Optimal Stress Levels in Accelerated Degradation Testing for Various Degradation Models

Helmi Shat () and Rainer Schwabe ()
Additional contact information
Helmi Shat: Otto-von-Guericke University Magdeburg, Institute for Mathematical Stochastics
Rainer Schwabe: Otto-von-Guericke University Magdeburg, Institute for Mathematical Stochastics

A chapter in Mindful Topics on Risk Analysis and Design of Experiments, 2022, pp 113-134 from Springer

Abstract: Abstract 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 contribute with analytical results in regards to optimal design for accelerated degradation testing with single failure mode that corresponds to single response component. The univariate degradation process is expressed using a gamma model where the concept of generalized linear model is introduced to facilitate the derivation of an optimal design. Subsequently, we extend the univariate model to characterize optimal designs for accelerated degradation tests under different bivariate degradation models. 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 for the marginal components. Design optimization is conducted with respect to the minimum asymptotic variance criterion for estimating some quantile of the failure time distribution. Sensitivity analysis is considered to study the behavior of the resulting optimal designs under misspecifications of parameter values.

Keywords: Accelerated degradation test; Gamma model; Linear mixed-effects model; The multiplicative algorithm; Elfving’s theorem; Locally c-optimal design (search for similar items in EconPapers)
Date: 2022
References: Add references at CitEc
Citations: View citations in EconPapers (1)

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-06685-6_9

Ordering information: This item can be ordered from
http://www.springer.com/9783031066856

DOI: 10.1007/978-3-031-06685-6_9

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().