Optimal designs for accelerated life tests with multiple stress factors and heteroscedasticity

ABSTRACT

Accelerated life testing (ALT) provides a means of obtaining data on product lifetime and reliability relatively quickly by subjecting products to higher-than-usual levels of stress factors. We present methods for obtaining optimal designs for multiple-factor ALTs with time censoring and heteroscedasticity in order to estimate percentiles of product life at usage conditions. We assume a Weibull life distribution and log-linear life–stress relationships with non constant shape parameter for the ALT stress factors. The primary optimality criterion is the minimization of the asymptotic variance of maximum likelihood estimator of the percentile estimator at usage stress. We also consider a secondary criterion for our design optimization. The design construction methods are illustrated by two practical examples.

KEYWORDS:

• C-optimality
• D-optimality
• Equal-probability curve
• Linearization
• Quantile estimation
• Shape–stress relationship

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62K05, 62F35
• Secondary 62J12

Funding

This research is supported by the Natural Sciences and Engineering Research Council of Canada.