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Degradation test is an effective method in assessing product reliability when measurements of degradation leading to failure can be observed. The accuracy of reliability inference in degradation analysis highly depends on the fitted model to the observed degradation data. Sometimes, observed degradation paths of the products exhibit multiphase pattern over the testing period. In this paper, we propose a change-point Wiener process with measurement errors (CPWPME) to fit two-phase degradation paths of organic light-emitting diodes (OLEDs). We assume the unit-specific parameters of the CPWPME model by using hierarchical Bayesian method. Based upon the proposed approach, the failure-time distribution and the remaining useful life distribution along with mean time to failure and mean residual life function are derived in closed form. A simulation study shows the utility of the proposed CPWPME model and the validity of the hierarchical Bayesian approach for the degradation data possessing two-phase degradation characteristics. In the analysis of OLED degradation data, the hierarchical Bayesian CPWPME model provides higher modeling flexibility and prediction power for future testing units than existing three degradation models. [ABSTRACT FROM AUTHOR]

Lifetime prognostic based on the degradation data has been widely investigated and adopted for reliability assessment and maintenance policy. However, the measurement error (ME) is usually inevitable, which leads to the bias of lifetime estimation and erroneous evaluation of the safety risk. In this paper, we mainly focus on an inverse issue: how to specify the sensor's performance (i.e., the ME range) for satisfying a given requirement of the lifetime estimation. Under this consideration, we first analyze the probability distribution functions of the lifetime estimation with/without the ME based on Wiener process degradation model. Then a distance measure based on the relative entropy is formulated to evaluate the difference between these two lifetime estimations. Furthermore, the permissible ranges of the time-dependent and time-independent ME are attained under a given allowable bias of lifetime estimation according to the proposed distance measure. In addition, the influence of the ME on maintenance policy is discussed. Finally, numerical examples and a case study are provided to illustrate. [ABSTRACT FROM AUTHOR]

Accelerated degradation analysis plays an important role in assessing reliability and making maintenance schedule for highly reliable products with long lifetime. In practical engineering, degradation data, especially measured under accelerated condition, are often compounded and contaminated by measurement errors, which makes the analysis more challenging. Therefore, a Wiener process model simultaneously incorporating temporal variability, individual variation and measurement errors is proposed to analyze the accelerated degradation test (ADT). The explicit forms of the probability distribution function (PDF) and the cumulative distribution function (CDF) are derived based on the concept of first hitting time (FHT). Then, combining with the acceleration models, the maximum likelihood estimations (MLE) of the model parameters are obtained. Finally, a comprehensive simulation study involving two examples and a practical application are given to demonstrate the necessity and efficiency of the proposed model. [ABSTRACT FROM AUTHOR]

Random effects are ubiquitous in the degradation processes of multiple performance characteristics (PCs) of a complex system, and these PCs are not commonly independent. Neglecting either of the above features will lead to bias in system reliability estimation. Therefore, this study develops a reliability estimation method for the complex systems with multiple PC degradations considering both of the features. First, a Wiener process-based marginal degradation model with random effects (including the random initial PC, unit-to-unit variability, temporal uncertainty, and measurement errors) is proposed to track the degradation path of each PC. A model based on D-vine copulas is put forward to describe the correlation among multiple PCs. Then, a system reliability function is derived based on the two models. Furthermore, a two-step statistical inference is developed to estimate the unknown parameters in the system reliability function. Finally, using a practical case, the effectiveness of the proposed method is illustrated. • A reliability estimation method is proposed for complex systems. • A marginal Wiener process-based degradation model with random effects is proposed. • The correlation among multiple performance characteristics is modeled by D-vine copulas. • A two-step statistical inference is developed to perform the parameter estimation. [ABSTRACT FROM AUTHOR]

Repeated degradation testing data have been widely used to assess lifetime of highly-reliable products or components with scarce failures. In this paper, we consider the problem of planning repeated degradation testing for products exhibiting three-source variability in their degradation characteristics, including the temporal variability, unit-to-unit variability, and measurement variability. The primary objective of this paper is centered on deciding the amount of units and the measurement schedule to achieve required estimation precision for some important statistics of interest. In such a planning process, the testing budget is limited and used as a constraint of an optimization model. To do so, a kind of Wiener degradation process, which has a random drift coefficient and a constant volatility coefficient, is used to model the repeated degradation testing data, where the measurement errors are considered and described as additive zero-mean random variables. Under the presented modeling framework, the lifetime distribution is formulated under the concept of the first passage time of the stochastic degradation process. Then, the large-sample approximate standard errors of the maximum likelihood estimations for the mean failure time and the quantile of the degradation distribution are derived, respectively. Furthermore, the constrained optimization model, which incorporates the cost of each degradation measurement, is proposed to plan the degradation testing by minimizing the testing cost under the condition of a maximum acceptable approximate standard error. Finally, an example is provided to illustrate the procedure and advantages of the presented method. [ABSTRACT FROM AUTHOR]

Degradation is a common phenomenon for many products. Because of a variety of reasons, the degradation rates of units from the same population are often heterogeneous. In addition, when the degradation process is monitored using dedicated sensors, the measurements are often inaccurate because of various noisy factors. To account for the heterogeneous degradation rate and the non-negligible measurement errors, we model the degradation observations using a random-effects Wiener process with measurement errors. Under the model, direct estimation of current degradation and prediction of future degradation are difficult. We thus develop a filtering algorithm that recursively estimates the joint distribution of the degradation rate and the current degradation levels. Based on the estimates, the distribution of the remaining useful life can be timely predicted. Our method is both computational efficient and storage efficient. Its effectiveness is demonstrated through simulation and real data. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]