Abstract
Many products wear out over time even before they fail or stop working, therefore, through accelerated degradation tests one is able to make inferences about statistical parameters or the distributions of a product useful life. Since many devices experience different types of variation due to unobservable factors during the manufacturing processes or under certain operating conditions; these situations lead to the need in developing accelerated degradation models with several variables of acceleration and random effects. The proposed model in this paper, is a model based on the gamma process with random effects to have a better analysis of degradation. This model is applied to the analysis of the temperature increase of metal stampings that are affected by multiple explanatory variables. In addition, a statistical inference method based on a Bayesian approach is used to estimate the unknown parameters to then perform a reliability analysis after obtaining the first-passage time distributions.
Highlights
The level of quality and reliability of the products offered to customers is essential to maintain competitiveness in the market
The case study consists in an accelerated degradation tests (ADT) performed to obtain the temperature increase of metal stampings that are incorporated in printed circuit boards (PCB)
We considered the Wiener and the inverse Gaussian process to model the dataset obtained from the ADT
Summary
The level of quality and reliability of the products offered to customers is essential to maintain competitiveness in the market. The analysis of this case study is carried using the gamma process by considering the use of a life-stress relationship such as the exponential link function This life-stress relationship is commonly used when the case of multiple stress variables is presented, some important applications can be found in: Park & Padgett [24] that suggested a hyper-cuboidal volume approach as a measure of acceleration that can incorporate several acceleration variables. The gamma process is introduced with random effects, and the exponential link relationship is presented as a life stress function that best fits the explanatory variables that affect the case study.
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