Exact inference for progressively Type-I censored exponential failure data

For reasons of time constraint and cost reduction, censoring is commonly employed in practice, especially in reliability engineering. Among various censoring schemes, progressive Type-I right censoring provides not only the practical advantage of known termination time but also greater flexibility to the experimenter in the design stage by allowing for the removal of test units at non-terminal time points. In this article, we consider a progressively Type-I censored life-test under the assumption that the lifetime of each test unit is exponentially distributed. For small to moderate sample sizes, a practical modification is proposed to the censoring scheme in order to guarantee a feasible life-test under progressive Type-I censoring. Under this setup, we obtain the maximum likelihood estimator (MLE) of the unknown mean parameter and derive the exact sampling distribution of the MLE under the condition that its existence is ensured. Using the exact distribution of the MLE as well as its asymptotic distribution and the parametric bootstrap method, we then discuss the construction of confidence intervals for the mean parameter and their performance is assessed through Monte Carlo simulations. Finally, an example is presented in order to illustrate all the methods of inference discussed here.