Bridging the Gap between Quantitative and Qualitative Accelerated Life Tests

Test planners have long sought the ability to incorporate the results of highly accelerated life testing (HALT) into an early estimate of system reliability. While case studies attest to the effectiveness of HALT in producing reliable products, the capability to translate the test's limited failure data into a meaningful measure of reliability improvement remains elusive. Further, a review of quality and reliability literature indicates that confusion exists over what defines a HALT and how HALT differs from quantitative accelerated life testing methods. Despite many authors making a clear distinction between qualitative and quantitative accelerated life tests, an explanation as to why this delineation exists cannot be found. In this paper, we consider an exemplary HALT composed of a single stressor to show that the HALT philosophy precludes the estimation of a system's hazard rate function parameters because of the test's fix implementation strategy. Four common accelerated failure data analysis methods are highlighted to show their limitations with respect to estimating reliability from HALT data. Finally, a modified accelerated reliability growth test is proposed as a way forward for future research in HALT scenarios to characterize the risk of attaining a reliability requirement and improve parameter estimation. Copyright © 2014 John Wiley & Sons, Ltd.     

Reliability analysis of exponentiated Poisson-exponential constant stress accelerated life test model

Accelerated life testing is an efficient tool frequently adopted for obtaining failure time data of test units in a lesser time period as compared to normal use conditions. We assume that the lifetime data of a product at constant level of stress follows an exponentiated Poisson-exponential distribution and the shape parameter of the model has a log-linear relationship with the stress level. Model parameters, the reliability function (RF), and the mean time to failure (MTTF) function under use conditions are estimated based on eight frequentist methods of estimation, namely, method of maximum likelihood, method of least square and weighted least square, method of maximum product of spacing, method of minimum spacing absolute-log distance, method of Cramér-von-Mises, method of Anderson–Darling, and Right-tail Anderson–Darling. The performance of the different estimation methods is evaluated in terms of their mean relative estimate and mean squared error using small and large sample sizes through a Monte Carlo simulation study. Finally, two accelerated life test data sets are considered and bootstrap confidence intervals for the unknown parameters, predicted shape parameter, predicted RF, and the MTTF at different stress levels, are obtained.     

Accelerated Degradation Tests: Modeling and Analysis

High reliability systems generally require individual system components having extremely high reliability over long periods of time. Short product development times require reliability tests to be conducted with severe time constraints. Frequently few or no failures occur during such tests, even with acceleration. Thus, it is difficult to assess reliability with traditional life tests that record only failure times. For some components, degradation measures can be taken over time. A relationship between component failure and amount of degradation makes it possible to use degradation models and data to make inferences and predictions about a failure-time distribution. This article describes degradation reliability models that correspond to physical-failure mechanisms. We explain the connection between degradation reliability models and failure-time reliability models. Acceleration is modeled by having an acceleration model that describes the effect that temperature (or another accelerating variable) has on the rate of a failure-causing chemical reaction. Approximate maximum likelihood estimation is used to estimate model parameters from the underlying mixed-effects nonlinear regression model. Simulation-based methods are used to compute confidence intervals for quantities of interest (e.g., failure probabilities). Finally we use a numerical example to compare the results of accelerated degradation analysis and traditional accelerated life-test failure-time analysis.     

Statistical Inference on Constant Stress Accelerated Life Tests under Generalized Gamma Lifetime Distributions

We will discuss the reliability analysis of the constant stress accelerated life tests when a parameter in the generalized gamma lifetime distribution is linear in the stress level. Statistical inference on the estimation of the underlying model parameters as well as the mean time to failure and the reliability function will be addressed on the basis of the maximum likelihood approach. Large sample theory will be derived for the goodness of fit of the data. Some simulation study and an illustrative real example will be presented to show the appropriateness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

Discrimination between accelerated life models via Approximate Bayesian Computation

Accelerated life testing (ALT) is widely used in high-reliability product estimation to get relevant information about an item's performance and its failure mechanisms. To analyse the observed ALT data, reliability practitioners need to select a suitable accelerated life model based on the nature of the stress and the physics involved. A statistical model consists of (i) a lifetime distribution that represents the scatter in product life and (ii) a relationship between life and stress. In practice, several accelerated life models could be used for the same failure mode and the choice of the best model is far from trivial. For this reason, an efficient selection procedure to discriminate between a set of competing accelerated life models is of great importance for practitioners. In this paper, accelerated life model selection is approached by using the Approximate Bayesian Computation (ABC) method and a likelihood-based approach for comparison purposes. To demonstrate the efficiency of the ABC method in calibrating and selecting accelerated life model, an extensive Monte Carlo simulation study is carried out using different distances to measure the discrepancy between the empirical and simulated times of failure data. Then, the ABC algorithm is applied to real accelerated fatigue life data in order to select the most likely model among five plausible models. It has been demonstrated that the ABC method outperforms the likelihood-based approach in terms of reliability predictions mainly at lower percentiles particularly useful in reliability engineering and risk assessment applications. Moreover, it has shown that ABC could mitigate the effects of model misspecification through an appropriate choice of the distance function.     

Integration of computation and testing for reliability estimation

This paper develops a methodology to integrate reliability testing and computational reliability analysis for product development. The presence of information uncertainty such as statistical uncertainty and modeling error is incorporated. The integration of testing and computation leads to a more cost-efficient estimation of failure probability and life distribution than the tests-only approach currently followed by the industry. A Bayesian procedure is proposed to quantify the modeling uncertainty using random parameters, including the uncertainty in mechanical and statistical model selection and the uncertainty in distribution parameters. An adaptive method is developed to determine the number of tests needed to achieve a desired confidence level in the reliability estimates, by combining prior computational prediction and test data. Two kinds of tests — failure probability estimation and life estimation — are considered. The prior distribution and confidence interval of failure probability in both cases are estimated using computational reliability methods, and are updated using the results of tests performed during the product development phase.     

Using degradation data to assess reliability: a case study on train wheel degradation

Degradation experiments are usually used to assess the lifetime distribution of highly reliable products, which are not likely to fail under the traditional life tests or accelerated life tests. In such cases, if there exist product characteristics whose degradation over time can be related to reliability, then collecting ‘degradation data’ can provide information about product reliability. In general, the degradation data are modeled by a nonlinear regression model with random coefficients. If we can obtain the estimates of parameters under the model, then the failure‐time distribution can be estimated. In order to estimate those parameters, three basic methods are available, namely, the analytical, numerical and the approximate. They are chosen according to the complexity of the degradation path model used in the analysis. In this paper, the numerical and the approximate methods are compared in a simulation study, assuming a simple linear degradation path model. A comparison with traditional failure‐time analysis is also performed. The mean‐squared error of the estimated 100pth percentile of the lifetime distribution is evaluated for each one of the approaches. The approaches are applied to a real degradation data set. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting reliability growth

This paper describes a method for estimating and forecasting reliability from attribute data, using the binomial model, when reliability requirements are very high and test data are limited. Integer data—specifically, numbers of failures — are converted into non-integer data. The rationale is that when engineering corrective action for a failure is implemented, the probability of recurrence of that failure is reduced; therefore, such failures should not be carried as full failures in subsequent reliability estimates. The reduced failure value for each failure mode is the upper limit on the probability of failure based on the number of successes after engineering corrective action has been implemented. Each failure value is less than one and diminishes as test programme successes continue. These numbers replace the integral numbers (of failures) in the binomial estimate. This method of reliability estimation was applied to attribute data from the life history of a previously tested system, and a reliability growth equation was fitted. It was then ‘calibrated’ for a current similar system's ultimate reliability requirements to provide a model for reliability growth over its entire life-cycle. By comparing current estimates of reliability with the expected value computed from the model, the forecast was obtained by extrapolation.     

Lifetime prediction and reliability estimation methodology for Stirling-type pulse tube refrigerators by gaseous contamination accelerated degradation testing

Lifetime and reliability are the two performance parameters of premium importance for modern space Stirling-type pulse tube refrigerators (SPTRs), which are required to operate in excess of 10 years. Demonstration of these parameters provides a significant challenge. This paper proposes a lifetime prediction and reliability estimation method that utilizes accelerated degradation testing (ADT) for SPTRs related to gaseous contamination failure. The method was experimentally validated via three groups of gaseous contamination ADT. First, the performance degradation model based on mechanism of contamination failure and material outgassing characteristics of SPTRs was established. Next, a preliminary test was performed to determine whether the mechanism of contamination failure of the SPTRs during ADT is consistent with normal life testing. Subsequently, the experimental program of ADT was designed for SPTRs. Then, three groups of gaseous contamination ADT were performed at elevated ambient temperatures of 40 °C, 50 °C, and 60 °C, respectively and the estimated lifetimes of the SPTRs under normal condition were obtained through acceleration model (Arrhenius model). The results show good fitting of the degradation model with the experimental data. Finally, we obtained the reliability estimation of SPTRs through using the Weibull distribution. The proposed novel methodology enables us to take less than one year time to estimate the reliability of the SPTRs designed for more than 10 years.     

An analytical procedure for estimating field lifetime and failure rate of electronic packages

To understand the reliability characteristics of electronic packages under field conditions, accelerated life tests (ALT) with higher stress levels are needed in practice. Instead of the time-consuming and costly ALT, an analytical procedure based on finite element simulation and a Weibull statistical method to estimate the lifetime and failure rate of electronic packages subjected to thermal cycling loadings is proposed in the present study. To consider uncertainties, geometric parameters and material properties are assumed as random variables and incorporated into numerical simulation. The result shows that the mean time to failure (MTTF) of a studied electronic package under a specific thermal cycling loading condition can be predicted accurately. From either the proposed analysis or based on a particular model found in literature, the acceleration factor (AF) can be predicted accurately as well. Furthermore, according to the outcome from the Weibull statistical method, the failure rate under either the field or a particular test condition can be determined. Accordingly, the MTTF and failure rate of the package under field conditions can be estimated from the result of a simulated accelerated test as well as the AF model. The present study indicates that the proposed analytical procedure can help engineers evaluate the reliability of electronic packages rapidly and effectively.     

A Bayesian framework for accelerated reliability growth testing with multiple sources of uncertainty

Reliability growth tests are often used for achieving a target reliability for complex systems via multiple test‐fix stages with limited testing resources. Such tests can be sped up via accelerated life testing (ALT) where test units are exposed to harsher‐than‐normal conditions. In this paper, a Bayesian framework is proposed to analyze ALT data in reliability growth. In particular, a complex system with components that have multiple competing failure modes is considered, and the time to failure of each failure mode is assumed to follow a Weibull distribution. We also assume that the accelerated condition has a fixed time scaling effect on each of the failure modes. In addition, a corrective action with fixed ineffectiveness can be performed at the end of each stage to reduce the occurrence of each failure mode. Under the Bayesian framework, a general model is developed to handle uncertainty on all model parameters, and several special cases with some parameters being known are also studied. A simulation study is conducted to assess the performance of the proposed models in estimating the final reliability of the system and to study the effects of unbiased and biased prior knowledge on the system‐level reliability estimates.     

Different Estimation Methods for Constant Stress Accelerated Life Test under the Family of the Exponentiated Distributions

The Accelerated Life Testing (ALT) has been used for a long time in several fields to obtain information on the reliability of product components and materials under operating conditions in a much shorter time. One of the main purposes of applying ALT is to estimate the failure time functions and reliability performance under normal conditions. This paper concentrates on the estimation procedures under ALT and how to select the best estimation method that gives accurate estimates for the reliability function. For this purpose, different estimation methods are used, such as maximum likelihood, least squares (LS), weighted LS, and probability weighted moment. Moreover, the reliability function under usual conditions is predicted. The estimation procedures are applied under the family of the exponentiated distributions in general, and for the exponentiated inverted Weibull (EIW) as a special case. Numerical analysis including simulated data and a real life data set is conducted to compare the performances between these four methods. It is found that the ML method gives the best results among other estimation methods. Finally, a comparison between the EIW and the Inverted Weibull (IW) distributions based on a real life data set is made using a likelihood ratio test. It is observed that the EIW distribution can provide better fitting than the IW in case of ALT. Copyright © 2015 John Wiley & Sons, Ltd.     

Analysis of correlated multivariate degradation data in accelerated reliability growth

Modern engineering systems have become increasingly complex and at the same time are expected to be developed faster. To shorten the product development time, organizations commonly conduct accelerated testing on a small number of units to help identify failure modes and assess reliability. Many times design changes are made to mitigate or reduce the likelihood of such failure modes. Since failure-time data are often scarce in reliability growth programs, existing statistical approaches used for predicting the reliability of a system about to enter the field are faced with significant challenges. In this work, a statistical model is proposed to utilize degradation data for system reliability prediction in an accelerated reliability growth program. The model allows the components in the system to have multiple failure modes, each associated with a monotone stochastic degradation process. To take into account unit-to-unit variation, the random effects of degradation parameters are explicitly modeled. Moreover, a mean-degradation-stress relationship is introduced to quantify the effects of different accelerating variables on the degradation processes, and a copula function is utilized to model the dependency among different degradation processes. Both a maximum likelihood (ML) procedure and a Bayesian alternative are developed for parameter estimation in a two-stage process. A numerical study illustrates the use of the proposed model and identifies the cases where the Bayesian method is preferred and where it is better to use the ML alternative.     

Accelerated failure time models for reliability data analysis

Despite the popularity of the proportional hazards model (PHM) in analysing many kinds of reliability data, there are situations in which it is not appropriate. The accelerated failure time model (AFT) then provides an alternative. In this paper, a unified treatment of the accelerated failure time model is outlined for the standard reliability distributions (Weibull, log-normal, inverse Gaussian, gamma). The problem of choosing between the accelerated failure time models and proportional hazard models is discussed and effects of misspecification are reported. The techniques are illustrated in the analysis of data from a fatigue crack growth experiment.     

Long‐term Reliability Prediction of 935 nm LEDs Using Failure Laws and Low Acceleration Factor Ageing Tests

Numerous papers have already reported various results on electrical and optical performances of GaAs‐based materials for optoelectronic applications. Other papers have proposed some methodologies for a classical estimation of reliability of GaAs compounds using life testing methods on a few thousand samples over 10 000 hours of testing. In contrast, fewer papers have studied the complete relation between degradation laws in relation to failure mechanisms and the estimation of lifetime distribution using accelerated ageing tests considering a short test duration, low acceleration factor and analytical extrapolation. In this paper, we report the results for commercial InGaAs/GaAs 935 nm packaged light emitting diodes (LEDs) using electrical and optical measurements versus ageing time. Cumulative failure distributions are calculated using degradation laws and process distribution data of optical power. A complete methodology is described proposing an accurate reliability model from experimental determination of the failure mechanisms (defect diffusion) for this technology. Electrical and optical characterizations are used with temperature dependence, short‐duration accelerated tests (less than 1500 h) with an increase in bias current (up to 50%), a small number of samples (less than 20) and weak acceleration factors (up to 240). Copyright © 2005 John Wiley & Sons, Ltd.     

A Bayes approach to reliability prediction utilizing data from accelerated life tests and field failure observations

A Bayes approach is proposed to improve product reliability prediction by integrating failure information from both the field performance data and the accelerated life testing data. It is found that a product's field failure characteristic may not be directly extrapolated from the accelerated life testing results because of the variation of field use condition that cannot be replicated in the lab‐test environment. A calibration factor is introduced to model the effect of uncertainty of field stress on product lifetime. It is useful when the field performance of a new product needs to be inferred from its accelerated life test results and this product will be used in the same environment where the field failure data of older products are available. The proposed Bayes approach provides a proper mechanism of fusing information from various sources. The statistical inference procedure is carried out through the Markov chain Monte Carlo method. An example of an electronic device is provided to illustrate the use of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.     

A Bayesian zero‐failure reliability demonstration test of high quality electro‐explosive devices

Usually, for high reliability products the production cost is high and the lifetime is much longer, which may not be observable within a limited time. In this paper, an accelerated experiment is employed in which the lifetime follows an exponential distribution with the failure rate being related to the accelerated factor exponentially. The underlying parameters are also assumed to have the exponential prior distributions. A Bayesian zero‐failure reliability demonstration test is conducted to design forehand the minimum sample size and testing length subject to a certain specified reliability criterion. Probability of passing the test design as well as predictive probability for additional experiments is also derived. Sensitivity analysis of the design is investigated by a simulation study. Copyright © 2009 John Wiley & Sons, Ltd.     

基于GaAs激光器性能退化的可靠性度量方法

针对传统可靠性度量方法对高可靠性及长寿命的激光产品进行可靠性度量存在因模型假设不准确而出现可靠性度量错误风险的问题,基于性能退化轨迹提出了利用非参数局部线性回归估计对实际的退化模型进行直接估计的方法.该方法在确定实际模型后,利用失效阈值外推获得伪失效寿命时间,进而采用完全寿命时间数据进行可靠性度量.最后通过对GaAs激光器的退化数据进行可靠性验证分析,结果表明此方法提高了可靠性的预测精度,拟合程度高,稳健性好.采用非参数局部线性回归估计方法得到的结果合理、准确.     

Estimation of time‐to‐failure distribution derived from a degradation model using fuzzy clustering

Some life tests are terminated with few or no failures. In such cases, a recent approach is to obtain degradation measurements of product performance that may contain some useful information about product reliability. Generally degradation paths of products are modeled by a nonlinear regression model with random coefficients. If we can obtain the estimates of parameters under the model, then the time‐to‐failure distribution can be estimated. In some cases, the patterns of a few degradation paths are different from those of most degradation paths in a test. Therefore, this study develops a weighted method based on fuzzy clustering procedure to robust estimation of the underlying parameters and time‐to‐failure distribution. The method will be studied on a real data set. Copyright © 2000 John Wiley & Sons, Ltd.     

Infant mortality modelling for vlsi devices using graphical estimation

This paper presents a practical methodology for the routine analysis of VLSI infant mortality data. Device families are modelled using established graphical parameter estimation techniques, and the model parameters are applied to individual device types within the family. Burn-in requirements are calculated to achieve a desired early life reliability level. A technical summary of the methods is presented, and a small data set is analysed as an example. The analysis results from three large device families are also presented.