Integration method for reliability assessment with multi-source incomplete accelerated degradation testing data

ABSTRACT

During the product life cycle, the lifetime information will be collected at each stage, mainly from different tests at the R&D phase, field usage, and maintenance. To comprehensively conduct reliability assessments, it generally requires the integration of multi-source datasets, even that from similar products. In this article, we considered the scenario that products have been arranged with several accelerated degradation tests (ADT) under different types of accelerated stresses with dependency. The obtained data is called incomplete ADT dataset with incomplete stress conditions which fails the traditional integration method for reliability assessments. A novel method is proposed to accomplish this task through mutually exclusive set (MES) theory. The probability assignments for each dataset are given through the union set of several MESs. Then, the multi-source ADT datasets are integrated with the assigned weights of probabilities. Finally, a simulation study and a real application are given to illustrate the effectiveness of the proposed methodology.     

Reliability analysis for accelerated degradation data based on the Wiener process with random effects

On the basis of the principle of degradation mechanism invariance, a Wiener degradation process with random drift parameter is used to model the data collected from the constant stress accelerated degradation test. Small-sample statistical inference method for this model is proposed. On the basis of Fisher's method, a test statistic is proposed to test if there is unit-to-unit variability in the population. For reliability inference, the quantities of interest are the quantile function, the reliability function, and the mean time to failure at the designed stress level. Because it is challenging to obtain exact confidence intervals (CIs) for these quantities, a regression type of model is used to construct pivotal quantities, and we develop generalized confidence intervals (GCIs) procedure for those quantities of interest. Generalized prediction interval for future degradation value at designed stress level is also discussed. A Monte Carlo simulation study is used to demonstrate the benefits of our procedures. Through simulation comparison, it is found that the coverage proportions of the proposed GCIs are better than that of the Wald CIs and GCIs have good properties even when there are only a small number of test samples available. Finally, a real example is used to illustrate the developed procedures.     

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.     

航天电连接器加速性能退化试验可行性研究

为解决高可靠长寿命的航天电连接器即使进行加速寿命试验也难以获得失效数据的问题,对电连接器失效模式以及长期贮存下接触性能变化结果进行分析,表明电连接器性能退化存在可能性,并根据长期贮存下试验数据的验证,得出电连接器性能具有退化特性.通过温度加速应力下电连接器接触性能数据的分析,得出其性能退化具有加速性,还具有一定的加速退化规律,这为采用加速性能退化试验对航天电连接器进行可靠性评估提供了依据.     

A hierarchical modeling approach to accelerated degradation testing data analysis: A case study

In this case study, we investigate the degradation process of light‐emitting diodes (LEDs), which is used as a light source in DNA sequencing machines. Accelerated degradation tests are applied by varying temperature and forward current, and the light outputs are measured by a computerized measuring system. A degradation path model, which connects to the LED function recommended in Mitsuo (1991), is used in describing the degradation process. We consider variations in both measurement errors and degradation paths among individual test units. It is demonstrated that the hierarchical modeling approach is flexible and powerful in modeling a complex degradation process with nonlinear function and random coefficient. After fitting the model by maximum likelihood estimation, the failure time distribution can be obtained by simulation. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

An approach that can quickly assess product reliability

One of the ways to determine the inherent reliability of a design is to test it under controlled environments based on the product usage that is understood by the development requirements. This can be accomplished by performing a reliability growth test on the product. A testing approach can be developed that enhances the product reliability and reduces the production testing cycle. Research performed to date points to the fact that this proposed methodology may not exist, and is the focus of continued research to refine the development of an approach to fill this gap. The combining of multiple testing approaches in order to ensure that the reliability requirement is met or exceeded while at the same time having the capability to reduce the testing cycle time when required due to schedule and cost constraints has not been addressed in the open literature till date. The methodology is to utilize a combination of multiple testing approaches to accomplish this task by exploring complementary testing ideas from various technologies that have been utilized previously with documented success. This approach demonstrated that component‐level testing reduced the product‐level failures by greater than 80% while at the same time reducing the schedule to complete all testing. Copyright © 2009 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 literature review on planning and analysis of accelerated testing for reliability assessment

Accelerated testing has been widely used for several decades. Started with accelerated life tests with constant‐stress loadings, more interest has been focused prominently on accelerated degradation tests and time‐varying stress loadings. Because accelerated testing is crucial to the assessment of product reliability and the design of warranty policy, it is important to develop an efficacious test plan that encompasses and addresses important issues, such as design of stress profiles, sample allocation, test duration, measurement frequency, and budget constraint. In recent years, extensive research has been conducted on the optimal design of accelerated testing plans, and the consideration of multiple stresses with interactions has become a big challenge in such experimental designs. The purpose of this study is to provide a comprehensive review of important methods for statistical inference and optimal design of accelerated testing plans by compiling the existing body of knowledge in the area of accelerated testing. In this work, different types of test planning strategies are categorized, and their drawbacks and the research trends are provided to assist researchers and practitioners in conducting new research in this area.     

小样本条件下双应力步降加速退化试验优化设计

针对小样本条件下高可靠性长寿命产品的性能往往受到多个应力的影响,且在加速退化试验中该类产品在有限试验时间内难以获得大量性能退化信息的问题,提出一种小样本条件下双应力步降加速退化试验优化设计方法。采用Monte-Carlo对加速试验进行仿真模拟,在样本量大小一定的条件下,以监测频率、应力水平数、监测次数作为设计变量,以总的试验费用作为约束条件,以正常使用应力下的p阶分位寿命渐进方差估计作为目标函数,建立小样本条件下双应力步降加速退化试验优化设计模型。通过仿真实例,验证该方法的有效性、可行性。     

Equivalence analysis of accelerated degradation mechanism based on stochastic degradation models

For an effective accelerated degradation test, it is important to ensure that the degradation mechanism under different stress levels remains unchanged. In this article, we are interested in the equivalence analysis of accelerated degradation mechanism based on degradation data rather than physical or chemical techniques. Under the assumption that products' underlying degradation follows stochastic degradation models, we first introduce the relationship between mechanism equivalence and parameters of stochastic degradation models based on the acceleration factor invariant principle. Then the necessary conditions for mechanism equivalence, which should be satisfied under different stress levels, are derived and tested by the proposed parameter equivalence test method based on the modified Bartlett statistic and T statistic. Next a novel selection method for stochastic degradation models is derived therefrom by comparing the variation of coefficients of acceleration factors. The accuracy of the necessary conditions and the parameter equivalence test method is demonstrated through a simulation study. In addition, an electrical connector example with real stress relaxation data is analyzed to illustrate the proposed method further.     

Planning constant-stress accelerated life tests with multiple stresses based on D-optimal design

With the rapid technological advances, products are becoming more reliable. Then, multistress accelerated life testing (MALT) has been adopted in engineering to obtain failure information in a limited time. In order to make the testing procedure more efficient, it is necessary to better design the test plan. However, to date, relevant research on planning of MALT is limited. Multiple stresses will lead to plenty of stress-level combinations that require too much cost and time to implement. Besides, there may be interactions among multiple stresses, which need more experiments for parameter estimation. To solve these problems, we propose a novel planning method for constant-stress MALT under lognormal distribution using D-optimal design, which can reduce required test points efficiently and deal with second-order effects in models. In ALT, the log-linear model is often used to describe the life-stress relationship. Hence, D-optimal design is adopted in this paper to select test points from the whole test region. Then, optimal unit allocation plans are formulated under V/D-optimality criterion, respectively, where type I and type II censoring are both discussed. A real case of light-emitting device (LED) is presented to compare the proposed approach with other two existing methods. The results show that the proposed method performs better than other two existing methods both in prediction accuracy and estimation precision. Moreover, a sensitivity analysis reveals the robustness of the optimal plans determined by the proposed method.     

Analysis of complex system reliability with correlated random vectors

The analysis of reliability of complex engineering systems remains a challenge in the field of reliability. It will be even more difficult if correlated random vectors are involved, which is generally the case as practical engineering systems invariably contain parameters that are mutually correlated. A new method for transforming correlated distributions, involving the Nataf transformation, is proposed that avoids the solution of integral equations; the method is based on the Taylor series expansion of the probability density function (PDF) of a bivariate normal distribution resulting in an explicit polynomial equation of the equivalent correlation coefficient. The required numerical results can be obtained efficiently and accurately.The proposed method for transformation of correlated random vectors is useful for developing a method for system reliability including complex systems with correlated random vectors. Based on the complete system failure process (originally defined as the development process of nonlinearity) and the fourth-moment method, the analysis of system reliability for elastic-plastic material avoids the identification of the potential failure modes of the system and their mutual correlations which are required in the traditional methods. Finally, four examples are presented – two examples to illustrate the potential of the new method for transformation of correlated random vectors, and two examples to illustrate the application of the proposed more effective method for system reliability.     

Analyzing experiments with degradation data for improving reliability and for achieving robust reliability

Statistically designed experiments provide a proactive means for improving reliability; moreover, they can be used to design products that are robust to noise factors which are hard or impossible to control. Traditionally, failure‐time data have been collected; for high‐reliability products, it is unlikely that failures will occur in a reasonable testing period, so the experiment will be uninformative. An alternative, however, is to collect degradation data. Take, for example, fluorescent lamps whose light intensity decreases over time. Observation of light‐intensity degradation paths, given that they are smooth, provides information about the reliability of the lamp, and does not require the lamps to fail. This paper considers experiments with such data for ‘reliability improvement’, as well as for ‘robust reliability achievement’ using Taguchi's robust design paradigm. A two‐stage maximum‐likelihood analysis based on a nonlinear random‐effects model is proposed and illustrated with data from two experiments. One experiment considers the reliability improvement of fluorescent lamps. The other experiment focuses on robust reliability improvement of light‐emitting diodes. Copyright © 2001 John Wiley & Sons, Ltd.     

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.     

The transformed gamma process for degradation phenomena in presence of unexplained forms of unit‐to‐unit variability

The transformed gamma process is a suitable model for degradation phenomena where damages accumulate gradually over time in a sequence of tiny increments. Attractiveness of the transformed gamma process mainly lies in the fact that it provides a relatively easy way for dealing with phenomena in which the degradation increments over disjoint time intervals are not independent. The transformed gamma process is also a very flexible model. In fact, it is indexed by 2 functions, the “age function” and the “state function,” whose mathematical form can be chosen ad hoc for modeling the dependence of the future degradation increment of a unit on its current age and state, respectively. In this paper, the transformed gamma process is adopted to describe the degradation paths of degrading units in the presence of an unexplained form of unit‐to‐unit variability. The degradation path of each unit is described via a transformed gamma process. Heterogeneity among paths of different units is accounted for by assuming that the scale parameters of the age and state functions vary randomly from unit to unit. Under these assumptions, a quite mathematically tractable model is obtained. The main properties of the proposed model are discussed, and inferential procedures based on the maximum likelihood criterion are implemented. A simple test is presented to check the goodness of fit of the proposed model. Three applicative examples, based on real degradation data, are developed.     

Impacts of networking effects on software reliability growth processes: A multi‐attribute utility theory approach

Software reliability growth models, which are based on nonhomogeneous Poisson processes, are widely adopted tools when describing the stochastic failure behavior and measuring the reliability growth in software systems. Faults in the systems, which eventually cause the failures, are usually connected with each other in complicated ways. Considering a group of networked faults, we raise a new model to examine the reliability of software systems and assess the model's performance from real‐world data sets. Our numerical studies show that the new model, capturing networking effects among faults, well fits the failure data. We also formally study the optimal software release policy using the multi‐attribute utility theory (MAUT), considering both the reliability attribute and the cost attribute. We find that, if the networking effects among different layers of faults were ignored by the software testing team, the best time to release the software package to the market would be much later while the utility reaches its maximum. Sensitivity analysis is further delivered.     

Designing an accelerated degradation experiment by optimizing the estimation of the percentile

Degradation tests are widely used to assess the reliability of highly reliable products which are not likely to fail under traditional life tests or accelerated life tests. However, for some highly reliable products, the degradation may be very slow and hence it is impossible to have a precise assessment within a reasonable amount of testing time. In such cases, an alternative is to use higher stresses to extrapolate the product's reliability at the design stress. This is called an accelerated degradation test (ADT). In conducting an ADT, several decision variables, such s the inspection frequency, sample size and termination time, at each stress level are influential on the experimental efficiency. An inappropriate choice of these decision variables not only wastes experimental resources but also reduces the precision of the estimation of the product's reliability at the use condition. The main purpose of this paper is to deal with the problem of designing an ADT. By using the criterion of minimizing the mean‐squared error of the estimated 100 th percentile of the product's lifetime distribution at the use condition subject to the constraint that the total experimental cost does not exceed a predetermined budget, a nonlinear integer programming problem is built to derive the optimal combination of the sample size, inspection frequency and the termination time at each stress level. A numerical example is provided to illustrate the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

Optimal Design of Step‐stress Accelerated Degradation Test with Multiple Stresses and Multiple Degradation Measures

Products with high reliability and long lifetimes undergo different types of stresses in use conditions. Often there are multiple performance indicators for products that gradually degrade over time. An accelerated degradation test (ADT) with multiple stresses and multiple degradation measures (MSMDM) may provide a more accurate prediction of the lifetime of these products. However, the ADT requires a moderate sample size, which is not practical for newly developed or costly products with only a few available test specimens on hand. Therefore, in this study, a step‐stress ADT (SSADT) with MSMDM is developed. However, it is a difficult endeavor to design SSADT with MSMDM to predict accurate reliability estimation under several constraints. Previous methods are used only for cases with a single stress or degradation measure, and are not suitable for SSADT with MSMDM. In this paper, an approach of optimal design is proposed for SSADT with MSMDM and its steps for a rubber sealed O‐ring are demonstrated to illustrate its validity. Results of the sensitivity analysis for the optimal test plan indicate robustness when the deviation of model parameters is within 10% of the estimated values. Copyright © 2017 John Wiley & Sons, Ltd.     

An orthogonal normal transformation of correlated non-normal random variables for structural reliability

In this paper, an efficient and explicit technique is proposed for transforming correlated non-normal random variables into independent standard normal variables based on the three-parameter (3P) lognormal distribution. In contrast with the classic Nataf transformation, the derived equivalent correlation coefficient in non-orthogonal standard normal space of the proposed transformation is expressed as an explicit formula, thereby avoiding tedious iteration algorithm or multifarious empirical formulas. Meanwhile, the applicable range of the original correlation coefficient is determined based on fundamental properties of the proposed expression of correlation distortion and the definition of correlation coefficient. The proposed transformation requires only the first three moments (i.e., mean, standard deviation, and skewness) of basic random variables, as well as their correlation matrix. Therefore, the proposed transformation can also be applied even when the joint distribution or marginal distributions of the basic random variables are unknown. Several numerical examples are presented to demonstrate the user-friendliness, efficiency, and accuracy of the proposed transformation applied in structural reliability analysis involving correlated non-normal random variables.