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In this paper we propose an objective Bayesian method to analyze the accelerated degradation model based on the new Wiener process stated in Ye, Chen, and Shen (Reliab. Eng. Syst. Safe., 2015, 139: 58–67). The Jeffreys prior and reference priors are derived after reparameterization, and the posterior properties under each prior are validated. A Metropolis random walk algorithm is then employed to generate samples from the posterior distributions, and a simulation study is carried out to reveal the frequentist properties of these priors. Finally, we apply the approach to a real data and obtain the mean-time-to-failure (MTTF) under the usage condition. [ABSTRACT FROM AUTHOR]

Existing joint maintenance decision research typically ignores remaining useful lifetime (RUL) predictions for the accelerated degradation of equipment. A joint maintenance decision method for the replacement and spare-parts ordering strategy based on RUL prediction using accelerated degradation data for equipment is proposed in this paper. First, an RUL prediction model under accelerated stress is built by considering the proportional relationship between the drift coefficient and diffusion coefficient in the Wiener process. Second, based on the principle of step-by-step estimation, accelerated degradation test (ADT) data of the equipment are used to estimate the a priori unknown parameters. Finally, based on the RUL prediction results, a joint optimization model for the replacement and spare-parts ordering strategy is developed. Through example verification and cost parameter sensitivity analysis, the proposed method is shown to effectively improve the accuracy of RUL prediction and the scientific value of the joint optimization plan for equipment replacement and spare-part ordering, which is important to many engineering applications.

In the field of reliability analysis, the constant-stress accelerated degradation test is one of the most commonly used methods to evaluate a product's reliability as degradation data are provided. In this paper, a constant-stress accelerated degradation test model of the Wiener process with random effects is proposed. First, the generalized confidence intervals of the model parameters are developed by constructing generalized pivotal quantities. Second, utilizing the substitution method, the generalized confidence intervals for the reliability function of lifetime, mean time to failure and the generalized prediction intervals for the degradation characteristic at the normal operating condition are also developed. Simulation studies are conducted to investigate the performances of the proposed generalized confidence intervals and prediction intervals. The simulation results reveal that the proposed generalized confidence intervals and prediction intervals work well in terms of the coverage percentage. In particular, a comparative analysis is made with the traditional bootstrap confidence intervals. At last, the proposed procedures are used for a real data analysis. [ABSTRACT FROM AUTHOR]

With its extensive use in industry, assessing the reliability of the micro inertial measurment unit (MIMU) has become a pressing need. Unfortunately, the MIMU is made up of several components, and the degradation processes of each are intertwined, making it difficult to assess the MIMU’s reliability and remaining useful life. In this research, we offer a reliability assessment approach for the MIMU, which has long-lifetime and multiple performance characteristics (PCs), based on accelerated degradation data and copula theory.Each PC model of MIMU is constructed utilizing drift Brownian motion to depict accelerated degradation process. The copula function is used to model the multivariate dependent accelerated degradation test data and to describe the dependency between multiple MIMU performance parameters. The particle swarm optimization algorithm is used to estimate the unknown parameters in the multi-dependent ADT model. Finally, the storage test and simulation example on MIMU’s accelerated degradation data verify the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A multi-objective optimization method for the accelerated degradation test based on Wiener process is proposed in this article in order to solve the problem that a single objective optimization cannot solve the difficulty or even conflicting test configurations caused by different optimization objective functions. An accelerated degradation model is established based on Wiener process, and the unknown parameters are solved by a two-step maximum likelihood estimation method. Considering both the accuracies of life estimation and the model parameter estimation, a multi-objective optimization model is established with the optimization goals of the minimum asymptotic variance of P-quantile of lifetime and the maximum determinant of Fisher information matrix. The Pareto solutions are set by the multi-objective genetic algorithm, and the test configurations for multi-objectives are obtained. Under the step stress accelerated degradation test and the constant stress accelerated degradation test, the effectiveness of the proposed method is verified by an optimization example of LEDs accelerated degradation test. [ABSTRACT FROM AUTHOR]

In the field of reliability analysis, the constant-stress accelerated degradation test is one of the most commonly used methods to evaluate a product’s reliability as degradation data are provided. In this paper, a constant-stress accelerated degradation test model of the Wiener process with random effects is proposed. First, the generalized confidence intervals of the model parameters are developed by constructing generalized pivotal quantities. Second, utilizing the substitution method, the generalized confidence intervals for the reliability function of lifetime, mean time to failure and the generalized prediction intervals for the degradation characteristic at the normal operating condition are also developed. Simulation studies are conducted to investigate the performances of the proposed generalized confidence intervals and prediction intervals. The simulation results reveal that the proposed generalized confidence intervals and prediction intervals work well in terms of the coverage percentage. In particular, a comparative analysis is made with the traditional bootstrap confidence intervals. At last, the proposed procedures are used for a real data analysis.

Accelerated degradation test (ADT) is generally used to accelerate degradation processes in products to estimate their lifespan and to assess their reliability in a short period of time. How to perform the failure mechanism consistency test is crucial in the application of the ADT method. Existing failure mechanism consistency test methods assume that degradation rates among individual products are the same. However, these methods do not take degradation dispersions caused by manufacturing technologies into consideration. To address this issue, a failure mechanism consistency test method for ADT based on the activation energy invariant method and the likelihood ratio test is proposed. First, a degradation modeling method for ADT is introduced. Then, the logarithmic maximum likelihood function values of the degradation models are estimated based on the two‐step maximum likelihood estimation (MLE) method. Finally, the decision rule is proposed based on the likelihood ratio test. The method mentioned above is, then, used on the real degradation data of carbon‐film resistors and bullet O‐rings, and its effectiveness is verified. Furthermore, based on the failure mechanism change point in RTV5370 siloxane rubbers, the simulated degradation data are degenerated to compare the proposed method with the method not considering individual differences in different ADT programs and degradation dispersions. [ABSTRACT FROM AUTHOR]

For reliability assessment based on accelerated degradation tests (ADTs), an appropriate parameter estimation method is very important because it affects the extrapolation and prediction accuracy. The well‐adopted maximum likelihood estimation (MLE) method focuses on interpolation fitting and obtains results via maximizing the likelihood of the observations. However, a best interpolation fitting does not necessarily yield a best extrapolation. In this paper, therefore, a pseudo‐MLE (P‐MLE) method is proposed to improve the prediction accuracy of constant‐stress ADTs by considering the degradation mechanism equivalence under Wiener process. In particular, the degradation mechanism equivalence is characterized by a mechanism equivalence factor which presents the proportional relationship between degradation rate and variation. Then, the mechanism equivalence factor is determined via a two‐step method. The other model parameters can be estimated by the general MLE method. The asymptotic variances of acceleration factors and the p‐quantile of product failure time under normal condition are adopted to compare the statistical properties of the proposed method and the general MLE approach. Numerical examples show that the novel P‐MLE method may not achieve a maximum likelihood but can provide more benefits regarding prediction accuracy enhancement especially when the sample size is limited. [ABSTRACT FROM AUTHOR]

Accelerated degradation test (ADT) has become an efficient approach to evaluate the reliability for highly reliable products. However, when modeling accelerated degradation data with degradation models, it is difficult to exactly figure out the changing rules of parameters with stress variables varying. At present, the changing rules are mainly assumed according to engineering experience or subjective judgements, which probably results in inaccurately extrapolating the reliability. To figure out the changing rules of parameters with stress variables varying, the acceleration factor constant principle and its application under ADT are studied in the paper. It is well known that the acceleration factor between any two different stress levels should be a constant under an effective ADT. For each degradation model, its parameters should obey special changing rules to satisfy that the acceleration factor maintains a constant throughout an ADT. Taking three extensively used stochastic process models as examples, including Wiener process model, gamma process model, and inverse Gaussian process model, the method of deducing the changing rules of the parameters according to the acceleration factor constant principle was demonstrated. A simulation test was conducted to validate the deduced changing rules of the parameters for the three stochastic process models. An illustrative example involving self-regulating heating cables was used to illustrate the application of the acceleration factor constant principle under ADT. Results indicate that the acceleration factor constant principle offers an appealing and credible approach to help model accelerated degradation data. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Constant-stress accelerated degradation test (CSADT) as an effective model is widely used in assessing product reliability when measurements of degradation leading to failure can be observed. We model the degradation process as a Wiener process. In this paper, we make inferences about the parameters of the CSADT using an objective Bayesian method. The noninformative priors (Jefferys prior and two reference priors) are derived, and we show that their posterior distributions are proper. Since the posterior distributions are very complicated, Gibbs sampling algorithms for the Bayesian inference based on the Jefferys prior and two reference priors are proposed. Some simulation studies are conducted to show the effectiveness of the objective Bayesian analysis. Finally, we apply the objective Bayesian method to a real data set and estimate the mean-time-to-failure (MTTF) under use condition. [ABSTRACT FROM AUTHOR]

Head wear becomes inevitable as the physical clearance between the head and disk in current hard disk drives is close to 1 nm or lower. Accurate characterization of the wear process is essential in understanding the wear mechanism, evaluating the reliability of hard disk drives (HDDs), and predicting the future evolution of wear as well as guiding the design of HDDs of later vintages. Due to the variations in the material and geometry of magnetic head, the wear process is dynamic and stochastic. To cope with the dynamics, a Wiener process with a positive drift is used to model the wear process. Furthermore, to evaluate the reliability quickly, an accelerated degradation model using the wear measurements is developed, from which the parameters/failure times under light loads can be effectively predicted. The developed model is then applied to a real wear problem of magnetic head to demonstrate the effectiveness. [ABSTRACT FROM AUTHOR]

Optimal accelerated degradation test (ADT) plans are developed assuming that the constant-stress loading method is employed and the degradation characteristic follows a Wiener process. Unlike the previous works on planning ADTs based on stochastic process models, this article determines the test stress levels and the proportion of test units allocated to each stress level such that the asymptotic variance of the maximum-likelihood estimator of the qth quantile of the lifetime distribution at the use condition is minimized. In addition, compromise plans are also developed for checking the validity of the relationship between the model parameters and the stress variable. Finally, using an example, sensitivity analysis procedures are presented for evaluating the robustness of optimal and compromise plans against the uncertainty in the pre-estimated parameter value, and the importance of optimally determining test stress levels and the proportion of units allocated to each stress level are illustrated. [ABSTRACT FROM AUTHOR]

For highly reliable products with very few test units, a progressive-stress accelerated degradation test (PSADT) has been proposed in the literature to obtain timely information of the product's lifetime distribution. The results, however, are restricted to the case where the product's degradation path follows a Wiener process (Brownian motion) with a linear drift rate. But in practical applications, the product's mean degradation path may be non-linear. Hence, how to address the lifetime distribution in this situation is a worthy topic for reliability analysts. In this paper, a PSADT with a non-linear degradation path is constructed using the cumulative exposure model. Then the product's lifetime distribution can be analytically obtained by the first passage time of its degradation path. Furthermore, we derive an exact relationship between the lifetime distributions of the PSADT, and the conventional constant-stress degradation test (CSDT), which allows us to extrapolate the product's lifetime distribution under typical stress. Finally, the usage of the proposed model, and the efficiency of PSADT to reduce the product's life testing time are demonstrated in the example. [ABSTRACT FROM AUTHOR]