The widespread use of flip-chip technology in the field of microelectronics packaging makes defect detection technology face great challenges, which requires the development of detection technology with less manual intervention, a lightweight network architecture, and high precision. Aiming at the dual-stability of the neural architecture search (NAS), and explicitly associating the network architecture searched by NAS with the architecture features of vibration signals. This study proposes a dual-convergence sparse feature extractor (DSFE) for visualization vibration signals architecture feature searching, which attempts to learn a representation whose architecture feature can uniquely represent the intrinsic information of the target signal. DSFE analyzed and summarized three deficiencies of gradient-based NAS, namely, “huge GPU memory consumption,” “high collapse probability,” and “rigid number of node precursor operations.” The corresponding solution modules are proposed in turn, which are “primary and secondary search spaces,” “skip_connect coefficient modification,” and “dynamic sparse selection of precursor operations.” The effectiveness of DSFE is verified with flip-chip vibration signals excited by the air-coupled ultrasonic wave. By comprehensive comparative experiments with fixed-structure networks and gradient-based NAS methods, it is proved that DSFE cannot only achieve dual-stability of detection precision and architecture searched, but also ensure less resource consumption and multifarious architecture, which can broaden the application scope of DSFE in practical engineering.

The large-scale retirement of electric vehicle traction batteries poses a huge challenge to environmental protection and resource recovery since the batteries are usually replaced well before their end of life. Direct disposal or material recycling of retired batteries does not achieve their maximum economic value. Thus, the second-life use of EV batteries has become the most economical and environmentally friendly solution. However, there are still many issues facing second-life batteries (SLBs). To better understand the current research status, this article reviews the research progress of second-life lithium-ion batteries for stationary energy storage applications, including battery aging mechanisms, repurposing, modeling, battery management, and optimal sizing. Energy management strategies are reviewed to maximize the economic benefits for SLBs, and the less-demanding applications of SLBs are presented. The technical challenges and future development trends of battery reusing technologies are also discussed. Finally, the conclusions and relevant recommendations for future studies are summarized.

Wheelset intermittent over-creeps (WIOs), i.e., slips or slides, can decrease the overall traction and braking performance of Electric Multiple Units (EMUs). However, they are difficult to detect and isolate due to their small magnitude and short duration. This paper presents a new index called variable-to-minimum difference (VMD) and a novel technique called weighted moving average (WMA). Their combination, i.e., the WMA-VMD index, which uses correlation information to find an optimal weight vector (OWV) for the VMD indices within a time window, is employed to detect and isolate WIOs in real time. The uniqueness of the OWV is proven, and its properties such as the symmetrical structure are revealed. WIO detectability and isolability conditions of the WMA-VMD index are provided, leading to the property analyses of two nonlinear, discontinuous operators,$\min $and VMDi. Experimental studies are conducted based on practical running data and a hardware-in-the-loop platform of an EMU, which show the effectiveness of the developed method.

This article develops new deep learning methods, namely, deep residual shrinkage networks, to improve the feature learning ability from highly noised vibration signals and achieve a high fault diagnosing accuracy. Soft thresholding is inserted as nonlinear transformation layers into the deep architectures to eliminate unimportant features. Moreover, considering that it is generally challenging to set proper values for the thresholds, the developed deep residual shrinkage networks integrate a few specialized neural networks as trainable modules to automatically determine the thresholds, so that professional expertise on signal processing is not required. The efficacy of the developed methods is validated through experiments with various types of noise.

Data-driven fault diagnostics of industrial systems suffer from class-imbalanced problems, which is a common challenge for machine learning algorithms as it is difficult to learn the features of the minority class samples. Synthetic oversampling methods are commonly used to tackle these problems by generating minority class samples to balance the majority and minority classes. Two major issues will influence the performance of oversampling methods which are how to choose the most appropriate existing minority seed samples, and how to synthesize new samples from seed samples effectively. However, many existing oversampling methods are not accurate and effective enough to generate new samples when dealing with high-dimensional faulty samples with different imbalanced ratios, since they do not take these two factors into consideration at the same time. This article develops a novel adaptive oversampling technique: expectation maximization (EM)-based local-weighted minority oversampling technique for industrial fault diagnostics. This method uses a local-weighted minority oversampling strategy to identify hard-to-learn informative minority fault samples and an EM-based imputation algorithm to generate fault samples based on the distribution of minority samples. To validate the performance of the developed method, experiments were conducted on two real-world datasets. The results show that the developed method can achieve better performances, in terms of F-measure, Matthews correlation coefficient (MCC), and Mean (average of F-measure and MCC) values, on multiclass imbalanced fault diagnostics in different imbalance ratios than state-of-arts' baseline sampling techniques.

In this paper, new modified configurations of CUK converter are proposed for high-voltage/low-current applications with the employment of multiple Voltage Lift Switched Inductor (VLSI) modules. Proposed CUK converter configurations are designed based on the placement of VLSI modules in modified CUK converter named as MCCVLSI-XYL, MCCVLSI-LYZ, MCCVLSI-XLZ, and MCCVLSI-XYZ. The mathematical evaluation of each configuration is done to find out the voltage conversion ratio. The outstanding qualities of the proposed CUK configurations are discussed in the paper. Also, the operating modes of MCCVLSI-XYZ configuration are discussed. Moreover, the proposed configurations are compared with non-inverting converters in terms of voltage gain and to each other in terms of reactive components, and semiconductor devices. The functionalities and performance of the proposed converters are verified by MatLab (R2016a) simulation results and which are always show a good agreement with the theoretical analysis.

Many industrial systems inevitably suffer performance degradation. Thus, predicting the remaining useful life (RUL) for such degrading systems has attracted significant attention in the prognostics community. For some systems like batteries, one commonly encountered phenomenon is that the system performance degrades with usage and recovers in storage. However, almost all of the current prognostic studies do not consider such a recovery phenomenon in stochastic degradation modeling. In this paper, we present a prognostic model for deteriorating systems experiencing a switching operating process between usage and storage, where the system degradation state recovers randomly after the storage process. The possible recovery from the current time to the predicted future failure time is incorporated in the prognosis. First, the degradation state evolution of the system is modeled through a diffusion process with piecewise but time-dependent drift coefficient functions. Under the concept of first hitting time, we derived the lifetime and RUL distributions for systems with specific constant working mode. Further, we extended the results of RUL distribution in specific constant working mode to the case of stochastic working mode, which is modeled through a flexible two-state semi-Markov model (SMM) with phase-type distributed interval times. The unknown parameters in the present model are estimated based on the observed condition monitoring data of the system, and the SMM model is identified on the basis of the operating data. A numerical study and a case study of Li-ion batteries are carried out to illustrate and demonstrate the proposed prognostic method. Experimental results indicate that the presented method can improve the accuracy of lifetime and RUL estimation for systems with state recovery.

The papers in this special section focus on the topic of industrial sensing intelligence. Examines the sensor and communications technologies that support these services and reports on industrial applications for their use.

Today's decreasing product development cycle time requires rapid and cost-effective reliability analysis and testing. Qualification is the process of demonstrating that a product is capable of meeting or exceeding specified requirements. Light-emitting diode (LED) qualification tests are often as long as 6000 h, but this length of time does not guarantee the typically required lifetime of 10 years or more. This paper presents a prognostics-based technique that reduces the LED qualification time. An anomaly detection technique called the similarity-based metric test is developed to identify anomalies without utilizing historical libraries of healthy and unhealthy data. The similarity-based metric test extracts features from the spectral power distributions (SPDs) using peak analysis, reduces the dimensionality of the features using principal component analysis, and partitions the data set of principal components into groups using a k-nearest neighbor (KNN)-kernel density-based clustering technique. A detection algorithm then evaluates the distances from the centroid of each cluster to each test point and detects anomalies when the distance is greater than the threshold. From this, the dominant degradation processes associated with the LED die and phosphors in the LED package can be identified. In our case study, anomalies were detected at less than 1200 h using the similarity-based metric test. Thus, our method could decrease the amount of LED qualification testing time by providing users with an earlier time to begin remaining useful life prediction without waiting 6000 h as required by industrial standards.

Counterfeit electronics have been reported in a wide range of products, including computers, medical equipment, automobiles, avionics, and military systems. Counterfeiting is a growing concern for original equipment manufacturers (OEMs) in the electronics industry. Even inexpensive passive components such as capacitors and resistors are frequently found to be counterfeit, and their incorporation into electronic assemblies can cause early failures with potentially serious economic and safety implications. This study examines counterfeit electrolytic capacitors that were unknowingly assembled in power supplies used in medical devices, and then failed in the field. Upon analysis, the counterfeit components were identified, and their reliability relative to genuine parts was assessed. This paper presents an offline reliability assessment methodology and a systematic counterfeit detection methodology for electrolytic capacitors, which include optical inspection, X-Ray examination, weight measurement, electrical parameter measurement over temperature, and chemical characterization of the electrolyte using Fourier Transform Infrared Spectroscopy (FTIR) to assess the failure modes, mechanisms, and reliability risks. FTIR was successfully able to detect a lower concentration of ethylene glycol in the counterfeit capacitor electrolyte. In the electrical properties measurement, the distribution of values at room temperature was broader for counterfeit parts than for the authentic parts, and some electrical parameters at the maximum and minimum rated temperatures were out of specifications. These techniques, particularly FTIR analysis of the electrolyte and electrical measurements at the lowest and highest rated temperature, can be very effective to screen for counterfeit electrolytic capacitors.

A hard disk drive (HDD) failure may cause serious data loss and catastrophic consequences. Online health monitoring provides information about the degradation trend of the HDD, and hence the early warning of failures, which gives us a chance to save the data. This paper developed an approach for HDD anomaly detection using Mahalanobis distance (MD). Critical parameters were selected using failure modes, mechanisms, and effects analysis (FMMEA), and the minimum redundancy maximum relevance (mRMR) method. A self-monitoring, analysis, and reporting technology (SMART) data set is used to evaluate the performance of the developed approach. The result shows that about 67% of the anomalies of failed drives can be detected with zero false alarm rate, and most of them can provide users with at least 20 hours during which to backup the data.

Degradation signals that reflect a system's health state are important for diagnostics and health management of complex systems. However, degradation signals are often compounded and contaminated by measurement errors, making data analysis a difficult task. Motivated by the wear problem of magnetic heads used in hard disk drives (HDDs), this paper investigates Wiener processes with measurement errors. We explore the traditional Wiener process with positive drifts compounded with i.i.d. Gaussian noises, and improve its estimation efficiency compared with the existing inference procedure. Furthermore, to capture the possible heterogeneity in a population, we develop a mixed effects model with measurement errors. Statistical inferences of this model are discussed. The mixed effects model subsumes several existing Wiener processes as its limiting cases, and thus it is useful for suggesting an appropriate Wiener process model for a specific dataset. The developed methodologies are then applied to the wear problem of magnetic heads of HDDs, and a light intensity degradation problem of light-emitting diodes.

There is no standard method for creating a hardware reliability prediction. Therefore, predictions vary widely in terms of methodological rigor, data quality, extent of analysis, and uncertainty. Documentation of the prediction process employed is often not presented. These inconsistencies can leave the user of the prediction confused, uncertain of the prediction's true value, and unable to compare the results of two reliability predictions of the same hardware. IEEE has created a standard [1], IEEE 1413, that, when followed, results in consistent, complete documentation of a prediction. The prediction users can then understand the strengths and weaknesses of a prediction, and compare the value and usefulness of multiple predictions. The standard creates consistency by requiring documentation for specific processes, activities, and levels of knowledge.

Safety, mission, and infrastructure critical systems are adopting prognostics and health management, a discipline consisting of technologies and methods to assess the reliability of a product in its actual life-cycle conditions to determine the advent of failure and mitigate system risks. The output from a prognostic system is the remaining useful life of the system; it gives the decision-maker lead-time and flexibility to manage the health of the system. This paper develops a decision support model based on options theory, a financial derivative tool extended to real assets, to valuate maintenance decisions after a remaining useful life prediction. We introduce maintenance options, and develop a hybrid methodology based on Monte Carlo simulations and decision trees for a cost-benefit-risk analysis of prognostics and health management. We extend the model, and combine it with least squares Monte Carlo methods to valuate one type of maintenance options, the waiting options; their value represents the cost avoidance opportunities and revenue obtained from running the system through its remaining useful life. The methodologies in this paper address the fundamental objective of system maintenance with prognostics: to maximize the use of the remaining useful life while concurrently minimizing the risk of failure. We demonstrate the methodologies on decision support for sustaining wind turbines by showing the value of having a prognostics system for gearboxes, and determining the value of waiting to perform maintenance. The value of the waiting option indicates that having the system available throughout the predicted remaining useful life is more beneficial than having downtime for maintenance, even if there is a high risk of failure.

Remaining useful life estimation is central to the prognostics and health management of systems, particularly for safety-critical systems, and systems that are very expensive. We present a non-linear model to estimate the remaining useful life of a system based on monitored degradation signals. A diffusion process with a nonlinear drift coefficient with a constant threshold was transformed to a linear model with a variable threshold to characterize the dynamics and nonlinearity of the degradation process. This new diffusion process contrasts sharply with existing models that use a linear drift, and also with models that use a linear drift based on transformed data that were originally nonlinear. Both existing models are based on a constant threshold. To estimate the remaining useful life, an analytical approximation to the distribution of the first hitting time of the diffusion process crossing a threshold level is obtained in a closed form by a time-space transformation under a mild assumption. The unknown parameters in the established model are estimated using the maximum likelihood estimation approach, and goodness of fit measures are applied. The usefulness of the proposed model is demonstrated by several real-world examples. The results reveal that considering nonlinearity in the degradation process can significantly improve the accuracy of remaining useful life estimation.

Prognostics is an engineering discipline utilizing in-situ monitoring and analysis to assess system degradation trends, and determine remaining useful life. This paper discusses the benefits of prognostics in terms of system life-cycle processes, such as design and development, production, operations, logistics support, and maintenance. Challenges for prognostics technologies from the viewpoint of both system designers and users will be addressed. These challenges include implementing optimum sensor systems and settings, selecting applicable prognostics methods, addressing prognostic uncertainties, and estimating the cost-benefit implications of prognostics implementation. The research opportunities are summarized as well.

This paper presents a model for optimal asset maintenance inspection services. The model is designed to support through-life service in the form of multiple nested inspections and maintenance to meet defined asset availability and capability requirements, as well as achieving successful through-life technology insertions. The inspections and maintenance activities are assumed to be performed at more than one level, but nested and aimed at different types of defects or subsystems over a fixed period of time (the designed asset life). This practice is common in many industries, particularly in the defense industry. The impact of technological insertions is reflected through changes in the failure behavior of the asset. We use the delay time concept to model the failure mechanism of the asset, and the arrivals of defects are assumed to follow Poisson processes. The decision variables are the inspection intervals, while the objective function can be expressed in terms of cost, downtime, or reliability. The model is demonstrated through a numerical example. The model can be used for optimizing two-level inspection intervals with technological insertions.

For electronic systems equipped with early warning devices known as canaries, the early warning of failure can provide the opportunity for better spare-parts ordering, timely replacement of parts, and a resulting reduction in system life cycle costs. This paper presents both theoretical and simulation-based models for spare-part ordering and system replacement decisions for systems equipped with canaries. We first develop a theoretical model for the expected total cost per unit time in terms of the order interval, and maximum allowable stock level. This model is then compared with a simulation algorithm to validate the model. On the basis of the simulation algorithm, at each ordering point, we remove the constraint of a maximum allowable stock level, and order a quantity proportional to the predicted replacement quantity based on the expected number of canary warnings over the next order period. We then further expand the model to consider the risk (after a canary warning) with respect to the expected cost for delaying the replacement until the next order arrival point if a spare is not available, and then decide whether to replace the system immediately or wait. Finally, we consider the case where a preventive maintenance plan is in place. The comparison using numerical examples among all developed models and algorithms shows that the expected total operating cost in terms of inventory and maintenance is lowered significantly when the canary is used, and particularly when the risk analysis is implemented.

The earlier warning of electronic systems failure provided by canaries attached to them can effectively reduce system life cycle operational costs with respect to spare parts and replacement decisions. This paper presents a theoretical model for the derivation of the expected total cost per unit time in terms of the order interval and maximum allowable stock level.

Health monitoring is used to analyze and predict the battery health status. However, no matter what health monitoring methods and parameters are, a major aim is to improve the battery reliability through surveillance and prognostics. Hence, the latest known methods of state estimation and life prediction based on battery health monitoring are discussed in this paper. Through comparing their characteristics respectively, a prognostics-based fusion technique is proposed that combines physics-of-failure (PoF) with data-driven technology. The fusion approach not only investigates battery failure mechanism caused by environmental and internal characteristics, but also assesses parameters with aid of real-time health monitoring. The specific method is presented to realize the estimation on remaining useful life (RUL) of batteries.

We present advanced condition monitoring technology based on electrostatic induction for detecting the debris in aero-engines exhaust gas. We also discuss the key technologies related to electrostatic monitoring systems, such as sensing technology, signal processing, feature extraction, and abnormal particle identification. The finite element method and data fitting method are applied to analyze the sensing characteristics of the sensor. We apply empirical mode decomposition and independent component analysis to effectively remove the noise mixed in with the monitoring signal. Certain diagnostic features extracted from the de-noised signal are presented here. A knowledge-acquisition model based on rough sets theory and artificial neural networks is constructed to identify the abnormal particles. The experiment results show the effectiveness of the methods proposed in this paper, and provide some guidelines for future research in this field for the aviation industry.

This paper investigates the use of a one-class support vector machine algorithm to detect the onset of system anomalies, and trend output classification probabilities, as a way to monitor the health of a system. In the absence of “unhealthy” (negative class) information, a marginal kernel density estimate of the “healthy” (positive class) distribution is used to construct an estimate of the negative class. The output of the one-class support vector classifier is calibrated to posterior probabilities by fitting a logistic distribution to the support vector predictor model in an effort to manage false alarms.

The statistical bases for current models of RAID reliability are reviewed and a highly accurate alternative is provided and justified. This new model corrects statistical errors associated with the pervasive assumption that system (RAID group) times to failure follow a homogeneous Poisson process, and corrects errors associated with assuming the time-to-failure and time-to-restore distributions are exponentially distributed. Statistical justification for the new model uses theory for reliability of repairable systems. Four critical component distributions are developed from field data. These distributions are for times to catastrophic failure, reconstruction and restoration, read errors, and disk data scrubs. Model results have been verified and predict between 2 to 1,500 times as many double disk failures as estimates made using the mean time to data loss method. Model results are compared to system level field data for RAID group of 14 drives and show excellent correlation and greater accuracy than either MTTDL.

We present a methodology based on the physics of failure, and the sequential probability ratio test, for modeling and monitoring electrical interconnects in health monitoring, and electronic prognostic applications. The resistance behavior of an electrical contact was characterized as a function of temperature. The physics of failure of the contact technology were analysed. A contact resistance model was selected, and its parameters were fitted using the temperature characterization data. The physics of failure model was evaluated with a reliability application (temperature cycle test), and was found to produce estimation errors of < 1 mOmega of during a training period. The temperature and resistance of ten sample contacts were continuously monitored during the temperature cycle test, identifying the maximum temperature and resistances for each cycle. Using the physics of failure model, maximum resistance estimates were generated for each test sample. The residual between the monitored and estimated resistance values was evaluated with the sequential probability ratio test. The method was shown to overcome the issues of traditional threshold-based monitoring approaches, providing accurate resistance estimates, and allowing the detection of abnormal resistance behavior with low false alarm and missed alarm probabilities.

Precursor parameters have been identified to enable development of a prognostic approach for insulated gate bipolar transistors (IGBT). The IGBT were subjected to thermal overstress tests using a transistor test board until device latch-up. The collector-emitter current, transistor case temperature, transient and steady state gate voltages, and transient and steady state collector-emitter voltages were monitored in-situ during the test. Pre- and post-aging characterization tests were performed on the IGBT. The aged parts were observed to have shifts in capacitance-voltage (C-V) measurements as a result of trapped charge in the gate oxide. The collector-emitter ON voltage VCE(ON)showed a reduction with aging. The reduction in the VCE(ON)was found to be correlated to die attach degradation, as observed by scanning acoustic microscopy (SAM) analysis. The collector-emitter voltage, and transistor turn-off time were observed to be precursor parameters to latch-up. The monitoring of these precursor parameters will enable the development of a prognostic methodology for IGBT failure. The prognostic methodology will involve trending precursor data, and using physics of failure models for prediction of the remaining useful life of these devices.

Land grid array (LGA) sockets are used as separable interconnects between printed circuit boards, and high I/O integrated circuit components. Because the socket contacts with the component and the circuit board on both sides, low and stable contact resistances among these interfaces are desirable for the reliable electrical connection of the LGA package. This paper compares the contact resistance degradation of two LGA socket designs, silver particles in an elastomer column, and silver-plated-nickel in an elastomer film, subjected to accelerated corrosion environment, or so-called mixed flowing gases (MFG). Increased contact resistance was observed in the sockets due to corrosion products over the contact surface after metal corrosion. Corrosion products were analysed using environmental scanning electron microscopy (E-SEM), energy dispersive spectroscopy (EDS), and x-ray photoelectron spectroscopy (XPS). AgCl, Aga2O, and Ag2SO4were identified after silver corrosion; NiCl2, Ni2SO4, and MS were found after Ni corrosion. The nickel corrosion product bridged the adjacent contacts as whiskers with time. The lifetime can be estimated by an acceleration factor: two day MFG Battelle Class II exposure equals one year of field service. The shelf life of conductive elastomer LGA sockets is expected to be longer than five years.

Prognostics and health management enables in-situ assessment of a product’s performance degradation and deviation from an expected normal operating condition. A unique hybrid prognostics and health management methodology combining both data-driven and physics-of-failure models is proposed for fault diagnosis and life prediction. The shortcomings of using data-driven and physics-of-failure methodologies independently are discussed. These approaches estimate future system health, based on a systems current health status, historical performance, and operating environmental conditions. Although these methodologies are applicable to legacy, current, and future electronics, and ranging from components to circuit assemblies and electronic products, the hybrid approach is preferred due to its capability to include potential failure precursor parameters with failure mechanism, thus improving accuracy in prognostic estimates. Various works on data-driven and physics-of-failure approaches to prognostics for electronics are summarized and a hybrid methodology case study is presented.

A flexible model for estimating reliability of RAID storage systems is presented. This model corrects errors associated with the common assumption that system times to failure follow a homogeneous Poisson process. Separate generalized failure distributions are used to model catastrophic failures and usage dependent data corruptions for each hard drive. Catastrophic failure restoration is represented by a three-parameter Weibull, so the model can include a minimum time to restore as a function of data transfer rate and hard drive storage capacity. Data can be scrubbed as a background operation to eliminate corrupted data that, in the event of a simultaneous catastrophic failure, results in double disk failures. Field-based times to failure data and mathematic justification for a new model are presented. Model results have been verified and predict between 2 to 1,500 times as many double disk failures as that estimated using the current mean time to data loss method.

This paper discusses contact discontinuity of electromechanical switches, and presents a model that considers the effect of vibration-induced inertial force on operational reliability. Using this model, the operational reliability of a switch with a specific contact assembly can be assessed for given vibration conditions. Under the vibration conditions, a minimum contact spring force is necessary for proper functioning of the switch, while the magnitude of contact uncertainty determines the need of an additional force to ensure operational reliability. With reduced contact uncertainty, the operational reliability of switches approaches either 0 or 1, solely depending upon the design & operational conditions. In this model, the parameters of c', b, & /spl sigma///spl mu/ need to be determined either empirically or experimentally before the model can be used for reliability assessment. To theoretically determine those parameters, Hertz contact with randomly distributed surface asperities needs to be considered. Finally, although this model starts from a log-normal distribution of electrical contact, the approach can be applied to other distributions, such as the inverse Gaussian and Weibull distributions.

The use of reliability predictions in the design and operation of electronic equipment has been an evolutionary and very controversial process, and over the past decade, reliability prediction methods have been a focal point for a flurry of books, papers, editorials, opinions, special sessions, and workshops. While it is generally believed that reliability assessment methods should be used to aid in product design and development, the integrity and auditability of the reliability prediction methods have been found to be questionable; in that, the models do not predict field failures, cannot be used for comparative purposes, and present misleading trends and relations. This paper discusses the role of reliability prediction and assessment in design, development, and deployment of electronic equipment; overviews the history of reliability predictions for electronics; discusses the advantages and disadvantages of some current methods; and presents some of the key research questions which need to be addressed.>

A coupled reliability and routability placement procedure for arranging electronic components on a convectively cooled two-dimensional workspace, printed wiring boards (PWBs), is developed. The objective is to improve the total reliability of all the components on the PWB by minimizing the sum of the individual component failure rates (i.e. minimizing the total failure rate) while also minimizing the total wire length. The placement procedures for reliability are based on a priority metric derived from a temperature-dependent failure rate equation and heat transfer equations for a single row of convectively cooled components. After a brief discussion of the force-directed methodology in terms of placement for routability and its relation to placement for reliability, a theory of placement for reliability on convectively cooled PWBs is discussed, and placement procedures for reliability along a row and an entire PWB are presented. A force-directed placement technique for reliability is developed, and the coupled placement procedure for reliability and routability is introduced. Examples of each procedure are presented and discussed.>

An optimization strategy is presented that provides a frame-work in which optimization algorithms and heuristic procedures can be coupled to solve nonlinearly constrained design optimization problems. These problems cannot be efficiently solved by either approach independently. The approach is based on an optimization algorithm dealing with local monotonicity and sequential quadratic programming techniques with heuristic procedures which are statistically derived from observations obtained by applying the optimization algorithm to different classes of test problems.