Accelerated life tests for products of unequal size

This paper considers 'estimation of the lifetime distribution' and 'optimal design of constant-stress accelerated life test plans' for products of unequal size. The distribution is Weibull with a scale parameter that is a 'log-linear function of stress' and a 'power function of product size with a size-effect parameter'. Maximum likelihood estimators (MLE) of model parameters are obtained, and their properties are studied. Two stress-level optimal test plans are obtained for products that come in two sizes, and a table useful for finding optimal test plans is given. The sum of asymptotic variances of MLE of a specified quantile of the distributions for products of both sizes is used as the optimality criterion. Optimum plans can be used when the ratio of two sizes is not too large. When the ratio is very large, the preestimate of size effect parameter should be carefully chosen.