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Register a new userOptimal Stress Levels in Accelerated Degradation Testing for Various Degradation Models
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Added by
Helmi Shat
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
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Accelerated degradation tests are used to provide accurate estimation of lifetime characteristics of highly reliable products within a relatively short testing time. Data from particular tests at high levels of stress (e.g., temperature, voltage, or vibration) are extrapolated, through a physically meaningful statistical model, to attain estimates of lifetime quantiles at normal use conditions. The gamma process is a natural model for estimating the degradation increments over certain degradation paths, which exhibit a monotone and strictly increasing degradation pattern. In this work, we derive first an algorithm-based optimal design for a repeated measures degradation test with single failure mode that corresponds to a single response component. The univariate degradation process is expressed using a gamma model where a generalized linear model is introduced to facilitate the derivation of an optimal design. Consequently, we extend the univariate model and characterize optimal designs for accelerated degradation tests with bivariate degradation processes. The first bivariate model includes two gamma processes as marginal degradation models. The second bivariate models is expressed by a gamma process along with a mixed effects linear model. We derive optimal designs for minimizing the asymptotic variance for estimating some quantile of the failure time distribution at the normal use conditions. Sensitivity analysis is conducted to study the behavior of the resulting optimal designs under misspecifications of adopted nominal values.
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Accelerated degradation testing (ADT) is one of the major approaches in reliability engineering which allows accurate estimation of reliability characteristics of highly reliable systems within a relatively short time. The testing data are extrapolated through a physically reasonable statistical model to obtain estimates of lifetime quantiles at normal use conditions. The Gamma process is a natural model for degradation, which exhibits a monotone and strictly increasing degradation path. In this work, optimal experimental designs are derived for ADT with two response components. We consider the situations of independent as well as dependent marginal responses where the observational times are assumed to be fixed and known. The marginal degradation paths are assumed to follow a Gamma process where a copula function is utilized to express the dependence between both components. For the case of independent response components the optimal design minimizes the asymptotic variance of an estimated quantile of the failure time distribution at the normal use conditions. For the case of dependent response components the $D$-criterion is adopted to derive $D$-optimal designs. Further, $D$- and $c$-optimal designs are developed when the copula-based models are reduced to bivariate binary outcomes.
Accelerated degradation tests are used to provide accurate estimation of lifetime properties of highly reliable products within a relatively short testing time. There data from particular tests at high levels of stress (e.,g. temperature, voltage, or vibration) are extrapolated, through a physically meaningful model, to obtain estimates of lifetime quantiles under normal use conditions. In this work, we consider repeated measures accelerated degradation tests with multiple stress variables, where the degradation paths are assumed to follow a linear mixed effects model which is quite common in settings when repeated measures are made. We derive optimal experimental designs for minimizing the asymptotic variance for estimating the median failure time under normal use conditions when the time points for measurements are either fixed in advance or are also to be optimized.
Accelerated destructive degradation tests (ADDT) are widely used in industry to evaluate materials long term properties. Even though there has been tremendous statistical research in nonparametric methods, the current industrial practice is still to use application-specific parametric models to describe ADDT data. The challenge of using a nonparametric approach comes from the need to retain the physical meaning of degradation mechanisms and also perform extrapolation for predictions at the use condition. Motivated by this challenge, we propose a semi-parametric model to describe ADDT data. We use monotonic B-splines to model the degradation path, which not only provides flexible models with few assumptions, but also retains the physical meaning of degradation mechanisms (e.g., the degradation path is monotonically decreasing). Parametric models, such as the Arrhenius model, are used for modeling the relationship between the degradation and accelerating variable, allowing for extrapolation to the use conditions. We develop an efficient procedure to estimate model parameters. We also use simulation to validate the developed procedures and demonstrate the robustness of the semi-parametric model under model misspecification. Finally, the proposed method is illustrated by multiple industrial applications.
In many real-life scenarios, system failure depends on dynamic stress-strength interference, where strength degrades and stress accumulates concurrently over time. In this paper, we consider the problem of finding an optimal replacement strategy that balances the cost of replacement with the cost of failure and results in a minimum expected cost per unit time under cumulative damage model with strength degradation. The existing recommendations are applicable only under restricted distributional assumptions and/or with fixed strength. As theoretical evaluation of the expected cost per unit time turns out to be very complicated, a simulation-based algorithm is proposed to evaluate the expected cost rate and find the optimal replacement strategy. The proposed method is easy to implement having wider domain of application. For illustration, the proposed method is applied to real case studies on mailbox and cell-phone battery experiments.
Ageing of lithium-ion batteries results in irreversible reduction in performance. Intrinsic variability between cells, caused by manufacturing differences, occurs throughout life and increases with age. Researchers need to know the minimum number of cells they should test to give an accurate representation of population variability, since testing many cells is expensive. In this paper, empirical capacity versus time ageing models were fitted to various degradation datasets for commercially available cells assuming the model parameters could be drawn from a larger population distribution. Using a hierarchical Bayesian approach, we estimated the number of cells required to be tested. Depending on the complexity, ageing models with 1, 2 or 3 parameters respectively required data from at least 9, 11 or 13 cells for a consistent fit. This implies researchers will need to test at least these numbers of cells at each test point in their experiment to capture manufacturing variability.
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