Accelerated Destructive Degradation Test Research Articles

A Nonlinear Quantile Regression for Accelerated Destructive Degradation Testing Data

Traditional regression approaches to accelerated destructive degradation test (ADDT) data have modeled the mean curve as representative. However, maximum likelihood estimates (MLEs) of the mean model are likely to be biased when the data are non-Gaussian or highly skewed. The median model can be an alternative for skewed degradation data. In this work, we introduce a nonlinear quantile regression (QR) approach for estimating quantile curves of ADDT data. We propose an iterative QR algorithm that uses the generalized expectation-maximization (GEM) framework to estimate the parameters of the nonlinear QR ADDT model, based on the asymmetric Laplace distribution to accommodate non-Gaussian and skewed errors. Using the asymptotic properties of the QR parameter estimates, we estimate variance-covariance matrix for the τ th QR parameters using order statistics and bootstrap methods. We propose a new prediction method of the quantile of the failure-time distribution in the normal use condition. Confidence intervals for the quantiles of the failure-time distribution are constructed using the parametric bootstrap method. The proposed model is illustrated using an industrial application and compared with the existing model. Various quantile curve estimates derived using the QR ADDT model provide a more flexible modeling framework than the traditional mean ADDT modeling approach.

A random‐effect gamma process model with random initial degradation for accelerated destructive degradation testing data

AbstractAn accelerated degradation test (ADT) hastens degradation mechanisms of products by loading higher stresses than normal use conditions to shorten testing time. In some situations, degradation levels during ADT can be measured only by destructive inspection where testing units must be destroyed or physical characteristics are significantly changed after measuring the performance degradation. For such an accelerated destructive degradation test (ADDT), initial degradation levels may vary from item to item. In this regard, we propose a random‐effect gamma process model with random initial degradation for the reliability analysis of ADDT data. Under the proposed modeling framework, we derive the maximum likelihood estimates (MLEs) of the model parameters and construct an inferential procedure for the parameters and reliability measures of interest, using asymptotic properties of the MLEs. In particular, the mean and the variance of the mean‐time‐to‐failure of the products from the ADDT data are explicitly derived in closed forms. Monte Carlo simulations under various scenarios are performed to validate the performance of proposed maximum likelihood estimation and inferential methods for the ADDT data. Finally, reliability estimation at a normal use condition and inferential procedures are illustrated through an ADDT example of return‐springs in a bi‐functional DC motor system of an automobile.

Reliability Analysis of Accelerated Destructive Degradation Testing Data for Bi-Functional DC Motor Systems

An accelerated degradation test (ADT) has become a popular method to accelerate degradation mechanisms by stressing products beyond their normal use conditions. The components of an automobile are degraded over time or cycle due to their constant exposure to friction or wear. Sometimes, the performance degradation can be measured only by destructive inspection such as operating torques of return-springs in a bi-functional DC motor system. Plastic deformation of the return-spring causes the degradation of actuating forces for shield movement, resulting in deterioration of the shield moving speed in a headlight system. We suggest a step-by-step procedure for a reliability analysis for a bi-functional DC motor in a headlight system, based mainly on accelerated destructive degradation test (ADDT) data. We also propose nonlinear degradation models to describe the ADDT data of the return-springs. Exposure effects of high temperatures on the return-springs are quantitatively modeled through the ADDT models. We compare the estimation results from both the closed-form expression and Monte Carlo simulation to predict the failure–time distribution at normal use conditions, showing that the lifetime estimation results from the closed-form formulation are more conservative.

Optimal constant-stress ADDT plan with one main effect and one interaction effect

PurposeDegradation measurement of some products requires destructive inspection; that is, the degradation of each unit can be observed only once. For example, observation on the mechanical strength of interconnection bonds or on the dielectric strength of insulators requires destruction of the unit. Testing high-reliability items under normal operating conditions yields a small amount of degradation in a reasonable length of time. To overcome this problem, the items are tested at higher than normal stress level – an approach called an accelerated destructive degradation test (ADDT). The present paper deals with formulation of constant-stress ADDT (CSADDT) plan with the test specimens subject to stress induced by temperature and voltage.Design/methodology/approachThe stress–life relationship between temperature and voltage is described using Zhurkov–Arrhenius model. The fractional factorial experiment has been used to determine optimal number of stress combinations. The product's degradation path follows Wiener process. The model parameters are estimated using method of maximum likelihood. The optimum plan consists in finding out optimum allocations at each inspection time corresponding to each stress combination by using variance optimality criterion.FindingsThe method developed has been explained using a numerical example wherein point estimates and confidence intervals for the model parameters have been obtained and likelihood ratio test has been used to test for the presence of interaction effect. It has been found that both the temperature and the interaction between temperature and voltage influence the quantile lifetime of the product. Sensitivity analysis is also carried out.Originality/valueMost of the work in the literature on the design of ADDT plans focusses on only a single stress factor. An interaction exists among two or more stress factors if the effect of one factor on a response depends on the levels of other factors. In this paper, an optimal CSADDT plan is studied with one main effect and one interaction effect. The method developed can help engineers study the effect of elevated temperature and its interaction with another stress factor, say, voltage on quantile lifetime of a high-reliability unit likely to last for several years.

Optimization of Accelerated Destructive Degradation Testing of Cementitious Materials for Their Performances Qualification under Aggressive Environments: The Case of Carbonation

In order to guarantee the performance or to qualify the risk of nonperformance of cementitious materials over time, a significant number of experimental data obtained from tests mimicking various degradation mechanisms are required. The slowness of the materials’ degradation under environmental service conditions is an issue, and thus, acceleration strategies are required to obtain reliable and comprehensive results in a shorter time. The objective of this research work is to provide a generic framework for the design of optimal accelerated destructive degradation tests (ADDTs) for cementitious materials qualification. The definition of the optimal design of experiments depends on the capacity to capture the influence of data variability and uncertainty from any sources; they are extracted either from physical models or from experimental tests. In this research, the evolution of carbonation depth is characterized with the Wiener process formalism and the random effects related to the material heterogeneity are taken into account. Once the process parameters are estimated through the maximum likelihood estimation (MLE), associated with the expectation-maximization (EM) algorithm, we provide a step-by-step and detailed method to investigate the optimal design of ADDTs. The latter is defined as the one for which we can estimate durability indicators such as mean-time-to-failure with the best accuracy based on three criteria (D-V-A optimality) considering constraints of time, total number of samples, or limited costs. The optimal total sample size for the accelerated carbonation test and the optimal sample size allocation proportions for each stress level are determined, and the effects of the stress level on the objective functions and of test time duration constraint are also discussed. A comparison of the relative efficiency of optimal three-level versus optimal two-level ADDT completes this work.

Optimal Design for Destructive Degradation Tests With Random Initial Degradation Values Using the Wiener Process

This study investigates modeling, estimation and optimization of destructive degradation tests (DDTs) for highly reliable products with random initial degradation values. It is common to observe that the degradation paths of distinct products start from different values specified by a random variable. The random initial value introduces additional uncertainties to the degradation of the product. In this study, Wiener-process-based degradation models are developed for products with random initial values. We first consider a DDT without stress acceleration. In a DDT, the measurement of the degradation destroys a test unit and, thus, only one measurement is available for each unit. Closed-form maximum likelihood (ML) estimators are derived. Then, an accelerated DDT (ADDT) is considered. Based on these results, we investigate optimal designs of both DDT and ADDT with the objective of minimizing the asymptotic variance of the estimated $p$ th-quantile of the failure time distribution under use conditions. The optimal test plans have to be obtained through a numerical approach. Optimality of the plans is verified by the general equivalence theorem. An adhesive bond example with real degradation data is analyzed to show the performance of the proposed methods.

Lifetime Inference for Highly Reliable Products Based on Skew-Normal Accelerated Destructive Degradation Test Model

The accelerated destructive degradation test (ADDT) method provides an effective way to assess the reliability information of highly reliable products whose quality characteristics degrade over time, and can be taken only once on each tested unit during the measurement process. Conventionally, engineers assume that the measurement error follows the normal distribution. However, degradation models based on this normality assumption often do not apply in practical applications. To relax the normality assumption, the skew-normal distribution is adopted in this study because it preserves the advantages of the normal distribution with the additional benefit of flexibility with regard to skewness and kurtosis. Here, motivated by polymer data, we propose a skew-normal nonlinear ADDT model, and derive the analytical expressions for the product's lifetime distribution along with its corresponding $100p$ th percentile. Then, the polymer data are used to illustrate the advantages gained by the proposed model. Finally, we addressed analytically the effects of model mis-specification when the skewness of measurement error are mistakenly treated, and the obtained results reveal that the impact from the skewness parameter on the accuracy and precision of the prediction of the lifetimes of products is quite significant.

Optimal Design for Accelerated Destructive Degradation Tests

Degradation tests are powerful and useful tools for lifetime assessment of highly reliable products. In some applications, the degradation measurement process would destroy the physical characteristic of units when tested at higher than usual stress levels of an accelerating variable such as temperature, so that only one measurement can be made on each tested unit during the degradation testing. An accelerated degradation test giving rise to such a degradation data is called an accelerated destructive degradation test (ADDT). The specification of the size of the total sample, the frequency of destructive measurements, the number of measurements at each stress level, and other decision variables are very important to plan and conduct an ADDT efficiently. A wrong choice of these decision variables may not only result in increasing the experimental cost, but may also yield an imprecise estimate of the reliability of the product at the use condition. Motivated by a polymer data, this article deals with the problem of designing an ADDT with a nonlinear model. Under the constraint that the total experimental cost does not exceed a pre-fixed budget, the optimal test plan is obtained by minimizing the asymptotic variance of the estimated 100 p th percentile of the product’s lifetime distribution at the use condition. A sensitivity analysis is also carried out to examine the effects of changes in the decision variables on the precision of the estimator of the 100 p th percentile. A simulation study further shows that the simulated values are quite close to the asymptotic values when the sample sizes are large enough.

Bayesian Methods for Accelerated Destructive Degradation Test Planning

Accelerated Destructive Degradation Tests (ADDTs) provide timely product reliability information in practical applications. This paper describes Bayesian methods for ADDT planning under a class of nonlinear degradation models with one accelerating variable. We use a Bayesian criterion based on the estimation precision of a specified failure-time distribution quantile at use conditions to find optimum test plans. A large-sample approximation for the posterior distribution provides a useful simplification to the planning criterion. The general equivalence theorem (GET) is used to verify the global optimality of the numerically optimized test plans. Optimum plans usually provide insight for constructing compromise plans which tend to be more robust, and practically useful. We present a numerical example with a log-location-scale distribution to illustrate the Bayesian test planning methods, and to investigate the effects of the prior distribution and sample size on test planning results.

Accelerated Destructive Degradation Tests Robust to Distribution Misspecification

Accelerated repeated-measures degradation tests (ARMDTs) take measurements of degradation or performance on a sample of units over time. In certain products, measurements are destructive, leading to accelerated destructive degradation test (ADDT) data. For example, the test of an adhesive bond needs to break the test specimen to measure the strength of the bond. Lognormal and Weibull distributions are often used to describe the distribution of product characteristics in life and degradation tests. When the distribution is misspecified, the lifetime quantile, often of interest to the practitioner, may differ significantly between these two distributions. In this study, under a specific ADDT, we investigate the bias and variance due to distribution misspecification. We suggest robust test plans under the criteria of minimizing the approximate mean square error.

Accelerated Destructive Degradation Test Planning

Accelerated destructive degradation tests (ADDTs) provide reliability information quickly. An ADDT plan specifies factor-level combinations of an accelerating variable (e.g., temperature) and evaluation time and the allocations of test units to these combinations. This article describes methods for finding good ADDT plans for an important class of destructive degradation models. First, a collection of optimum plans is derived. These plans minimize the large sample approximate variance of the maximum likelihood (ML) estimator of a specified quantile of the failure-time distribution. The general equivalence theorem is used to verify the optimality of these plans. Because an optimum plan is not robust to the model specification and the planning information used in deriving the plan, a more robust and useful compromise plan is proposed. Sensitivity analyses show the effects that changes in sample size, time duration of the experiment, levels of the accelerating variable, and misspecification of the planning information have on the precision of the ML estimator of a failure-time quantile. Monte Carlo simulations are used to evaluate the statistical characteristics of the ADDT plans. The methods are illustrated with an application for an adhesive bond.