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ABSTRACT
Accelerated life tests are usually used as time and cost efficient reliability industrial experiments. They consist of submitting items to levels of stress higher than the usual working conditions. The main interest of such experiments is to obtain measures of the reliability of the devices under the usual working conditions via data obtained under stress levels. Usually the deterministic component of an accelerated life tests model, known as stress-response relationship, which relates the mean lifetime (or a function of this parameter) to the stress levels, is log-linear. The problem however is that in practice is not uncommon we find phenomenon that cannot be accommodated by a log-linear relationship. In this paper we propose an accelerated life tests model with a log-non-linear stress-response relationship. The advantage of such a formulation is that the general framework accommodates several stress-response relationship usually considered on accelerated life tests, while is enough flexible for fitting the data that cannot be accommodate by a simple log-linear stress-response relationship. By considering a particular experiment design we verify the effect of the term of non-linearity on the variability of the other coefficients of the model. We also determine what is the additional number of items that should be considered for achieving the same precision in the parameter estimation if a log-non-linear stress-response relationship is considered rather than a log-linear one. We establish the adequacy of the bootstrap tests based on the likelihood ratio statistics for testing the effect of a covariate for small and moderate sample sizes by studying their size and power. A numerical example illustrates the methodology.
ACKNOWLEDGMENT
The research was partially supported by the Brazilian Organization CNPq.