A simple and efficient eM-algorithm for one-shot device data analysis

In this paper, we propose a simple and efficient EM-algorithm for estimating the model parameters based on one-shot device data. Traditionally, in the classical Expectation Maximization algorithm (EM-algorithm), unobserved failure times are regarded as the missing information and then imputed. In contrast, we consider here the counts of failures occurring between two successive inspection times to be missing. We provide detailed procedures, assuming that the lifetimes of one-shot devices follow the exponential and Weibull distributions, respectively. A Monte Carlo simulation study reveals that this simple approach markedly increases the convergence speed, a perennial challenge when using the EM-algorithm. The new method consistently finds the maximum likelihood estimates, unlike the traditional method which fails sometimes because some expectations do not exist based on the parameter estimates obtained from the previous M-step. Finally, an example is provided for illustrative purpose.