Inference for two-parameter exponential distribution under block censoring

The two-parameter exponential distribution is widely used in reliability analysis and quality control, particularly for modeling failure times of products or processes. However, in practical scenarios, data collection is often incomplete due to time and resource limitations, necessitating the use of censoring techniques. One such method is the block censoring scheme, where test units are divided into groups that are tested simultaneously. The test stops in each group after a predefined number of failures. This method optimally balances data quality with resource efficiency. In this paper, we focus on developing some statistical procedures for unknown parameters of the two-parameter exponential distribution under block-censored data. By deriving estimators for the unknown parameters, constructing confidence intervals, and developing hypothesis tests, we provide a comprehensive toolkit for statistical inference based on block-censored data coming from the two-parameter exponential distribution. These tools enable data-driven decision-making in scenarios such as lifetime testing, warranty analysis, and process reliability assessment. For illustrative proposes, we analyze two real-world datasets using the proposed procedures.