian frameworks for image reconstruction and restoration. Typically, these MRF models have parameters that allow the prior model to be adjusted for best performance. However, optimal estimation of these parameters (sometimes referred to as hyperparameters) is difficult in practice for two reasons: (i) direct parameter estimation for MRFs is known to be mathematically and numerically challenging; (ii) parameters can not be directly estimated because the true image cross section is unavailable. We propose a computationally efficient scheme to address both these difficulties for a general class of MRF models, and we derive specific methods of parameter estimation for the MRF model known as generalized Gaussian MRF (GGMRF). We derive methods of direct estimation of scale and shape parameters for a general continuously valued MRF. For the GGMRF case, we show that the ML estimate of the scale parameter, sigma, has a simple closed-form solution, and we present an efficient scheme for computing the ML estimate of the shape parameter, p, by an off-line numerical computation of the dependence of the partition function on p. We present a fast algorithm for computing ML parameter estimates when the true image is unavailable. To do this, we use the expectation maximization (EM) algorithm. We develop a fast simulation method to replace the E-step, and a method to improve the parameter estimates when the simulations are terminated prior to convergence. Experimental results indicate that our fast algorithms substantially reduce the computation and result in good scale estimates for real tomographic data sets.     

Comment on “Electromagnetic missile launched from a uniformcurrent sheet of arbitrary shape”

For original paper, see Zhan and Wan (IEEE Trans. Electromagn. Compat. vol.33, no.1, p.61-3, Feb. 1991). Theoretical findings by Wu (1985) of some previously unexpected behaviors of the energy flux carried by a very-broad-band pulse makes it desirable to investigate the electromagnetic missile (EMM) launchers. Previously, current pulse distributions over a surface, or along a line, or a point source in certain reflecting or defracting systems, have been investigated. Some authors have begun to investigate an arbitrary current distribution for EMM launchers. The present authors think that this is possible directly. A circular current plate with a proper time characteristic has been found that can radiate an EMM. One may think of a current with a proper time characteristic of arbitrary shape, to be comprised of many circular current distributions whose radii are very small. Each circular current can generate an EMM on its center axis, thus a current of arbitrary shape is capable of launching an EMM over the area equal to that of the shape. Zhan and Wan tried to prove the idea in the time domain. The results show that it seems to be exact, but there is a problem in the process of the derivation. By discussing the problem, the present authors point out an additional conclusion that only a current with a proper time characteristic can generate an EMM