Determining Optimum Burn-In and Replacement Times Using Bayesian Decision Theory

An important problem facing a manufacturer is the determination of the amount of time to burn-in items (in order to eliminate early failures) and the age at which to replace items (to avoid failures due to wearout). This problem becomes difficult to solve if the time-to-failure distribution of an item is unknown and must be estimated from test and operational data. This paper describes a method of statistical data analysis which is readily applied to the solution of this decision problem under a realistic but general loss (or gain) function. The method is a multiparameter Bayesian analysis which requires multiple integration of the (multivariate) posterior of the parameters of the time-to-failure distribution to obtain the expected loss (or gain) resulting from a particular choice of burn-in time and item replacement age. This integration is performed by a Monte Carlo Procedure using importance sampling. An example demonstrates the flexibility of this method of analysis. The data are a mixture of ``point' and truncated data, which often create difficulties when using conventional methods of decision analysis. In addition, since the method permits up to ten parameters for the family of time-to-failure distributions, a ``bathtub' hazard rate function is used to generate the data for the example. The results are presented in the form of Bayesian confidence intervals for the true hazard rate function and a presentation of the expected loss as a function of burn-in time and age at replacement.     

A nonparametric approach to estimate system burn-in time

System burn-in can get rid of more residual defects than component and subsystem burn-ins because incompatibility exists not only among components, but also among different subsystems and at the system level. There are two major disadvantages for performing the system burn-in: the high burn-in cost and the complicated failure rate function. This paper proposes a nonparametric approach to estimate the optimal system burn-in time. The Anderson-Darling statistic is used to check the constant failure rate (CFR), and the pool-adjacent-violator (PAV) algorithm is applied to “unimodalize” the failure rate curve. Given experimental data, the system burn-in time can be determined easily without going through complex parameter estimation and curve fittings     

Reliability Enhancement Through Optimal Burn-In

Burn-in is an important screening method used in predicting, achieving, and enhancing field reliability. Although electronics burn-in has been studied qualitatively, no comprehensive quantitative approach exists for determining optimal burn-in periods. This paper presents a cost-optimization model from a system viewpoint, with burn-in periods for the components as the decision variables. This model is applied to an electronic product recently developed which uses many ICs. State-of-the-art ICs have high early-failure rates and long infant mortality periods. Proper use of burn-in reduces early failure rates and reduces system deployment costs. The total cost to be minimized is formulated as a function of the mean costs of the component, device burn-in, shop repair, and field repair, which in turn are functions of the mean number of failures during and after burn-in. Component and system reliability are constraints that have to be satisfied. The early device failures are assumed to have a Weibull distribution. The formulated problem, with failure rates and cost factors, is optimized. Some basic properties of reliability and cost functions are discussed.     

A relation model of gate oxide yield and reliability

The relationship between yield and reliability is obviously important for predicting and improving reliability during the early production stage, especially for new technologies. Previous research developed models to relate yield and reliability when reliability is defined as the probability of a device having no reliability defects. This definition of reliability is not a function of mission time and thus is not consistent with reliability estimated from the time-to-first-failure data which is commonly used. In this paper, we present a simple model to tie oxide yield to time-dependent reliability by combining the oxide time to breakdown model with a defect size distribution. We show that existing models become special cases when a single mission time is considered. As the proposed reliability function has a decreasing failure rate, the result is useful for a manufacturer seeking to find an optimal burn-in policy for burn-in temperature, burn-in voltage, and burn-in time.     

FPGA电路动态老化技术研究

近年来,随着FPGA电路在军工和航天领域的广泛应用,用户对FPGA电路的可靠性要求也越来越高。在集成电路的可靠性评估试验中,动态老化试验是最重要的试验之一,FPGA动态老化技术的实现可以提高FPGA电路的可靠性。文章通过研究FPGA电路内部结构和功能模块,讨论FPGA电路加载配置过程的原理和流程,通过对动态老化和静态老化的对比试验和结果分析,研究出FPGA电路动态老化试验方法,并在工程实践中得到了成功实现和应用。     

Burn-in effect on yield

By removing infant mortalities, burn-in of semiconductor devices improves reliability. However, burn-in may affect the yield of semiconductor devices since defects grow during burn-in and some of them end up with yield loss. The amount of yield loss depends upon burn-in environments. Another burn-in effect is the yield gain. Since yield is a function of defect density, if some defects are detected and removed during burn-in, the yield of the post-burn-in process can be expected to increase. The amount of yield gain depends upon the number of defects removed during burn-in. In this paper we present yield loss and gain expressions and relate them with the reliability projection of semiconductor devices in order to determine burn-in time     

Facing the headaches of early failures: A state-of-the-art review of burn-in decisions

System screening during electronic equipment manufacturing often cost-effective opportunities to remove and replace defective items. Burn-in is an important screening method used in predicting, achieving, and enhancing field reliability. Based on a simple calculation, we would expect the number of failures in the field to be a decreasing function of burn-in period. Especially, the expected number of failures drops significantly in the first part of the curve. Thus only a few hours of burn-in greatly reduces the failure rate, hence enhancing reliability. Qualitative studies on electronics burn-in have been done. It is well known that burn-in is costly. However, a comprehensive quantitative approach is lacking in the determination of optimal burn-in periods. This paper thoroughly reviews the studies of burn-in screenings applied to industrial products. Papers published in the past have been critically commented and systematically classified. This state-of-the-art review can serve as a guide in studying the burn-in problems.     

Identification of quasi-periodically varying systems using the combined nonparametric/parametric approach

The problem of identification of quasi-periodically varying finite impulse response systems is considered. Neither the number of system frequency modes nor the initial frequency values are assumed to be known a priori. The proposed solution is a blend of the parametric (model based) and nonparametric (discrete Fourier transform based) approach to system identification. It is shown that the results of nonparametric analysis can be used to identify the number of frequency modes and to determine initial conditions needed to smoothly start (or restart) the model-based tracking algorithm. Such a combined nonparametric/parametric approach allows one to preserve advantages of both frameworks, leading to an estimation procedure which guarantees global frequency search, high-frequency resolution, fast initial convergence, and good steady-state tracking capabilities.     

Minimizing cost-functions related to both burn-in and field-operation under a generalized model

Summary and Conclusions-Burn-in is a method used to improve the quality of products. In field operation, only those units which survived the burn-in procedure will be used. This paper considers various additive cost structures related to both burn-in procedure and field operation under a general failure model. The general failure model includes two types of failures. Type I (minor) failure is removed by a minimal repair, whereas type II failure (catastrophic failure) is removed only by a complete repair (replacement). We introduce the following cost structures: (i) the expenses incurred until the first unit surviving burn-in is obtained; (ii) the minimal repair costs incurred over the life of the unit during field use; and (iii) either the gain proportional to the mean life of the unit in field operation or the expenditure due to replacement at a catastrophic failure during field operation. We also assume that, before undergoing the burn-in procedure, the unit has a bathtub-shaped failure rate function with change points t/sub 1/ & t/sub 2/. The optimal burn-in time b/sup */ for minimizing the cost function is demonstrated to be always less than t/sub 1/. Furthermore, a large initial failure rate is shown to justify burn-in, i.e. b/sup */>0. A numerical example is presented.     

Determination of Optimum Burn-In Time: A Composite Criterion

The object of this paper is to present a mathematical model capable of determining the optimum amount of time that semiconductor devices, which have specified life characteristics, must be placed on burn-in to obtain maximum performance versus total cost. To make the model operational and realistic, the traditional assumption of an exponential (more recently, Weibull) distribution of life is omitted in favor of the generalized gamma distribution (GGD). This is done because the GGD includes, as special cases, such distributions as the normal, Rayleigh, Maxwell, chi, chi2, Weibull, exponential, ordinary gamma, etc. The use of the greater representational capability of the GGD is justified in the results of the studies showing that (other things being equal) small changes in parametric values of life characteristics can cause vast differences in the optimum burn-in time and maximum system effectiveness. The physical performance sector of the model incorporates system effectiveness that includes such factors as availability, expected time to repair, mission reliability, system use coefficient, storage survival probability, and operational readiness. The costs considered are those due to burn-in operation, production, and sales. The model has been studied by use of computer runs from the standpoint of critical analysis and parametric sensitivity analysis.     

VLSI老化筛选试验技术的挑战

通过对集成电路老化试验技术的研究,指出了VLSI老化筛选试验技术仍然是集成电路产品质量和可靠性保障的重要手段。但是随着集成电路技术的飞速发展,老化技术面临许多有待解决的技术问题,从VLSI产品质量和可靠性保障的角度出发,急需制定可操作的VLSI老化试验技术规范。     

Generalized linear models in software reliability: parametric andsemi-parametric approaches

The penalized likelihood method is used for a new semi-parametric software reliability model. This new model is a nonparametric generalization of all parametric models where the failure intensity function depends only on the number of observed failures, viz. number-of-failures models (NF). Experimental results show that the semi-parametric model generally fits better and has better 1-step predictive quality than parametric NF. Using generalized linear models, this paper presents new parametric models (polynomial models) that have performances (deviance and predictive-qualities) approaching those of the semi-parametric model. Graphical and statistical techniques are used to choose the appropriate polynomial model for each data-set. The polynomial models are a very good compromise between the nonvalidity of the simple assumptions of classical NF, and the complexity of use and interpretation of the semi-parametric model. The latter represents a reference model that we approach by choosing adequate link and regression functions for the polynomial models     

Projecting gate oxide reliability and optimizing reliabilityscreens

The effect of time-dependent stress voltage and temperature on the reliability of thin SiO₂ films is incorporated in a quantitative defect-induced breakdown model. Based on this model, design curves which can be used along with a breakdown voltage distribution for an oxide technology to determine optimal burn-in conditions are presented. The tradeoff between improved reliability and lower burn-in yield for different gate oxide technologies can also be examined quantitatively using the model     

集成电路动态老化新技术的实施

在集成电路的可靠性评估试验中,动态老化项目是最重要的试验之一。文章提出了利用新技术对集成电路进行动态老化测试的全新方法,该新方法可以对老化线路板的关键电路信息和老化环境进行多路全面测试的监控,全面提高监控范围,及时发现老化过程中的工作异常,并减少人工,提高评估试验的可靠性,和其他方法相比有独特的优势。文中在技术上就集成电路具体实施动态老化试验过程中的技术细节和功能的实现进行探讨,分析和介绍老化技术中老化信号的生成和加载方法以及实时监控、数据采集方案。     

Coordinated warranty and burn-in strategies

In product reliability assurance, the warranty and burn-in (W&BI) strategies are usually selected separately, despite the fact that both depend on the early-life failure behavior of the product. This paper treats W&BI strategies together in order to examine the possible benefits of coordinated strategies for product performance management. As these strategies are meaningful only for decreasing hazard-rate systems, a Weibull life distribution is assumed for each system component. A net-profit model that includes an increase in product price as a function of warranty duration is constructed. The model shows how a coordinated W&BI strategy can be selected. The model is quite general and its extension to other cases is explained. A central point that is treated thoroughly is the renewal analysis necessary to determine replacement costs during burn-in and during the warranty period. As part of the analysis, a useful approximation is defined, and efficient optimization routines are identified. An example illustrates the use of analytical methods. The analysis and discussion of the example show that there are advantages in coordinating the selection of W&BI strategies     

Simultaneous Quality and Reliability Optimization for Microengines Subject to Degradation

Micro-Electro-Mechanical Systems (MEMS) represent an exciting new technology, but to achieve more widespread usage and wider adoption within more industrial applications, they must be highly reliable, and manufactured to stringent quality standards. Many challenging manufacturing issues are of concern during the fabrication of MEMS, such as precise dimensional inspection, reliability modeling, burn-in scheduling, avoiding stiction, and maintenance strategies. However, only limited mathematical tools for improving MEMS reliability, quality, and productivity are currently available. This paper proposes a mathematical model to jointly determine inspection & preventive replacement policies for surface-micromachined microengines subject to wear degradation, which is a major failure mechanism for certain MEMS devices. The optimal specification limits for inspection, and the replacement interval are determined by simultaneously optimizing MEMS quality and reliability. The proposed model can be used as a tool for decision-makers in MEMS manufacturing to make sound economical and operational decisions on reliability, quality, and productivity. While illustrated considering one specific microengine design, the proposed model can be applied to a broader range of MEMS devices that experience wear degradation between rubbing surfaces.      

An overview of manufacturing yield and reliability modeling forsemiconductor products

This paper presents an overview of yield, reliability, burn-in, cost factors, and fault coverage as practiced in the semiconductor manufacturing industry. Reliability and yield modeling can be used as a foundation for developing effective stress burn-in, which in turn can warranty high-quality semiconductor products. Yield models are described and their advantages and disadvantages are discussed. Both yield reliability relationships and relation models between yield and reliability are thoroughly analyzed in regard to their importance to semiconductor products     

Modeling and maximizing burn-in effectiveness

System burn-in can get rid of many residual defects left from component and subsystem burn-in since incompatibility exists not only among components but also among different subsystems and at the system level. Even if system, subsystem, and component burn-in are performed, the system reliability often does not achieve the requirement. In this case, redundancy is a good way to increase system reliability when improving component reliability is expensive. This paper proposes a nonlinear model to: estimate the optimal burn-in times for all levels, and determine the optimal amount of redundancy for each subsystem. For illustration, a bridge system configuration is considered; however, the model can be easily applied to other system configurations. Since there are few studies on system, subsystem, and component incompatibility, reasonable values are assigned for the compatibility factors at each level     

Burn-in optimization under reliability and capacity restrictions

Burn-in is a method to screen out early failures of electronic components. The burn-in problems that minimize the system life-cycle cost have been investigated reasonably well in many applications, but physical constraints during the decision process have not been considered. The authors search for optimal burn-in time and develop a cost-optimization model. Two types of constraint are to be satisfied during decision making: (1) the minimum system reliability requirement, and (2) the maximum capacity available for burn-in. Guidelines are suggested for making burn-in decisions. An example is given to illustrate a practical application. The model generalizes the burn-in problems that were oversimplified in a previous study     

一种星载电子产品老练试验加速因子估计方法

提出一种基于可靠性预计数据的星载电子产品老练试验加速因子的估计方法。在该方法中,温度对产品失效过程的影响通过器件失效率预计模型中的温度应力参数予以刻画。通过比较产品在工作环境温度与老练试验温度下的预计失效率数据来估计老练试验加速因子。该方法简单、易行,含义明确,有望增强可靠性评估结果与可靠性预计结果的可比性。