Experimental Designs for Accelerated Degradation Tests Based on Gamma Process Models
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Accelerated degradation tests (ADTs) are used to provide an accurate estimation of lifetime properties of highly reliable products within a relatively short testing time. In this regard, data from particular tests at high levels of stress (e.g., temperature, voltage, or vibration) are extrapolated, through a physically reasonable statistical model, to obtain estimates of lifetime quantiles at normal stress levels. The gamma process is a natural model for estimating the degradation increments over the degradation path, which exhibit a monotone and strictly increasing degradation pattern. In this work, we derive optimal experimental designs for repeated measures ADTs with single and multiple failure modes where the observational times are assumed to be known and fixed. The primary degradation path is assumed to follow a Gamma process where a generalized linear model (GLM) is derived in order to represent the observational data and facilitate obtaining an optimal design. The optimal design is obtained by minimizing the asymptotic variance of the estimator of the p-th quantile of the failure time distribution at the normal use conditions In order to avoid components damages and further experimental costs that depends on high stress levels, a penalty function is used to derive a penalized locally optimal design.
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