Inference from Accelerated Life Tests Using Arrhenius Type Re-Parameterizations

The scale parameter of an exponential distribution is reparameterized as a function of the stress according to the Arrhenius Re-action Rate Model. The location parameter is reparameterized as a linear function of the stress. Maximum likelihood estimators of the parameters of the Arrhenius model and the weighted least squares estimators of the linear model are obtained using data from censored sample accelerated life tests. The asymptotic normality of the maximum likelihood estimators is ascertained by examining the shapes of their maximum relative likelihood functions. The asymptotic normality of the least squares estimators is ascertained by establishing certain criteria for convergence. An unbiased estimator for the mean life of the device at use condition stress μ u is obtained. Confidence limits for μ u , are difficult to obtain, and alternatively a plausibility interval for μ u is obtained.