On the maximum likelihood estimation based on one-shot test device data and the associated adaptive design

In this paper, we develop iterative methods to estimate parameters based on one-shot device test data using maximum likelihood estimation (MLE) for parametric, semi-parametric and non-parametric models. The EM-algorithm has been widely used to obtain the MLE in a variety of situations. But, the discussion on the direct Newton-Raphson algorithm seems to be scarce. To fill this gap, we develop the iterative method based on the Newton-Raphson algorithm and the method of scoring, which could be used in many commonly used reliability models. We also suggest a method for obtaining initial values under different model assumptions. The derived information matrix is further used for the optimal adaptive design, a topic that has not been studied much. Monte Carlo simulation studies reveal that the proposed method converges quickly and that the initial values obtained through the proposed least-square method are quite close to the MLE and leads to faster convergence in turn, particularly with large samples. Finally, two datasets from the literature are used to demonstrate all the methods developed here.