Accelerated Degradation Tests Modeling Based on the Nonlinear Wiener Process with Random Effects

Accelerated testing has been widely used for several decades. Started with accelerated life tests with constant‐stress loadings, more interest has been focused prominently on accelerated degradation tests and time‐varying stress loadings. Because accelerated testing is crucial to the assessment of product reliability and the design of warranty policy, it is important to develop an efficacious test plan that encompasses and addresses important issues, such as design of stress profiles, sample allocation, test duration, measurement frequency, and budget constraint. In recent years, extensive research has been conducted on the optimal design of accelerated testing plans, and the consideration of multiple stresses with interactions has become a big challenge in such experimental designs. The purpose of this study is to provide a comprehensive review of important methods for statistical inference and optimal design of accelerated testing plans by compiling the existing body of knowledge in the area of accelerated testing. In this work, different types of test planning strategies are categorized, and their drawbacks and the research trends are provided to assist researchers and practitioners in conducting new research in this area.

y ((),, t, s) = italicνη ((),, t, s) + italicσB ((), η ((),, t, s)) + ϵ

Section: Fundamentals Of At Methodsmentioning

confidence: 99%

A literature review on planning and analysis of accelerated testing for reliability assessment

Limon

Yadav

Liao

2017

“…Let us consider the data set given in Tang et al that refers to the light intensity of m = 12 LEDs that operate under a constant level of electric current of 40 mA. The degradation level of each unit, that is given by the percent loss of light intensity with respect to the initial intensity at time t = 0, was measured every 50 hours until 250 hours (see Table ).…”

Section: Numerical Applicationsmentioning

confidence: 99%

“…The degradation level of each unit, that is given by the percent loss of light intensity with respect to the initial intensity at time t = 0, was measured every 50 hours until 250 hours (see Table ). As done in Tang et al, the diodes are assumed to be failed when the percent loss of light intensity exceeded the threshold limit w max = 50.…”

Section: Numerical Applicationsmentioning

confidence: 99%

The transformed gamma process for degradation phenomena in presence of unexplained forms of unit‐to‐unit variability

Giorgio

Guida

Pulcini

2018

The transformed gamma process is a suitable model for degradation phenomena where damages accumulate gradually over time in a sequence of tiny increments. Attractiveness of the transformed gamma process mainly lies in the fact that it provides a relatively easy way for dealing with phenomena in which the degradation increments over disjoint time intervals are not independent. The transformed gamma process is also a very flexible model. In fact, it is indexed by 2 functions, the “age function” and the “state function,” whose mathematical form can be chosen ad hoc for modeling the dependence of the future degradation increment of a unit on its current age and state, respectively. In this paper, the transformed gamma process is adopted to describe the degradation paths of degrading units in the presence of an unexplained form of unit‐to‐unit variability. The degradation path of each unit is described via a transformed gamma process. Heterogeneity among paths of different units is accounted for by assuming that the scale parameters of the age and state functions vary randomly from unit to unit. Under these assumptions, a quite mathematically tractable model is obtained. The main properties of the proposed model are discussed, and inferential procedures based on the maximum likelihood criterion are implemented. A simple test is presented to check the goodness of fit of the proposed model. Three applicative examples, based on real degradation data, are developed.

“…When product's degradation follows the Wiener degradation model, the degradation path can be represented as follows:

y ((), t) = μ normalΛ ((), t) + σ normalB ((), normalΛ ((), t)),

where μ is the drift parameter reflecting the rate of degradation, σ is the diffusion parameter, Λ( t ) is a monotonic increasing function representing a general time scale with Λ(0) = 0, and B(⋅) is the standard Brownian motion, which represents the stochastic dynamics of the degradation process.…”

Section: Necessary Conditions For Degradation Mechanism Equivalencementioning

confidence: 99%

Equivalence analysis of accelerated degradation mechanism based on stochastic degradation models

Wang

Zhao

et al. 2017

For an effective accelerated degradation test, it is important to ensure that the degradation mechanism under different stress levels remains unchanged. In this article, we are interested in the equivalence analysis of accelerated degradation mechanism based on degradation data rather than physical or chemical techniques. Under the assumption that products' underlying degradation follows stochastic degradation models, we first introduce the relationship between mechanism equivalence and parameters of stochastic degradation models based on the acceleration factor invariant principle. Then the necessary conditions for mechanism equivalence, which should be satisfied under different stress levels, are derived and tested by the proposed parameter equivalence test method based on the modified Bartlett statistic and T statistic. Next a novel selection method for stochastic degradation models is derived therefrom by comparing the variation of coefficients of acceleration factors. The accuracy of the necessary conditions and the parameter equivalence test method is demonstrated through a simulation study. In addition, an electrical connector example with real stress relaxation data is analyzed to illustrate the proposed method further.