Accelerated Degradation Process Analysis Based on the Nonlinear Wiener Process with Covariates and Random Effects

Abstract

It is assumed that the drift parameter is dependent on the acceleration variables and the diffusion coefficient remains the same across the whole accelerated degradation test (ADT) in most of the literature based on Wiener process. However, the diffusion coefficient variation would also become obvious in some applications with the stress increasing. Aiming at the phenomenon, the paper concludes that both the drift parameter and the diffusion parameter depend on stress variables based on the invariance principle of failure mechanism and Nelson assumption. Accordingly, constant stress accelerated degradation process (CSADP) and step stress accelerated degradation process (SSADP) with random effects are modeled. The unknown parameters in the established model are estimated based on the property of degradation and degradation increment, separately for CASDT and SSADT, by the maximum likelihood estimation approach with measurement error. In addition, the simulation steps of accelerated degradation data are provided and simulated step stress accelerated degradation data is designed to validate the proposed model compared to other models. Finally, a case study of CSADT is conducted to demonstrate the benefits of our model in the practical engineering.

Modeling and Analysis of Performance Degradation Data for Reliability Assessment: A Review

“…Recently, Chen et al [59] incorporated random effects and the measurement variability into a nonlinear Wiener process, and then proposed an optimization algorithm to decide ideal stress levels, the number of test units allocated to each stress level, the inspection frequency, as well as the total measurement time for minimizing the asymptotic variance of maximum likelihood estimation (MLE) of unknown parameters under normal working conditions with the constraints of sample sizes, test durations, and test costs. Then, Sun et al [16] further investigated the impact of environmental covariates when planning ADT, in which a transformed Eyring model, the inverse power law model, and the Arrhenius relationship are employed to describe the life-stress relationships, respectively. Besides, Pan et al [104] proposed a CSADT optimization scheme under the V-optimality, in which the degradation process is characterized by a modified Wiener process.…”

“…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]. At this stage, the multi-source variability, such as the nonlinearity [12], [13], individual differences [14], [15], environmental stress factors [16], [17], measurement errors [18], [19], the temporal variability [20], model uncertainties [21], [22], and change points [23], has gradually been taken into account in performance degradation modeling. Besides, a few scholars have carried out research on multiple performance degradation processes (MPDPs) [24], dependent competing failure processes (DCFPs) [25], and the degradation analysis under dynamic environmental conditions [26].…”

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

“…Step 4: β (h+1) can be obtained by solving equation (12), or can be approximated by using (14) Step 5: put β (h+1) into equation (13) to obtain σ 2(h+1)…”

“…. (11) for m d � 2: (t A /f d ) do (12) if TC ≤ C b , d k�1 n k m k ≤ N A then (13) if det(I(Θ)) ≥ I max (D-optimality) then (14) Plan D � (n 1 , . .…”

“…Under each stress level, the corresponding samples are inspected independently, and their degradation paths are recorded at the prespecified times. In the CSA(D)DT, the experienced stress level does not change for each sample, which requires more samples than for SSA(D)DT [14]. At the same time, the failure mechanisms affected by stress level do not change, which makes CSA(D)DT easier to deal with than SSA(D)DT.…”