Estimation of the mean exponential survival time under a sequential censoring scheme

The exponential distribution can provide a simple and appealing survival-time model in reliability analysis and life tests. Due to certain experimental designs, time limitations, budgetary requirements, and other reasons, however, only censored data can be obtained. In this paper, we propose a novel estimation procedure for the mean survival time of an exponential distribution under a sequential censoring scheme, which can be treated as a combination of type I censoring and type II censoring. The procedure makes a trade-off between estimation error and sampling cost, using the minimum number of observations. An extensive set of Monte Carlo simulations is conducted to further validate its remarkable performance. To demonstrate the practical applicability, we then implement this newly proposed procedure to assess the reliability of various Backblaze's hard disk models.