Bayesian optimal design of step stress accelerated degradation testing

This study presents a Bayesian methodology for de- signing step stress accelerated degradation testing （SSADT） and its application to batteries. First, the simulation-based Bayesian de- sign framework for SSADT is presented. Then, by considering his- torical data, specific optimal objectives oriented Kullback-Leibler （KL） divergence is established. A numerical example is discussed to illustrate the design approach. It is assumed that the degrada- tion model （or process） follows a drift Brownian motion; the accele- ration model follows Arrhenius equation; and the corresponding parameters follow normal and Gamma prior distributions. Using the Markov Chain Monte Carlo （MCMC） method and WinBUGS software, the comparison shows that KL divergence is better than quadratic loss for optimal criteria. Further, the effect of simulation outiiers on the optimization plan is analyzed and the preferred sur- face fitting algorithm is chosen. At the end of the paper, a NASA lithium-ion battery dataset is used as historical information and the KL divergence oriented Bayesian design is compared with maxi- mum likelihood theory oriented locally optimal design. The results show that the proposed method can provide a much better testing plan for this engineering application.

Analysis of Incomplete Data of Accelerated Life Testing with Competing Failure Modes

Data obtained from accelerated life testing （ALT） when there are two or more failure modes, which is commonly referred to as competing failure modes, are often incomplete. The incompleteness is mainly due to censoring, as well as masking which might be the case that the failure time is observed, but its corresponding failure mode is not identified. Because the identification of the failure mode may be expensive, or very difficult to investigate due to lack of appropriate diagnostics. A method is proposed for analyzing incomplete data of constant stress ALT with competing failure modes. It is assumed that failure modes have s-independent latent lifetimes and the log lifetime of each failure mode can be written as a linear function of stress. The parameters of the model are estimated by using the expectation maximum （EM） algorithm with incomplete data. Simulation studies are performed to check＇model validity and investigate the properties of estimates. For further validation, the method is also illustrated by an example, which shows the process of analyze incomplete data from ALT of some insulation system. Because of considering the incompleteness of data in modeling and making use of the EM algorithm in estimating, the method becomes more flexible in ALT analysis.

Optimum design of equivalent accelerated life testing plans based on proportional hazards-proportional odds model

The optimum design of equivalent accelerated life testing plan based on proportional hazards-proportional odds model using D-optimality is presented. The defined equivalent test plan is the test plan that has the same value of the determinant of Fisher information matrix. The equivalent test plan of step stress accelerated life testing （SSALT） to a baseline optimum constant stress accelerated life testing （CSALT） plan is obtained by adjusting the censoring time of SSALT and solving the optimization problem for each case to achieve the same value of the determinant of Fisher information matrix as in the baseline optimum CSALT plan. Numer- ical examples are given finally which demonstrate the equivalent SSALT plan to the baseline optimum CSALT plan reduces almost half of the test time while achieving approximately the same estimation errors of model parameters.

Parameter Estimation Based on Censored Data under Partially Accelerated Life Testing for Hybrid Systems due to Unknown Failure Causes

In general,simple subsystems like series or parallel are integrated to produce a complex hybrid system.The reliability of a system is determined by the reliability of its constituent components.It is often extremely difficult or impossible to get specific information about the component that caused the system to fail.Unknown failure causes are instances in which the actual cause of systemfailure is unknown.On the other side,thanks to current advanced technology based on computers,automation,and simulation,products have become incredibly dependable and trustworthy,and as a result,obtaining failure data for testing such exceptionally reliable items have become a very costly and time-consuming procedure.Therefore,because of its capacity to produce rapid and adequate failure data in a short period of time,accelerated life testing(ALT)is the most utilized approach in the field of product reliability and life testing.Based on progressively hybrid censored(PrHC)data froma three-component parallel series hybrid system that failed to owe to unknown causes,this paper investigates a challenging problem of parameter estimation and reliability assessment under a step stress partially accelerated life-test(SSPALT).Failures of components are considered to follow a power linear hazard rate(PLHR),which can be used when the failure rate displays linear,decreasing,increasing or bathtub failure patterns.The Tempered random variable(TRV)model is considered to reflect the effect of the high stress level used to induce early failure data.The maximum likelihood estimation(MLE)approach is used to estimate the parameters of the PLHR distribution and the acceleration factor.A variance covariance matrix(VCM)is then obtained to construct the approximate confidence intervals(ACIs).In addition,studentized bootstrap confidence intervals(ST-B CIs)are also constructed and compared with ACIs in terms of their respective interval lengths(ILs).Moreover,a simulation study is conducted to demonstrate the performance of the estimation procedures and the methodology discussed in this paper.Finally,real failure data from the air conditioning systems of an airplane is used to illustrate further the performance of the suggested estimation technique.

Efficient Method for Accelerated Reliability Qualification Testing

Based on the theoretical inference and experiment verification,a method was proposed to carry out the accelerated reliability qualification testing. First,theoretical inference was used to get the acceleration coefficients of super Gauss vibration stress and temperature stress. Then, by applying these coefficients, an accelerated reliability qualification testing curve was obtained from the standard tests. Finally,the actual experiment on a digital marine control device was carried out under the proposed testing method.The experiment result shows that the proposed method can reduce the total experiment time and improve the efficiency of the reliability qualification test.

Optimal Design of Multiple Stresses Accelerated Life Test Plan Based on Transforming the Multiple Stresses to Single Stress

For planning optimum multiple stresses accelerated life test plans, a commonly followed guiding principle is that all parameters of the life-stress relationship should be estimated, and the number of the stress level combinations must be no less than the number of parameters of the life-stress relationship. However, the general objective of an accelerated life test（ALT） is to assess thep-th quantile of the product life distribution under normal stress. For this objective,estimating all model parameters is not necessary, and this will increase the cost of test. Based on the theoretical conclusion that the stress level combinations of the optimum multiple stresses ALT plan locate on a straight line through the origin of coordinate, it is proposed that a design idea of planning the optimum multiple stresses ALT plan through transforming the problem of designing an optimum multiple stresses ALT plan to designing an optimum single stress ALT plan. Moreover, a method of planning the optimum multiple stresses ALT plan which can avoid estimating all model parameters is established. An example shows that, the proposed plan which only has two stress level combinations could achieve an accuracy no less than the traditional plan, and save the test time and cost on one stress level combination at least; when the actual product life is less than the design value, even the deviation of the model initial parameters value is up to 20%, the variance of the estimation of thep-th quantile of the proposed plan is still smaller than the traditional plans approximately 25%. A design method is provided for planning the optimum multiple stresses ALT which uses the statistical optimum degenerate test plan as the optimum multiple stresses accelerated life test plan.

Optimum Constant-stress Plan for Accelerated Life Test with Censoring Ⅱ

In this paper, we obtain the optimum plan by discussing a constant-stress accelerated life test (ALT) satisfying the condition (3.3) at k stresses under an exponential distribution.

New method of online testing and data processing for LED lamps

In order to achieve quick and accurate lifetime prediction of LED lighting products under the testing time of 2 000 h, a method of online testing of luminous flux is proposed under the condition of temperature stress.Exponential fitting of lumen maintenance, the Bayesian estimation of failure probability, the Weibull distribution of lifetime and the Arrhenius model of the decay rate are used in combination to acquire the distribution of failure probability over time at the ambient temperatures of 25 ℃. The lifetime test of the same lamps based on the Energy Star standard under the testing time of 6 000 h is also implemented to verify the effectiveness of the method. The errors of lifetimes acquired with the proposed method are 7%, 4%, 3% and 1% at the failure probabilities of 62. 3%, 10%, 5% and 1%,respectively.

Accelerated Degradation Reliability Modeling and Test Data Statistical Analysis of Aerospace Electrical Connector

As few or no failures occur during accelerated life test,it is difficult to assess reliability for long-life products with traditional life tests.Reliability assessment using degradation data of product performance over time becomes a significant approach.Aerospace electrical connector is researched in this paper.Through the analysis of failure mechanism,the performance degradation law is obtained and the statistical model for degradation failure is set up; according to the research on statistical analysis methods for degradation data,accelerated life test theory and method for aerospace electrical connector based on performance degradation is proposed by improving time series analysis method,and the storage reliability is assessed for Y11X series of aerospace electrical connector with degradation data from accelerated degradation test.The result obtained is basically consistent with that obtained from accelerated life test based on failure data,and the two estimates of product＇s characteristic life only have a difference of 8.7%,but the test time shortens about a half.As a result,a systemic approach is proposed for reliability assessment of highly reliable and long-life aerospace product.

Step-stress Accelerated Degradation Test Modeling and Statistical Analysis Methods

In order to get a rapid assessment on the storage reliability of high-reliable and long-life products within the storage period, accelerated degradation test data with a large amount of reliability information of product is adopted. Conducting a constant-stress accelerated degradation test（CSADT） is generally very costly as it requires a large sample size and long time for test. To overcome this problem, it is necessary to carry out research on modeling and statistical analysis methods of step-stress accelerated degradation test （SSADT）. Taking electrical connectors as the object, a research is conducted on statistical model and assessment method for SSADT. On the basis of mixed-effect degradation path model, the statistical model of SSADT for electrical connectors is presented, the maximum likelihood method for SSADT data based on mixed-effect degradation model is proposed. SSADT accelerated by temperature stress is conducted to Y11X-1419 type of electrical connectors, and the storage reliability is assessed with the SSADT data. Compared with the result obtained from accelerated life test, the reliability estimation of 32-year storage period for electrical connectors obtained from S SADT data only have a difference of 0.869%, which validates the accuracy of the degradation model and the feasibility of the test data statistic analysis method put forward.

Residual lifetime prediction model of nonlinear accelerated degradation data with measurement error

For the product degradation process with random effect (RE), measurement error (ME) and nonlinearity in step-stress accelerated degradation test (SSADT), the nonlinear Wiener based degradation model with RE and ME is built. An analytical approximation to the probability density function (PDF) of the product's lifetime is derived in a closed form. The process and data of SSADT are analyzed to obtain the relation model of the observed data under each accelerated stress. The likelihood function for the population-based observed data is constructed. The population-based model parameters and its random coefficient prior values are estimated. According to the newly observed data of the target product in SSADT, an analytical approximation to the PDF of its residual lifetime (RL) is derived in accordance with its individual degradation characteristics. The parameter updating method based on Bayesian inference is applied to obtain the posterior value of random coefficient of the RL model. A numerical example by simulation is analyzed to verify the accuracy and advantage of the proposed model.

Optimal Design of Multiple Stress Constant Accelerated Life Test Plan on Non-rectangle Test Region

For optimal design of constant stress accelerated life test（CSALT） with two-stress, if the stresses could not reach the highest levels simultaneously, the test region becomes non-rectangular. For optimal CSALT design on non-rectangle test region, the present method is only focused on non-rectangle test region with simple boundary, and the optimization algorithm is based on experience which can not ensure to obtain the optimal plan. In this paper, considering the linear-extreme value model and the optimization goal to minimize the variance of lifetime estimate under normal stress, the optimal design method of two-stress type-I censored CSALT plan on general non-rectangular test region is proposed. First, two properties of optimal test plans are proved and the relationship of all the optimal test plans is determined analytically. Then, on the basis of the two properties, the optimal problem is simplified and the optimal design method of two-stress CSALT plan on general non-rectangular test region is proposed. Finally, a numerical example is used to illustrate the feasibility and effectiveness of the method, The result shows that the proposed method could obtain the optimal test plan on non-rectangular test regions with arbitrary boundaries. This research provides the theory and method for two-stress optimal CSALT planning on non-rectangular test regions.

Estimation for constant-stress accelerated life test from generalized half-normal distribution

In the constant-stress accelerated life test, estimation issues are discussed for a generalized half-normal distribution under a log-linear life-stress model. The maximum likelihood estimates with the corresponding fixed point type iterative algorithm for unknown parameters are presented, and the least square estimates of the parameters are also proposed. Meanwhile, confidence intervals of model parameters are constructed by using the asymptotic theory and bootstrap technique. Numerical illustration is given to investigate the performance of our methods.

Constant-step stress accelerated life test of VFD under Weibull distribution case

Constant-step stress accelerated life test of Vacuum Fluorescent Display (VFD) was conducted with increased cathode temperature. Statistical analysis was done by applying Weibull distribution for describing the life, and Least Square Method (LSM)for estimating Weibull parameters. Self-designed special software was used to predict the VFD life. Numerical results showed that the average life of VFD is over 30000 h, that the VFD life follows Weibull distribution, and that the life-stress relationship satisfies linear Arrhenius equation completely. Accurate calculation of the key parameter enabled rapid estimation of VFD life.

Property changes of anchor grout calcined ginger nuts admixed with fly ash and quartz sand after accelerated ageing tests

Calcined ginger nuts admixed by fly ash and quartz sand (CGN-(F+S)) has been validated to be basically compatible to earthen sites as an anchor grout. Accelerated ageing tests including water stability test, temperature and humidity cycling test, soundness test and alkali resistance test are conducted with the objective to further research the property changes of CGN-(F+S) grout. Density, surface hardness, water penetration capacity, water permeability capacity, soluble salt, scanning electron microscopy (SEM) images and energy dispersive spectrometry (EDS) spectrum of these samples have been tested after accelerated ageing tests. The results show that densities of samples decrease, surface hardness, water penetration capacity and water permeability capacity of samples increase generally. Besides, soluble salt analysis, SEM and EDS results well corroborate the changes. Based on the results it can be concluded that property changes are most serious after temperature and humidity cycling test, followed by water stability, soundness and alkali resistance test in sequence. But in general, CGN-(F+S) still has good durability.

Laboratory and field testing of bolting systems subjected to highly corrosive environments

The capacity of ground support components which have been affected by corrosion is reduced and may ultimately lead to dynamic failure of the component and the strata. In order to maintain an effective,long-term ground support system, significant campaigns of rehabilitation are often required in corrosion affected areas which also expose the workers to hazardous conditions. The most common corrosion protection for steel ground support utilises sacrificial systems such as galvanising. Galvanising has previously been proven to be susceptible to some corrosion processes. Stainless steel is the most effective in resistance to corrosion, but can be cost prohibitive, and its mechanical properties often make it unsuited to use in ground support components. Providing an outer protective plastic coating to bolts has proven to be an effective means of protecting the inner steel bar from corrosion. However, these support systems tend to be susceptible to coating damage, and require post cement grouting to provide full encapsulation. In comparison to a standard bolt/resin system, they can be slow to install and expensive.These systems have also been shown to reduce overall load transfer performance of the bolting system. In order to provide a higher level of corrosion protection whilst maintaining current installation practices and bolting cycle times, Minova has developed the Enduro^(TM)steel ground support range. The Enduro^(TM) range consists of standard Minova steel ground support components which have been treated with a unique coating process. The Enduro^(TM)coating has been tested in the harshest of conditions, in laboratory controlled conditions and in underground trials. It has been proven to effectively resist or completely eliminate the formation of corrosion, even in the most aggressive environments. This paper explains the process and provides the details of the laboratory and underground corrosion performance testing carried out on Enduro^(TM)ground support products.

Design of Accelerated Life Test Plans——Overview and Prospect

Accelerated life test(ALT) is currently the main method of assessing product reliability rapidly, and the design of efficient test plans is a critical step to ensure that ALTs can assess the product reliability accurately, quickly, and economically. With the promotion of the national strategy of civil-military integration, ALT will be widely used in the research and development(R&D) of various types of products, and the ALT plan design theory will face further challenges. To aid engineers in selecting appropriate theories and to stimulate researchers to develop the theories required in engineering, with focus on the demands for theory research that arise from the implementation of ALT, this paper reviews and summarizes the development of ALT plan design theory. The development of the theory and method for planning optimal ALT for location-scale distribution, which is the most applied and mature theory of designing the optimal ALT plan, are described in detail. Taking this as the center of radiation, some problems that ALT now faces, such as the verification of the statistical model, limitation of sample size, solutions of resource limits, optimization of the test arrangement, and management of product complexity, are discussed, and the general ideas and methods of solving these problems are analyzed. Suggestions for selecting appropriate ALT plan design theories are proposed, and the urgent solved theory problems and opinions of their solutions are proposed. Based on the principle of convenience for engineers to select appropriate methods according to the problems found in practice, this paper reviews the development of optimal ALT plan design theory by taking the engineering problems arising from the ALT implementation as the main thread, provides guidelines on selecting appropriate theories for engineers, and proposes opinions about the urgent solved theory problems for researchers.

Strength Degradation of Wood Members Based on the Correlation of Natural and Accelerated Decay Experiments

An accelerated decay test and a natural decay test were conducted synchronically to explore the strength degradation of decaying wood members under long-term exposure to natural environment.A natural decay test was carried out to measure the bending strength,compressive strength parallel to grain and modulus of elasticity of the wood members,with 6 groups of specimens decayed in natural environment for 3 to 18 months respectively.To compare with corresponding decay test,in which 6 other groups of specimens were measured under accelerated conditions.The experimental data collected were evaluated by Pearson productmoment for the correlation.The results indicate that the mechanical properties of the accelerated decay were highly correlated with those in natural environment,both of which decreased in the same trend.Under the given test conditions,the mean value of the accelerated decay test data were curve-fitted to achieve the time-dependent degradation model of the bending strength,the compressive strength parallel to grain,as well as the modulus of elasticity.Due to the high correlation,the acceleration shift factors(ASF)of the two tests were derived,where the bending strength of 2.934,the compressive strength parallel to grain of 2.519 and the elastic modulus of 2.346 were employed to formulate the strength degradation models in the long-term natural environment.The results verify that the exponential function
σ=σ0e^(-βt)enables to exactly capture the degradation of the mechanical properties of wood members decayed in natural environment.

A New Approach of Studying Correlation between Outdoor Exposure and Indoor Accelerated Corrosion Test for High Polymer Materials

The correlation between outdoor exposure and indoor accelerated corrosion test for high polymer materials was investigated according to the variation of the functional group of exposure models aged. Environment aging intensities at different zones （ Wuhan and Lasa with the same latitude ） and the influences of indoor accelerating factors including water and ultraviolet on weathering performant.e of high polymer materials were also studied by comparing different indoor accelerated corrosion testing results. The experimental results show that ： by testing variations of carbonyl exponent of polythene （ which represented the degradation behavior of high polymer materials due to ultraviolet oxidation of douIole bond） and ultraviolet absorbance of polycarbonate （which represented the degradation behavior of high polymer materials due to abevacuation of branched chain ）, the degradation behavior of high polymer materials could be studied. Carbonyl exponent of polythene exposed in Wuhan and Lasa for 1 year was equal to that exposed in indoor cycle ultraviolet for 128 h anti 170 It, respectively, the ultraviolet absorbance of polycarbonate exposed in Wuhan for 1 year was equal to that exposed in indoor cycle ultraviolet for 240 h. The ratio of environment aging intensity of Lasa to Wuhan was around 1.2. With the prolongation of cycle accelerated ultraviolet exposure time, the variations of carbonyl exponent of polythene and the ultraviolet absorbance of polycarbonate were in the same shape of first order exponential decay curiae. Accompanied with ultraviolet, the effect of water condensated on the sample on weathering performance of polythene was more .significant than that of polycarbonate.

ACCELERATED LIFE TEST STUDIES OF NEW COATED DISPENSER CATHODES

The life of impregnated Ba-W cathodes with a new construction have been evaluated using an accelerated life test at three different temperatures (1170℃,1130℃,1090℃) and constant current density (2A/cm^2).According to the relationship of life with operating temperatures,an accelerated equation has been set up.The cathode life at normal operating temperature is deducted based on the accelerated equation.The results show that life of the novel cathode exceeds 190,000 hour at a current density of 2A/cm^2.