Variance of system-reliability estimates with arbitrarily repeatedcomponents

A model is developed to determine the variance of system reliability estimates and to estimate confidence intervals for series-parallel systems with arbitrarily repeated components. For these systems, different copies of the same component-type are used several or many times within the system, but only a single reliability estimate is available for each distinct component-type. The single estimate is used everywhere the component appears in the system design, and component estimation-error is then magnified at the system-level. The "system-reliability estimate" variance and confidence intervals are derived when the number of component failures follow the binomial distribution with an unknown, yet estimable, probability of failure. The "system-reliability estimate" variance and confidence intervals are obtained by expressing system reliability as a linear sum of products of higher order moments for component unreliability. The generating function is used to determine the moments of the component-unreliability estimates. This model is preferable for many system reliability estimation problems because it does not require independent component and subsystem reliability estimates; it is demonstrated with an example     

Prioritizing system-reliability prediction improvements

This method prioritizes system-reliability prediction activities once a preliminary reliability-prediction has been made. System-reliability predictions often use data and models from a variety of sources, each with differing degrees of estimation uncertainty. Since time and budgetary constraints limit the extent of analyzes and testing needed to estimate component reliability, it is necessary to allocate limited resources intelligently. A reliability-prediction prioritization index (RPPI) is defined to provide a relative ranking of components based on their potential for improving the accuracy of a system-level reliability prediction by decreasing the variance of the system-reliability estimate. If a component has a high RPPI, then additional testing or analysis should be considered to decrease the variance of the component reliability estimate. RPPI is based on a decomposition of the variance of the system-reliability or on a mean-time-to-failure estimate. Using these indexes, the effect of individual components within the system can be compared, ranked, and assigned to priority groups. The ranking is based on whether a decrease of the component-reliability estimate variance meaningfully decreases the system-reliability estimate variance. The procedure is demonstrated with two examples     

Commentary-caution: constant failure-rate models may be hazardousto your design

This commentary examines the consequences, from a system perspective, of modeling system components using only their failure-rates, viz, the inverse of their MTTF, when, in actuality, they have a lifetime distribution with either an increasing or a decreasing hazard function. Such models are often used because: they are tractable; they are thought to be "robust;" they depend only on average values; or only small amounts of data are available for calculations. However, the results of such models can greatly understate the system-reliability for some time periods and overstate it for others. Using MTTF as a figure of merit for system-reliability can be especially misleading. Furthermore, the redundancy in a redundant system might provide very little of the reliability improvement predicted by the constant failure-rate model, and series systems might, in fact, be much more reliable than predicted. The overall result is that a constant failure-rate model can give very misleading guidance for system-design     

Effect of Uncertainty in Failure Rates on Memory System Reliability

This paper investigates the effect of uncertainty in chip failure rates on memory system reliability. It is shown, using real data on memory failures, that the dispersion in failure rates can be as large as 80%. An important consequence is to increase the unreliability of a memory system by up to 65%. Two simple models are proposed to evaluate the variability in memory reliability. The first is a worst case estimate and the second is a probabilistic model which needs only the mean and the standard deviation of the chip failure rate. With high failure rates, the maximum uncertainty in reliability occurs in the early system lifetime; with low failure rates, this effect is reversed.     

An improved reliability model for Si and GaN power FET

The existing standard reliability models for power devices are not satisfactory and they fall short of predicting failure rates or wear-out lifetime of semiconductor products. This is mainly attributed to two reasons; the lack of a unified approach for predicting device failure rates and the fact that all commercial reliability evaluation methods relay on the acceleration of one dominant failure mechanism. Recently, device reliability research programs are aimed to develop new theoretical models and experimental methods that would result a better assessment of the device lifetime as well as point out on the dominating failure mechanism for particular operating conditions. A new model, named Multi failure mechanism, Overstress Life test (MOL) has been introduced and posed a better understanding of the dominating failure mechanisms under various stressed conditions in advanced FPGA devices (for 45 and 28 nm technologies). In this work we present, for the first time, the implementation of the MOL model to investigate the reliability of silicon power MOSFET and GaN power FET devices. Both, LTSpice simulation and experimental data are presented for a test circuit of a ring oscillator, based on CMOS-FET, NMOS-FET, PMOS-FET and N-channel e-GaN FET. The monitored data was acquired in-situ in form of the ring frequency or Vds values that enabled to assess the lifetime and determine the dominating mechanism during accelerated wearout by temperature, applied bias voltage, thermal cycling, gamma and electron irradiation. Moreover, in the case of GaN devices, RDS-On monitoring circuit has also been operated during thermal cycling of the tested component and the acceleration factor was derived for various operational parameters.     

Failure rate estimation of known failure mechanisms of electronic packages

Product reliability is one of the key factors for a successful product launch. However, electronic components can still fail in various stages of applications due to certain failure mechanisms. A constant failure rate typically describes a majority of non-solder joint related package failures in the accelerated testing or the field application. Historically, the failure rate for a constant failure phenomenon is estimated by using the Chi-square value or the expected number of failures.This paper will discuss the statistical characteristics of the number of failures observed in tests or applications and their confidence bounds. Several methods used to estimate the confidence bounds will be described, and a new approach will be proposed and validated through case studies. The estimation of the acceleration factor (AF) used in the failure rate modeling is also discussed. The conclusion will help engineers to understand the statistical meaning of the failures observed in stress tests or in the field applications, additionally, obtain a meaningful failure rate based on the expected failure data.     

可靠性寿命试验的动态截尾方法

为节省试验时间和资源，可靠性寿命试验通常采用定数截尾和定时截尾两种方法。但是它们有相同的不足，就是在试验结束后才进行数据分析，无法进行实时的动态控制。为解决这一问题．提出了寿命试验的动态截尾方法，利用该方法研究寿命服从指数型分布产品的可靠性试验．提出了试验动态截尾的数据处理模型及判据。该方法的思想可以推广应用于其它产品的可靠性试验与分析中。     

Reliability evaluation of a first order standby system with module redundancy

By defining a module to be a coherent subsystem of independently operating components each with a constant failure rate, this article derives expressions for the reliability of a standby redundant system consisting of an operating module together with a cold or warm standby module. The closed form reliability expressions are dependent upon the minimal path sets of each module as well as the component failure rates. Expressions are also derived for the mean time to system failure as well as the variance of the system time to failure distribution.     

高温恒定电场栅氧化层TDDB寿命测试方法研究

介绍了薄栅氧化层TDDB可靠性评价的高温恒定电场试验方法,并完成了E模型的参数提取,同时以MOS电容栅电流Ig为失效判据。对某工艺的MOS电容栅氧化层TDDB寿命进行了评价。该试验方法解决了在高温条件下对工作器件进行可靠性评价的问题,方法简便可靠,适用于亚微米和深亚微米工艺线的可靠性评价。     

基于加速性能退化试验的板级可靠性评估

传统的可靠性评估方法一般基于失效寿命数据,而目前对于高可靠长寿命的电子产品,很难通过加速试验获得其失效寿命时间。为解决这一矛盾,将性能退化理论引入到传统可靠性评估中,提出了基于失效数据及加速性能退化的可靠性评估的新方法。应用某型雷达24V/2A稳压电源板加速性能退化试验进行验证,结果表明该方法用于高可靠长寿命电子装备的可靠性评估是正确有效的。     

Availability and reliability of system with dependent componentsand time-varying failure and repair rates

System reliability depends not only on the reliabilities of components in the system but also on their interactions. Generally, in a system, not only s-independent failures but also s-dependent failures among components can occur; thus there are many studies where the s-dependencies among components are taken into account in system reliability and availability analysis, but in which the failure and repair rates were assumed constant. Whereas, from a practical viewpoint, the constant failure rate assumption for components has been, and is repeatedly challenged by knowledgeable reliability practitioners. Therefore, there are other studies which handled the problem of time-varying failure rates, among which all concerned repairable systems did not involve s-dependent failures. In most cases, however, to combine s-dependent failures and time-varying failure and repair rates in system reliability and availability analysis is the most appropriate for real systems. But it is very difficult to obtain the analytic solution and, in most cases, the closed-form solution for system reliability and availability does not exist, so that numerical or simulation methods must be used. This paper studies one kind of system that endures environmental shocks, and where one or more components can fail simultaneously due to a cumulative shock-damage process. An approach for reliability and availability analysis of such kinds of repairable systems is presented, where failure and repair rates of components can be varied with time. One type of special vehicle with such mechanical systems illustrates system reliability and availability solutions     

Cost analysis of a system with partial failure mode and abnormal weather conditions

This paper deals with the cost analysis of a system having three modes (normal, partial failure and total failure) in two weather conditions—normal and stormy. Failure rates of the system and rates of change of weather conditions are constant while the repair rates are general. The repair time distribution depends upon the starting state of the repair and it does not alter with the change in weather. The system is observed at suitable regenerative epochs in order to obtain reliability characteristics of interest to system designers and operations managers. Earlier results are verified as particular cases.     

A comparison of electronic-reliability prediction models

One of the most controversial procedures in reliability is the use of reliability prediction techniques based on component failure data to estimate system failure rates. The International Electronics Reliability Institute (IERI) at Loughborough University is in a unique position. Over many years, much reliability information has been collected from leading British and Danish electronic manufacturing companies. These data are of such high quality that IERI can perform the comparison exercise with many circuit boards (CB) of different types. Several CB were selected from the IERI field-failure database and their reliability was predicted and compared with the observed field-performance. The prediction techniques were based on the: M217E [US Mil-Hdbk-217E]; HRD4; Siemens (SN29500); CNET; and Bellcore (TR-TSY-000332) models. For each model, the associated published failure rates were used. Hence, parts count analyses were performed on several CB from the database; these analyses were compared with the field failure rate. The prediction values differ greatly from the observed field behavior and from each other. Further analysis showed that each prediction model was sensitive to widely different physical parameters. The results are summarized. Some of the models are more sensitive to a factor that varies according to an Arrhenius model, such as temperature and electrical stress, while others are more sensitive to the discrete π factors used to model environment and quality     

Comparisons of block diagram and Markov method system reliability and mean time to failure results for constant and non-constant unit failure rates

This paper presents a comparison of system reliability and mean time to failure results obtained using two different methods (i.e. block diagram and Markov) for the same system with constant and non-constant unit failures rates. The device of stages approach is used to obtain the non-constant unit failure rate when using the Markov method.     

基于Bayes和Fiducial方法的指数分布区间估计

在已知产品失效率不超过某个值的条件下,对定时截尾寿命试验,采用Bayes方法进行可靠性评估;对定数截尾寿命试验,采用参数受限制的Fiducial方法进行可靠性评估。根据这两种方法,分别给出了平均寿命单侧置信下限计算公式,同时讨论了先验分布参数的取值方法。最后,通过算例验证了这两种方法的有效性,算例表明两种方法均能够减少试验时间、提高可靠性评估精度。     

On estimating the mean time to failure with unknown censoring

Sometimes, in reliability studies, neither the life of all failed units nor the number of units still functioning is known at any specific time due to problems such as administrative delays. Consequently, one might consider an estimate of the mean time to failure (MTTF) based only on known failure times of part of the units. An investigation is conducted into the bias and efficiency of such an estimator for either an exponential or a Weibull distribution. In the exponential case, exact expressions are obtained, and, for the Weibull case, a Monte Carlo simulation was used. The estimate of MTTF based on known lifetimes of failed units alone underestimates with smaller variance and higher mean squared error than does the estimate based on the total accumulated lifetime of both failed and surviving units     

Stochastic analysis of a two-unit parallel system with partial and catastrophic failures and preventive maintenance

This paper studies a two-unit parallel system with each unit having two types of failure and two modes of operation—normal or partial failure mode. A unit fails either due to change in operating characteristics or due to catastrophe. The system goes for preventive maintenance randomly (in time). Failure rates are constant while repair and (preventive) maintenance rates are general. Using the theory of regenerative and Markov-renewal processes several important measures of reliability are obtained.     

How to Hand-Calculate System Reliability and Safety Characteristics

A simple method is given for calculating a) reliability characteristics of repairable and nonrepairable systems, and b) the importance of the individual system components. Assumptions made include independent component failures and constant failure and repair rates for the components. The methods can easily be implemented in a computer program that would be inexpensive to execute and would always overpredict (usually very slightly) the system failure characteristics.     

Recursive Disjoint Products, Inclusion-Exclusion, and Min-Cut Approximations

Three different ways to estimate the reliability of an s-coherent system are compared: 1) recursive disjoint products (DP), 2) recursive inclusion-exclusion (IE), and 3) minimal-cut approximations based on partial information. The following three points are made. 1. Recursive DP and recursive IE are mathematically identical and obtain the same numerical values at each step of the recursion, although the recursive system-reliability functions are different. 2. Recursive DP seems to result in fewer comparisons and a shorter polynomial than recursive IE, and therefore also less work, for small scale systems, such as the 2-out-of-4:G example discussed herein. I do not yet know if this comparative advantage persists for larger systems. 3. For complex highly reliable systems, min-cut approximations based on partial information, that sacrifice some accuracy for convenience and ease of computation are preferable to min-path exact methods since the approximations come very close to the true value of the reliability with comparably little effort, in some cases requiring only hand calculations.     

Reliability matrix solution to multiple mechanism prediction

We present a method for predicting the failure rate and thus the reliability of an electronic system by summing the failure rate of each known failure mechanism. We use a competing acceleration factor methodology by combining the physics of failure for each mechanism with its own effect as observed by High/Low temperature and High/Low voltage stresses. Our Multiple High Temperature Overstress Life-test (M-HTOL) method assumes that the lifetime of each failure mechanism follows constant rate distribution whereby each mechanism is independently accelerated by its own stress factors. Stresses include temperature, frequency, current, and other factors that can be entered into a reliability model. The overall failure rate thus, also follows an exponential distribution and is described as the standard FIT (Failure unIT or Failure in Time). This method combines mathematical models for known failure mechanism and solves them simultaneously for a multiplicity of accelerated life test results to find a consistent set of weighting factors for each mechanism. The result of solving the system of equations is a more accurate and a unique combination for each system model by proportional summation of each of the contributing failure mechanisms.