On optimal burn-in procedures - a generalized model

Burn-in is a manufacturing technique that is intended to eliminate early failures. In this paper, burn-in procedures for a general failure model are considered. There are two types of failure in the general failure model. One is Type I failure (minor failure), which can be removed by a minimal repair or a complete repair; and the other is Type II failure (catastrophic failure), which can be removed only by a complete repair. During the burn-in process, two types of burn-in procedures are considered. In Burn-In Procedure I, the failed component is repaired completely regardless of the type of failure; whereas, in Burn-In Procedure II, only minimal repair is done for the Type I failure, and a complete repair is performed for the Type II failure. Under the model, various additive cost functions are considered. It is assumed that the component before undergoing the burn-in process has a bathtub-shaped failure rate function with the first change point t/sub 1/, and the second change point t/sub 2/. The two burn-in procedures are compared in cases when both the procedures are applicable. It is shown that the optimal burn-in time b/sup */ minimizing the cost function is always before t/sub 1/. It is also shown that a large initial failure rate justifies burn-in, i.e., b/sup */>0. The obtained results are applied to some examples.     

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.     

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。     

Hazard Versus Renewal Rate of Electronic Items

Two different indexes, the hazard rate and the renewal rate, which are implied by conventional uses of the bathtub-shaped curve, are often noted in reliability. The hazard rate is applicable for a single failure time of each item, such as that of a nonrepairable part; the renewal rate is applicable for multiple failure times of each item, such as those of repairable equipment. Occasionally, remarks are made in the literature concerning the mathematical models for the bathtub-shaped hazard rate but not for the renewal rate. Furthermore, bathtub-shaped hazard and renewal curves as conventionally used are each based on certain assumptions concerning failure time distributions. Little data have been recorded for electronic parts and equipment which would substantiate the widespread use of the conventional implications of the bathtub-shaped hazard and renewal rates. The validity of the assumptions concerning the underlying distributions of failure times affects the accuracy of the results of reliability analyses, such as prediction, data analysis, formal assurance tests, operational planning, and maintenance planning. A study of the applications-oriented literature suggests that the distinction between the hazard rate and the renewal rate, as well as some associated implications, are not generally appreciated. Thus the existing situation is apt to lead engineers astray as well as others with application interests. Basic concepts and definitions are emphasized and extensions and implications are sketched. References are selected and noted for those interested in further pursuit.     

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.     

Benefits of Integrated-Circuit Burn-In to Obtain High Reliability Parts

The technique of integrated circuit (IC) burn-in is applied industry-wide with the assumption that burned-in ICs have a much lower failure rate during operating life than ICs which are not burned-in. Several years ago this approach was valid for all ICs, but today burn-in procedures for some ICs provide little, if any, benefit. However, some customers still request burned-in ICs, assuming that this will produce better reliability. This paper provides historical data for linear ICs and presents a procedure to help the user determine if burn-in is worthwhile. An example for linear ICs where minimum benefit produced from burn-in is provided. By repeating this exercise with any other parts, the user can decide whether burn-in will decrease the failure rate appreciably for his application. This article deals specifically with decreases in failure rates through burn-in. It is not within the scope of this paper to describe general factors that could decrease failure rates.     

Une modelisation bayesienne du taux de defaillance en fiabilite

The classical approach in reliability in which no difference is made between the failure rates of various electronic components making up an assumed homogeneous batch, leads to some formal difficulties which will be demonstrated. A new approach is proposed in which each component in the batch is characterized by its own “stress resistance capability”. This approach leads us to postulate the existence of an individual “lambda” attached to each component and thus that of a statistical distribution of the “lambdas” at batch level. Taking this distribution as a distribution a priori, a bayesian treatment is then applied. The result is a formalisation of an unconditional failure rate reflecting the mean failure rate of the batch considered. Choosing a priori a gamma type distribution (justified by reasons of a practical and theoretical nature), it will be shown that the unconditional failure rate decreases hyperbolically with time. Consequently, a new “bath-curve” profile is obtained in which the horizontal line becomes slightly inclined. Lastly, the proposed model reveals a simple relationship between the burn-in time for a batch of components and the unconditional failure rate of the same batch after burn-in.     

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     

A Model for Burn-In Programs for Components with Eliminateable Defects

We consider a component with a random number of defects which can be discovered and corrected during the course of a burn-in program. The failure rate after burn-in is constant (in time) and depends on the number of remaining defects. A sufficient condition is given for a burn-in program to lead to increased mean time to failure; it is given in terms of the prior distribution of the number of defects and the failure rates.     

浅谈对集成电路加速寿命试验的认识

老炼、稳态寿命等加速寿命试验是衡量集成电路使用寿命的主要手段。文中简要介绍了集成电路的主要可靠性指标——FIT,呈现集成电路失效特征的"浴盆曲线",以及不同失效阶段的主要影响因素、失效率与时间相关的统计分布特征。在此基础上,文章对老炼和稳态寿命的试验目的进行了说明,并列出稳态寿命试验的等效试验条件表以及通过该试验的集成电路使用寿命的一些参考数据。     

Optimal burn-in for minimizing cost and multiobjectives

In general, a small proportion of components will be weak because of some imperfection in the control of the production process or in the design of the components. This paper discusses an optimal burn-in procedure to minimize total costs based on the assumption that some of the components are weak and deteriorate faster than the strong components. The procedure will define the costs of burn-in errors. In practice, it may be impossible to eliminate all weak components through burn-in due to a nonzero proportion of defectives of the components. Therefore, burn-in errors could occur for some reasons. Probability models and cost models are formulated to find the optimal burn-in time that minimizes the expected total cost. An example is included to show how to use the results. Finally, multiobjective optimal burn-in for series systems is presented using the surrogate worth trade-off method.     

A Model for Upside-Down Bathtub-Shaped Mean Residual Life and Its Properties

Mean residual life is an important statistic in reliability analysis. Based on a general functional form of the derivative of the mean residual life, we propose a new lifetime distribution with an upside-down bathtub-shaped mean residual life function. The model has its mean residual life function in a simple, closed form so that further analysis based on the mean residual life can be easily carried out. We study the analysis and applications on both the mean residual life function, and the failure rate function of this model. Maximum likelihood method is used for parameter estimation. Numerical examples and comparisons indicate that the new model performs well in modeling lifetime data with bathtub-shaped failure rate functions, and upside-down bathtub-shaped mean residual life function.     

An extended model for optimal burn-in procedures

In this paper, the problem of determining optimal burn-in time is considered under the general failure model. There are two types of failure in the general failure model. One is Type I failure (minor failure) which can be removed by a minimal repair, and the other is Type II failure (catastrophic failure) which can be removed only by a complete repair. In the researches on optimal burn-in, the assumption of a bathtub shaped failure rate function is commonly adopted. In this paper, upper bounds for optimal burn-in times are obtained under a more general assumption on the shape of the failure rate function, which includes the bathtub shaped failure rate function as a special case.     

Critical time of the lognormal distribution

The critical time is the time point as the failure rate starts to decrease and also as the mean residual lifetime starts to increase. The estimated critical time is useful for determining the duration of a burn-in process. The method for estimating the critical time of the failure rate for lognormal lifetime distribution is discussed. A single time censored data is used as a example for illustration.     

半导体器件老炼筛选试验设计

老炼筛选试验是有效剔除内含固有工艺缺陷的半导体器件,以及保证半导体器件使用可靠性的重要途径。本文阐述了半导体器件早期失效的基本概念,并给出了半导体器件早期失效率的预计方法。在此基础上提出了半导体器件老炼筛选试验设计方法,以期最大限度地保证半导体器件出厂后的使用可靠性。     

基于系统连续运行的功率管老炼筛选方法

提出了一种可以在试验台上进行无条件的筛选、或对已装机而又存在某种隐患的功率管进行老炼筛选的方法,并介绍了如何进行老炼筛选应力的确定和控制,以及试验的过程检测和故障处理。通过理论分析和试验证明,这种方法是切实可行的,能达到老炼筛选的预期目标。     

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     

A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type 1 extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.     

A dual burn-in policy for defect-tolerant memory products using the number of repairs as a quality indicator

In most existing studies on the optimization of burn-in for semiconductor products, all chips are treated equally and subjected to burn-in of the same duration (i.e. a single burn-in (SBI) policy is employed). However, the quality levels of chips before burn-in are not the same in general, and therefore, it may be more advantageous to treat chips differently at the burn-in process based on appropriate quality indicators. This paper considers defect-tolerant memory products and develops a dual burn-in (DBI) policy in which the chips submitted to burn-in are classified into two groups according to the number of repairs, a quality indicator that can be obtained from the wafer probe test results, and different burn-in durations are applied to different groups of chips. Then, cost models are developed for the SBI and DBI policies, and their relative performances are compared in terms of the expected total cost per chip. The effectiveness of the proposed DBI policy is demonstrated using the actual data for a certain type of 256M DRAM products.     

Cost Effective Burn-In and Replacement Times

Bum-in and replacement policies have been used to reduce the cost of maintaining a system function. Existing solutions to the burn-in and the combined burn-in, replacement problems are typically difficult to apply. A simpler solution to this problem is given. The only distributional property required is the reliability function. Thus either parametric or nonparametric estimates of reliability can be used in the solution. The nonparametric solution is appealing in the case of a combined burn-in and replacement policy because the U shaped failure rate makes parametric estimation of reliability difficult.