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The performance degradation rates of the missile tank are generally time-varying functions uneasily evaluated by general classical evaluation methods. This paper develops a segmented nonlinear accelerated degradation model (SNADM) based on the equivalent method of accumulative damage theory, which tackles the problem that product life is difficult...
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... where 0 is a constant, which depends on the product's geometry, the specimen size and test method, etc.; / EK = , E is the activation energy of the reaction; K the Boltzmann's constant, equals to 5 8.6171 10 eV / C − ; S is accelerated stress level, where it is the absolute temperature in Kelvin. ...
... When the leakage reaches the threshold (Df =1.2g), the tank cooling effect does not meet the seekers' requirements, then the tank is determined to fail. In [5] the step-down-stress ADT of a certain type of missile tank was conducted, in which temperature is accelerate stress. Average storage lifetime of the tank was predicted based on the equivalent method of accumulative damage theory in [5]. ...
... In [5] the step-down-stress ADT of a certain type of missile tank was conducted, in which temperature is accelerate stress. Average storage lifetime of the tank was predicted based on the equivalent method of accumulative damage theory in [5]. Now, we use the same test data in [5] to validate the proposed evaluation method in this paper. ...
In view of the disadvantage that traditional evaluation method of accelerated degradation testing (ADT) complex statistical analysis, in this paper, the randomness and monotonicity of the degradation path for products with high reliability and long lifetime are taken into consideration based on Inverse Gaussian (IG) process. The evaluation method of step-down-stress ADT as well as its reliability function are established based on IG process. At same time, both the simple IG process and IG process with random effects are considered, respectively. The maximum likelihood estimation method and Markov Chain Monte Carlo (MCMC) estimation method are presented to estimate the unknown parameters in the proposed degradation models, respectively. Finally, the proposed evaluation methods are demonstrated by the step-down-stress ADT data of a certain type of missile tank. The results show that the proposed evaluation method is reasonable and valid in this paper. In addition, compared with simple IG process model, IG process with random effects model has many superb properties when dealing with random effects of products in ADT.
... At the same time, the emergence of highly reliable products has also promoted the fast development of accelerated reliability tests for reliability assessment. For instance, AT methods have evolved from constant-stress [2], [3] to step-up-stress [4], step-down-stress [5], [6], progressive-stress [7], [8], and cyclic-stress approaches [9], [10]. Being exposed to higher stress levels, modern engineering systems will generate more unknown failure mechanisms, random uncertainties, and interactions, especially in multi-component systems [11]. ...
... After nearly 60 years' development, ADT methods can be classified as constant-stress ADT (CSADT) [35], [36], stepup-stress ADT (SUADT) [4], [37], step-down-stress ADT (SDADT) [5], [38], progressive-stress ADT (PSADT) [8], and cyclic-stress ADT [10], as shown in Fig. 2. Among these AT approaches, CSADT received the most applications for the convenience of stress application and statistical inference. ...
Reliability engineering plays an important role in the design, manufacture, maintenance, and replacement of industrial products. Over the last few decades, accelerated degradation testing (ADT) has been largely utilized to shorten test durations, reduce the samples needed, and provide sufficient degradation data to ensure the effective reliability assessment of the concerned products. Meanwhile, performance degradation modeling has been recognized as an essential approach to help researchers and producers understand the health conditions of the deteriorating systems. However, the diversity in reliability tests, degradation models, and statistical analysis techniques has increased the difficulty in selecting appropriate reliability assessment methods in specific scenarios. Besides, there are no systematic reviews focused on modeling and analysis of performance degradation data. Therefore, this paper aims to (1) present ADT fundamentals, including the basic theory, ADT methods, accelerated stress variables, type of acceleration models, as well as ADT optimization, (2) comprehensively review current states and future challenges in degradation modeling, (3) discuss the problem of model mis-specification and compare different approaches for parameter estimation, (4) highlight future opportunities and possible directions deserving further research.
... On the basis of a mixed-effect degradation path model, a statistical model of SSADT connectors was presented by Chen [13]. Yao [15] developed a segmented nonlinear accelerated degradation model to solve the problem of time-varying degradation rates of missile tanks. However, these models are regression-based; thus, they cannot capture the dynamics or random variations of the degradation process [16]. ...
The rotary encoder is an important sensor for measuring rotational motion. A step–stress accelerated degradation test (SSADT) is conducted with respect to accuracy to evaluate the reliability rapidly. The existing errors in output signals are identified as degradation indicator to characterize performance degradation. A methodology for the encoder SSADT modeling is presented. Wiener process theory with unit–to–unit variation is utilized in the model to describe the degradation process of each error. Considering the correlation among the degradation processes, a multivariate degradation modeling method is developed based on the Copula function to estimate the reliability of rotary encoder with multiple degradation indicators. The reliability of the encoder under the use–stress level is derived by combining the margin distributions and Copula function.
... In comparison, step-stress ADT (SSADT) is less difficult to implement and has higher efficiency, which can be able to achieve comparable evaluation accuracy at lower sample sizes [15]. Therefore, SSADT has been widely applied in the reliability assessment and RUL estimation for many products (see e.g., [11], [15], [16], [17] and references therein). ...
In the absence of sufficient degradation data of long-lifetime and highly reliable products, a step-stress accelerated degradation model based on nonlinear diffusion process is proposed to estimate the remaining useful life (RUL), with the advantage of requiring small sample size and short test time. For multiple uncertainties caused by inherent properties, individual differences, measurement equipment performance and artificial deviations in the degradation process, this model considers the temporal variability, unit-to-unit variability and measurement errors in both performance degradation and covariates. To estimate the RUL, we derive an analytical approximation to the first hitting time (FHT) of the nonlinear diffusion process crossing a predetermined threshold with the consideration of measurement errors. Based on maximum likelihood estimation (MLE), a modified simulation and extrapolation (SIMEX) method, called MLE-SIMEX, is developed for estimating unknown parameters in the established model. The usefulness of the proposed model is demonstrated by a simulation case and a real-world example. The results reveal that considering nonlinearity and multiple sources of variability in the step-stress accelerated degradation process can improve the model fitting and the accuracy of RUL estimation.
... SSADT has an advantage over CSADT since it allows a comparable assessment accuracy with a lower sample size [4] . Therefore, the last few decades have witnessed wide application of SSADT in reliability tests for LEDs [5] , electrical connectors [6] , missile tanks [7] and transistors [8] . The purpose of this study is to model the Actual degradation measurement at time t S ′ Measurement error-prone covariates S 0 Normal stress level of the products T 0 Lifetime of products under normal stress level f 0 ( t ) Pdf for exponential nonlinear Wiener process with random effects f 1 ( t ) Pdf for exponential nonlinear Wiener process with random effects and covariates f ( t ) Pdf for exponential nonlinear Wiener process with random effects, covariates and random initial degradation values nonlinearity is another feature commonly encountered in SSADTs conditions. ...
In the absence of enough run-to-failure data, step-stress accelerated degradation testing (SSADT) is often an attractive alternative way to evaluate the reliability of a product, with the advantage of requiring small sample size and short test time. However, the development of a statistical SSADT model for reliability assessment should take into account different sources of variability in the degradation process that generate uncertainty: 1) temporal variability determining the inherent variability of degradation process over time; 2) unit-to-unit variability in three aspects: degradation rates, initial degradation values, time-points of elevating stress levels; and 3) measurement errors in both covariates and degradation performance. As a contribution towards this aim, a new nonlinear Wiener-process-based SSADT model considering simultaneously nonlinearity and three sources of variability is proposed. Using the proposed SSADT model, the lifetime law of the tested product under normal conditions is derived based on the concept of first hitting time (FHT) of a predetermined failure threshold. Following an approach based on genetic algorithms (GA), a modified simulation and extrapolation method, called GA-SIMEX, is also developed for the model parameter estimation. Finally, a simulation study of fatigue crack length growth is presented to illustrate the implementation of the proposed SSADT model.
... SDSADT, which applies an opposite order of thermal stresses compared with SUS-ADT, should address the issue of increased optical parameters to reduce accelerated duration. The step-down-stress testing process was applied for the accelerated assessment of product reliability, such as evaluating the product storage life of a missile tank based on SDSADT [26] and predicting the industrial lifetime of a pneumatic cylinder with a double-cross step-down-stress accelerated life testing based on the cumulative damage model [27]. The step-down-stress degradation model was further applied based on the Arrhenius model, Gamma process, and Wiener process [28][29][30]. ...
... Therefore, the Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ress SSADT has been widely applied in reliability tests for LEDs [21,22], transistors [23], and missile tanks [24]. Based on Nelson's equivalent accumulative damage theory, Tseng [18] and Weiqiang [25], respectively, presented a segmented nonlinear accelerated degradation model (SNADM), which tackles the problem that the degradation rate of the products varies with time during SSADT. ...
Modern engineering products usually have complex structures and different functions, which means that products may have multiple degradation failure mechanisms. At present, the study of multivariate degradation reliability is mostly limited to copula function with constant parameters. For high-reliability products with multiple degradation processes, a bivariate accelerated degradation reliability estimation method based on time-varying copula is proposed. For accelerated degradation data, the marginal degradation model is constructed by using the nonlinear Wiener process with random effect, and the influence of environmental covariates is considered in combination with the acceleration model. The joint-dependence structure between two degradation processes is described by time-varying copula. A Simulation study validates this approach and the consequences of model misspecification are evaluated too. Furthermore, a real-world example is presented to demonstrate the effectiveness of the method. The results show that this method has some advantages over the existing methods.
To completely meet the requirements of reliability design in the product designing, an axiom-based Design-in Reliability approach is proposed. In light of the axiomatic design principles, products are designed preliminarily to establish their functional requirements. According to these, functions preserving requirements are augmented, which constitute a Functional Requirement Preserving domain included in functional domain, and derives the parameterized solution for reliability design systematically. Subsequently, the design parameters are augmented and optimized to achieve the functions preserving requirements. Mapping model of the augmented functional domain and the physical domain is established. And a solutions evaluation approach based on Independence Axiom is proposed. Ultimately, via identifying the potential failure modes from the perspective of the disappearance or reduction of functions preserving capability, a control process is elaborated to mitigate the failure modes on the basis of independence axiom and logic decision in order for the reliability requirements to be implemented. Being exemplified by the design of a temperature sensor, the present study demonstrates that all approaches are feasible, efficient, and could be applied in real engineering scenarios.
For many high-reliability and long-life products, the accuracies of some existing life prediction models are not high enough, which may limit their fast development. For this purpose, four groups of constant-stress accelerated degradation tests (ADTs) were carried out by increasing the temperature of a vacuum fluorescent display (VFD) cathodic filament, and the equivalent average luminance degradation model (EALDM) was proposed to predict VFD life. In this model, firstly, a two-parameter Weibull function was used to fit average test data at each accelerated stress, and the corresponding formula of luminance degradation was obtained. Secondly, a power function was determined to fit multi-groups of data points formed by an accelerated stress and time at different given luminance, and then the work time under normal stress was extrapolated. Finally, by reusing the Weibull function to fit the data points, including the work time and given luminance, the life prediction of products was achieved. The results indicate that the test design of constant-stress ADTs is correct and feasible; the Weibull function well reveals the VFD luminance decaying law at both accelerated and normal stresses, and the power function objectively reflects the relationship between work time and stress. It is found by comparing the predicted life with the reference value that EALDM has high precision, which paves the way for following research in life prediction methodology and acts as a guide for professional technicians.
