Designing Adaptive Multiple Dependent State Sampling Plan for Accelerated Life Tests

A novel adaptive multiple dependent state sampling plan(AMDSSP)was designed to inspect products from a continuous manufacturing process under the accelerated life test(ALT)using both double sampling plan(DSP)and multiple dependent state sampling plan(MDSSP)concepts.Under accelerated conditions,the lifetime of a product follows the Weibull distribution with a known shape parameter,while the scale parameter can be determined using the acceleration factor(AF).The Arrhenius model is used to estimate AF when the damaging process is temperature-sensitive.An economic design of the proposed sampling plan was also considered for the ALT.A genetic algorithm with nonlinear optimization was used to estimate optimal plan parameters to minimize the average sample number(ASN)and total cost of inspection(TC)under both producer’s and consumer’s risks.Numerical results are presented to support the AMDSSP for the ALT,while performance comparisons between the AMDSSP,the MDSSP and a single sampling plan(SSP)for the ALT are discussed.Results indicated that the AMDSSP was more flexible and efficient for ASN and TC than the MDSSP and SSP plans under accelerated conditions.The AMDSSP also had a higher operating characteristic(OC)curve than both the existing sampling plans.Two real datasets of electronic devices for the ALT at high temperatures demonstrated the practicality and usefulness of the proposed sampling plan.

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.

Inference and optimal design on step-stress partially accelerated life test for hybrid system with masked data

Under Type-Ⅱ progressively hybrid censoring, this paper discusses statistical inference and optimal design on stepstress partially accelerated life test for hybrid system in presence of masked data. It is assumed that the lifetime of the component in hybrid systems follows independent and identical modified Weibull distributions. The maximum likelihood estimations(MLEs)of the unknown parameters, acceleration factor and reliability indexes are derived by using the Newton-Raphson algorithm. The asymptotic variance-covariance matrix and the approximate confidence intervals are obtained based on normal approximation to the asymptotic distribution of MLEs of model parameters. Moreover,two bootstrap confidence intervals are constructed by using the parametric bootstrap method. The optimal time of changing stress levels is determined under D-optimality and A-optimality criteria.Finally, the Monte Carlo simulation study is carried out to illustrate the proposed procedures.

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.

Aging effect and test-retest reliability of the sinusoidal harmonic acceleration test and velocity step test using nanotorque rotatory chair

Introduction:Rotatory chair testing has been used to evaluate horizontal canal function.Frequently used tests include sinusoidal harmonic acceleration test(SHAT)and velocity step test(VST).Objectives:Assessment of age effect on the SHAT and VST and assessment of test-retest reliability of the parameters of those two tests.Methods:A prospective study was performed on 100 subjects with no ear or vestibular complaints and normal vestibular evaluation.They were divided into two groups;Group A:below 50 years of age and Group B:50 years of age or above.SHAT was presented at frequencies 0.02,0.04,0.08,0.16,0.32,0.64 Hz with a peak velocity of 60°/s.VST was performed using a maximum velocity of 100°/s with acceleration and deceleration of 200°/s2.Thirty subjects were tested twice to assess reliability.Results:Study participants ranged in age from 20 to 67 years.Regarding group A,the mean age was30.92±7.31 and 55.36±4.61 for group B.No significant differences were found in SHAT parameters between the two groups.As well,there was no significant difference in VST per-rotatory time constant,however,post-rotatory time constant was significantly longer for Group B(P value<0.05).Intraclass correlation coefficient(ICC)values showed moderate to good reliability(ICC 0.5800.818)for SHAT parameters for the lower frequencies and indicated moderate reliability for VST time constant(ICC 0.5090.652).Conclusions:Age has no significant effect on the parameters of SHAT and VST.Test-retest reliability is generally good for both tests.

Design,fabrication,and testing of an X-band 9-MeV standing-wave electron linear accelerator

In this study,an X-band standing-wave biperiodic linear accelerator was developed for medical radiotherapy that can accel-erate electrons to 9 MeV using a 2.4-MW klystron.The structure works atπ/2 mode and adopts magnetic coupling between cavities,generating the appropriate adjacent mode separation of 10 MHz.The accelerator is less than 600-mm long and constitutes four bunching cells and 29 normal cells.Geometry optimizations,full-scale radiofrequency(RF)simulations,and beam dynamics calculations were performed.The accelerator was fabricated and examined using a low-power RF test.The cold test results showed a good agreement with the simulation and actual measurement results.In the high-power RF test,the output beam current,energy spectrum,capture ratio,and spot size at the accelerator exit were measured.With the input power of 2.4 MW,the pulse current was 100 mA,and the output spot root-mean-square radius was approximately 0.5 mm.The output kinetic energy was 9.04 MeV with the spectral FWHM of 3.5%,demonstrating the good performance of this accelerator.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Statistical Analysis for Constant-stress Partially Accelerated Life Test with Interval Censored Data

In this paper, a statistical analysis method is proposed to research life characteristics of products based on the partially accelerated life test. We discuss the statistical analysis for constant-stress partially accelerated life tests with Lomax distribution based on interval censored samples. The EM algorithm is used to obtain the maximum likelihood estimations(MLEs) and interval estimations for the shape parameter and acceleration factor.The average relative errors(AREs), mean square errors(MSEs), the confidence intervals for the parameters, and the influence of the sample size are discussed. The results show that the AREs and MSEs of the MLEs decrease with the increase of sample size. Finally, a simulation sample is used to estimate the reliability under different stress levels.

Priori information analysis of optocoupler accelerated degradation experiment based on failure mechanism verification test

The optocoupler is a weak link in the inertial navigation platform of a kind of guided munitions.It is necessary to use accelerated storage test to verify the storage life of long storage products.Especially for small sample products,it is very important to obtain prior information for the design and implementation of accelerated degradation test.In this paper,the optocoupler failure mechanism verification test is designed and the experimental results are analyzed and the prior information is obtained.The results show that optocouplers have two failure modes,one is sudden failure and the other is degradation failure;the maximum temperature stress of optocoupler can’t exceed 140℃;the increase of leakage current of optocoupler is caused by movable ions contaminating the LED chip.The surface leakage current is proportional to the adsorption amount.The increase of leakage current makes p-n junction tunneling effect occur which LEDs the failure of the optocoupler.The lifetime distribution model of the optocoupler is determined by the failure physics.The lifetime of the optocoupler is subject to the lognormal distribution.The degeneracy orbit of the optocoupler leakage current is described by a power law model.The estimated values of the orbital parameters are initially calculated and the parameters of its life distribution function are deduced.The above information lays a good foundation for the optimization design and data processing of the accelerated degradation experiment.

Inference for accelerated bivariate dependent competing risks model based on Archimedean copulas under progressive censoring

Dependent competing risks model is a practical model in the analysis of lifetime and failure modes.The dependence can be captured using a statistical tool to explore the re-lationship among failure causes.In this paper,an Archimedean copula is chosen to describe the dependence in a constant-stress accelerated life test.We study the Archimedean copula based dependent competing risks model using parametric and nonparametric methods.The parametric likelihood inference is presented by deriving the general expression of likelihood function based on assumed survival Archimedean copula associated with the model parameter estimation.Combining the nonparametric estimation with progressive censoring and the non-parametric copula estimation,we introduce a nonparametric reliability estimation method given competing risks data.A simulation study and a real data analysis are conducted to show the performance of the estimation methods.

A Comprehensive Review of Accelerated Life Test

Accelerated life test (ALT) is an important branch of reliability test and is a focus of research both for statisticians and reliability engineers. The paper outlines the four topics of study embodied in ALT: statistical analysis of constant-stress test, step-stress test and progressive stress test, and optimal design of ALT. It gives a general review of engineering applications of ALT, and points out some possible directions in ALT, gives some suggestions for further study.

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.