Abstract
An accelerated life test of a product or material consists of the observation of its failure time when it is subjected to conditions that stress the usual ones. The purpose is to obtain the parameters of the distribution of the time-to-failure for usual conditions through the observed failure times. A widely used method to provoke an early failure in a mechanism is to modify the temperature at which it is used. In this paper, the statistically optimal plan for Accelerated Failure Time (AFT) models, when the accelerated failure process is described making use of Arrhenius or Eyring equations, was calculated. The result was a design that had only two stress levels, as is common in other AFT models and that is not always practical. A new compromise plan was presented as an alternative to the widely used “4:2:1 plan”. The three-point mixture design proposed specified a support point in the interval that was optimal for the estimation of the parameters in AFT models, rather than simply the middle point. It was studied in comparison to different commonly used designs, and it proved to have a higher D-efficiency than the others.
Highlights
Accelerated testing consists of subjecting a product or material to a high stress that shortens its life or hastens the degradation of its performance
Estimating the failure time distribution of the long-term performance of a product or material is important in the field of manufacturing to demonstrate product or material reliability [3,4,5,6], Accelerated Failure Time (AFT) models are used for analyzing clinical trial data [7,8,9] and genomic studies [10,11]
Following the results presented by Rivas-López et al [33] and assuming known variance, the Fisher Information Matrix (FIM) for one particular observation is: I(μ, θ; x) =
Summary
Accelerated testing consists of subjecting a product or material to a high stress that shortens its life or hastens the degradation of its performance. The main reasons to perform over-stress testing is to estimate the life expectancy of the product under normal conditions (at lower or null stress levels) [1], i.e., to obtain the parameters of the distribution of the time-to-failure for usual conditions through the observed failure times. AFT models are mostly fully parametric, which facilitates their interpretation measuring the effect of the corresponding covariate on the survival time. Estimating the failure time distribution of the long-term performance of a product or material is important in the field of manufacturing to demonstrate product or material reliability [3,4,5,6], AFT models are used for analyzing clinical trial data [7,8,9] and genomic studies [10,11]
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