A new reliability growth model: its mathematical comparison to the Duane model

The Duane reliability growth model has been traditionally used to model electronic systems undergoing development testing. This paper proposes a new reliability growth model derived from variance stabilisation transformation theory which surpasses the Duane model in typical reliability growth situations. This new model is simpler to plot and fits the data more closely than the Duane model whenever the Duane slope is less than 0.5. This paper explores the mathematical relationships between these two models; and shows that at a Duane slope of 0.5, both models are mathematically equivalent in their capacity to fit the observed data. The instantaneous MTBF of the new model is also developed and compared to that of Duane. As the new model is influenced by the later failures, compared to early failures for the Duane model, it has the further advantage of leading to reduced test times for achieving a specified instantaneous MTBF. As the reliability of electronic systems increases, this has positive implications for testing.     

On some reliability growth models with simple graphical interpretations

Some useful reliability growth models, which have simple graphical interpretations, are studied in this paper. The proposed models are inspired by the Duane model. For each of the models, the plot of the cumulative number of failures against the running time, when a suitable scale is used, will tend to be on a straight line if the model is valid. Otherwise the model should be rejected. The slope of the fitted line and its intercept on the vertical axis will give us the estimates of the parameters. Hence, it provides us with a simple graphical model validation and parameter estimation tool. In particular, we propose a “first-model-validation-then-parameter-estimation” approach which will simplify the model validation and parameter estimation problem in software reliability analysis. Numerical analysis of several sets of software failure data are also provided to enlighten the ideas.     

Reliability Growth and Duane Learning Curves

This paper examines Duane learning curves for reliability improvement between successive reliability tests. A constant failure rate ratio between successive tests gives curved lines on a Duane plot. Gordon's observation that dominant failures appear exponentially with test time leads to exponential failure rate ratio models. These models, although not the only possible ones, give results that agree well with observations from practice.     

Operational repairable equipments and the duane model

For many years, the assessment of the rate of reliability growth during the development of repairable equipments has been carried out using the Duane model. As part of a design-to-life-cycle cost study, it was required to determine whether the Duane model was also applicable to operational equipment data. Observation of data trends indicated that the majority of the 370 data sets tested possessed nonconstant failure rates. Further analysis revealed nearly 80% of the data sets accepted a Weibull repairable model (which is equivalent to Duane). However, fitting the model to the data using either or both the least squares and maximum likelihood regression methods produced problems which led to the conclusion that the Duane model was unsuitable for use on operational failure data.     

A simple goodness-of-fit test for the power-law process, based on the Duane plot

The PLP (power-law process) or the Duane model is a simple model that can be used for both reliability growth and reliability deterioration. GOF (goodness-of-fit) tests for the PLP have attracted much attention. However, the practical use of the PLP model is its graphical analysis or the Duane plot, which is a log-log plot of the cumulative number of failures versus time. This has been commonly used for model validation and parameter estimation. When a plot is made, and the coefficient of determination, R/sup 2/, of the regression line is computed, the model can be tested based on this value. This paper introduces a statistical test, based on this simple procedure. The distribution of R/sup 2/ under the PLP hypothesis is shown not to depend on the true model parameters. Hence, it is possible to build a statistical GOF test for the PLP. The critical values of the test depend only on the sample size. Simulations show that this test is reasonably powerful compared with the usual PLP GOF tests. It is sometimes more powerful, especially for deteriorating systems. Implementing this test needs only the computation of a coefficient of determination. It is much easier than, for example, computing an Anderson-Darling statistic. Further study is needed to compare more precisely this new test with the existing ones. But the R/sup 2/ test provides a very simple and useful objective approach for decision making with regard to model validation.     

The common thread for operational reliability and failure physics

Operational reliability and failure physics constitute the two extreme ends of the reliability engineering spectrum. One critical common thread that ties these two extremes together is stress. Studies that relate failures and failure mechanisms to operational reliability through this common thread have been near non-existent. This paper is an attempt to stimulate interest to fill the gap for electronic systems. Flaws exist in a piece of electronic equipment at the time of manufacture, and stresses exacerbate these flaws to the point of equipment failure. There are no random failures. Every failure is relatable to certain stresses. Estimated flaw population distributions and stress versus time-to-failure characteristics show that electronic equipment failure rates should decrease with respect to time of stress application, such as operating time. Failure rate expressions have been developed for selected stresses (i.e., high temperature, thermal cycling, electrical stresses and vibration) and are discussed in detail in the text. Much more work is still required in equating the quantitative measures of stress to failure rates and operational reliability. This paper will help in paving the way towards that end.     

Reliability Evaluation and Prediction for Discrete Semiconductors

The use of accelerated step-stress and constant stress-in-time test techniques is demonstrated for generating models for predicting reliability at use conditions. Reliability prediction models were obtained for a signal diode, signal and power transistors, silicon trolled rectifier, and metal oxide varistor. Each of these device types follows the Arrhenius model for reliability prediction. Techniques are demonstrated for determining 1) the acceleration factor between extremely high acceleration testing conditions and field operating conditions on the signal diode; and 2) the acceleration or multiplying factor between high level stresses and use conditions which can be used to predict the performance of the signal diode over time. The effect of relative humidity on reliability is discussed. Devices under power operation have a lower relative humidity (RH) than the environment. This low RH suppresses humidity activated mechanisms. A transistor high-reliability screen which removes devices with early manufacturing type defects is described. This screen was effective, efficient and economical for improving the reliability of systems. A technique of combining acceleration factors for a number of items which affect reliability was demonstrated for the diode. This same technique should be useful for most device reliability predictions. The acceleration factors, however, can not be extrapolated into stress levels much above maximum ratings where new failure modes may appear that override the established failure rate relation with stress. The straight line plots of failure rates in this paper are terminated before these threshold limits.     

A Quantitative Analysis of Semiconductor Device Failure Rates as Graphically Indicated in Military Handbook 217

A graphical presentation of semiconductor device failure rates is made in Figs. 13B and 14B of Mil-Hdbk-217 (see Figs. 1 and 2). From this presentation, Equations may be derived which indicate interesting properties, to failure physicists, device engineers, and equipment designers. On the basis of the equations it may be concluded that: (1) extrapolating room temperature failure rates from failure rates of devices stored at elevated temperatures is not likely to be meaningful; (2) there is a definite relationship between storage failure rate and failure rate in actual use (in the temperature range of interest); (3) the storage failure rate is large enough at normal storage temperatures so that, if semiconductor device failure rates influence the reliability of equipment in which they are used, they will contribute significantly to the finite storage life of the equipment (another way of expressing the last statement is that a manufacturer with a large storage inventory of semiconductors will find a significant decrease in the percentage of usable devices with time);(4) there are some instances (as delineated earlier by equations), when increasing the number of semiconductor devices and dividing the load proportionately improves reliability, and there are other cases when it does not. While the analysis makes no claim as to the validity or accuracy of Figs. 1 and 2, the mathematics permits statements about conditions necessary to confirm the data.     

Reliability Investment and Life-Cycle Cost

The reliability of avionic equipment profoundly influences life-cycle cost; the level of reliability attained largely depends upon the investment in reliability programs during development. As more investment is made in reliability improvement, some cost elements increase and others decrease. These opposing cost trends yield a unique minimum life-cycle cost (LCC). In order to find the level of investment in a reliability improvement program that minimizes LCC, the Reliability Investment Optimization (RIO) model has been developed. It identifies, for a particular avionic system, the level of reliability investment that minimizes the LCC of the equipment. This model employs a reliability-growth relationship based on the Duane model. The RIO model uses this reliability growth pattern to compute LCC as a function of MTBF (mean time between failures) where LCC comprises: 1) research, development, test and evaluation (RDT&E), 2) procurement, and, 3) operations and support (O&S). The RIO model uses summary level data that are appropriate for the timeframe of its most advantageous use, i.e., prior to detail design of the system. The degree of accuracy for the input parameters need not be high because results are not very sensitive to data accuracy. The model's results thus are quite stable. The RIO model was designed with avionic systems in mind. However, the model applies to a wider range of systems. Certain assumptions should be particularly scrutinized in extending usage beyond avionics, e.g., Poisson demand assumption versus a wearout failure pattern (failure rate increases over time), scheduled maintenance, and LCC element breakdown.     

Comparison of the effects of ionizing radiation at twelve dose rates from 0.0015 to 100 rad(Si)/s

Evidence is presented that two competing failure mechanisms exist in the Si-SiO₂ system with one mechanism dominating at low dose rates and the other at high. Much lower dose failures than expected were discovered at low dose rates (<0.1 rad(Si)/s) and very low dose rates (∼0.001 rad(Si)/s) in commercial SGS 4007 CMOS devices. These failure doses plotted versus dose rate have a bell-shaped curve, rather than the expected straight line (decreasing with increasing dose rate), indicating that a different failure mechanism is dominant at low dose rates than at high.     

A survey of reliability-prediction procedures for microelectronicdevices

The author reviews six current reliability prediction procedures for microelectronic devices. The device models are described and the parameters and parameter values used to calculate device failure rates are examined. The procedures are illustrated by using them to calculate the predicted failure rate for a 64 K DRAM; the resulting failure rates are compared under a variety of assumptions. The models used in the procedures are similar in form, but they give very different predicted failure rates under similar operating and environmental conditions, and they show different sensitivities to changes in conditions affecting the failure rates     

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.     

Estimation of system reliability using a "non-constant failurerate" model

One of the most controversial techniques in the field of reliability is reliability-prediction methods based on component constant-failure-rate data for the estimation of system failure rates. This paper investigates a new reliability-estimation method that does not depend upon constant failure rates. Many boards were selected from the Loughborough University field-reliability database, and their reliability was estimated using failure-intensity based methods and then compared with the actual failure intensity observed in the field. The predicted failure-intensity closely agrees with the observed value for the majority of a system operating lifetimes. The general failure intensity method lends itself very easily to system-reliability prediction. It appears to give an estimate of the system-reliability throughout the operating lifetime of the equipment and does not make assumptions, such as constant failure rate, which can be detrimental to the validity of the estimate. The predictions seem, on present evidence, to track the observed behavior well, given the uncertainties that are evident in the field. The failure intensity method should be investigated further to see if it is feasible to estimate the system reliability throughout its lifetime and hence provide a more realistic picture of the way in which electronic systems behave in the field     

A system approach to reliability and life-cycle cost of processsafety-systems

An analytic method, PDS, allows the designer to assess the cost effectiveness of computer-based process safety-systems based on a quantification of reliability and life-cycle cost. Using PDS in early system design, configurations and operating philosophies can be identified in which the reliability of field devices and logic control units is balanced from a safety and an economic point of view. When quantifying reliability, the effects are included of fault-tolerant and fault-removal techniques, and of failures due to environmental stresses and failures initiated by humans during engineering and operation. A failure taxonomy allows the analyst to treat hardware failures, human failures, and software failures of automatic systems in an integrated manner. The main benefit of this taxonomy is the direct relationship between failure cause and the means used to improve safety-system performance     

VMOS reliability

Whenever a new technology such as VMOS emerges, one key element to its success is the reliability of the products manufactured in that technology. The results of a reliability study to examine the fundamental VMOS device stability, high-temperature operating life (HTOL) failure rates, and electrostatic protection are presented for the VMOS technology. Experimental data for more than five (5) million device-hours of HTOL predict a reliability failure rate of less than 0.01 percent/1000 h at 70°C for products fabricated in the VMOS technology. In addition, an electrostatic protection capability greater than 1800 V is possible with specially designed VMOS input protection devices.     

A comprehensive review of the lognormal failure distribution with application to LED reliability

Life-test data for many semiconductor devices obey the lognormal law of failure. In this paper we offer a survey of the key statistical properties of the lognormal distribution which are relevant in device engineering. The statistical developments are illustrated throughout by specific examples drawn from life-test data for GaP red LEDs which show lognormal failure behavior. Additional theoretical justification for accepting the lognormal distribution in the case of these devices is provided by the statistical recasting of the diffusion theory of red LED degradation.The treatment of the fundamental concepts of reliability in terms of cumulative failure function, instantaneous failure rate, mean time for failure (MTTF), etc., although concise, is self-contained. Moreover, the estimation of the two characteristic parameters (median life, standard deviation) of the lognormal distribution from sample data by means of a number of alternative procedures (graphical, least-square, maximum likelihood) is discussed in detail. The efficient determination of the MTTF and failure rate is facilitated by convenient charts developed here which relate these quantities to the parameters median life and standard deviation at 5, 10, 20 and 40 years of device service life. In order to assess the uncertainty associated with the estimates, the confidence limits on the median life and standard deviation of the population as a function of confidence level and sample size are given in novel graphical forms. Finally, error bounds for the MTTF and failure rate of the population are also presented.     

浅析地铁双机牵引ZDJ9型转辙机故障原因

双机牵引转辙机已成为现在地铁正线转换道岔设备的主流设计,较以往的单机牵引转辙机,室内的继电电路更加复杂,转辙机也改为两种型号配合使用,出现了一些单机不曾有的故障。文章重点从室内的继电电路和室外转辙机的接点等方面,分析总结故障出现的原因,并制出相应的预防措施来规避该类故障的发生,降低转辙机设备的故障率,从而提高地铁的运行效率。     

Investigation of information loss mechanisms in EPROMs

The paper reports the results of accelerated life tests on p-and n-chanenl EPROMs, and compares the indication thus obtained with data from the field.The results of our experiments demonstrate that, even in recent production, contaminant diffusion significantly affects device reliability. The presence of this mechanism invalidates any effort to draw reliability information from lognormal plots of the cumulative distribution of the times to failure of all the bits in a device or in a set of devices: only the times to first bit failure for the devices of a batch should be considered. Furthermore, charge loss and contaminant diffusion seem to be uncorrelated processes.From the point of view of reliability it seems reasonable to conclude that, in spite of their increased complexity, 16 K n-channel EPROMs promise to be more reliable than 2 K devices, thanks probably to the improved technology.     

真空电子器件工作和非工作可靠性的探讨

论述了几个军用真空电子器件在不同应用条件下的工作和非工作的可靠性情况 ,提出器件在非工作贮存期内的预计失效率模型 ,并讨论在长期非工作贮存期内出现的失效机理及定性得出存放寿命与时间相关的结论。     

Roughness-enhanced reliability of MOS tunneling diodes

Both electrical and optical reliabilities of PMOS and NMOS tunneling diodes are enhanced by oxide roughness, prepared by very high vacuum prebake technology. For rough PMOS devices, as compared to flat PMOS devices, the Weibull plot of T_BD shows a 2.5-fold enhancement at 63% failure rate, while both the D₂ and H₂-treated flat PMOS devices show similar inferior reliability. For rough NMOS devices, as compared to flat NMOS devices, the Weibull plot of T_BD shows a 4.9-fold enhancement at 63% failure rate. The time evolutions of the light emission from rough PMOS and NMOS diodes degrade much less than those of flat PMOS and NMOS diodes. The momentum reduction perpendicular to the Si/SiO₂ interface by roughness scattering could possibly make it difficult to form defects in the bulk oxide and at the Si/SiO₂ interface by the impact of the energetic electrons and holes