This paper explores a progressive-stress accelerated life test under progressive type-II censoring with binomial random removal. It assumes a cumulative exposure model in which the lifetimes of test units follow a Marshall–Olkin length-biased exponential distribution. The study derives maximum likelihood and Bayes estimates of the model parameters and constructs Bayes estimates of the unknown parameters under various loss functions. In addition, this study provides approximate, credible, and bootstrapping confidence intervals for the estimators. Moreover, it evaluates three optimal test methods to determine the most effective censoring approach based on various optimality criteria. A real-life dataset is analyzed to demonstrate the proposed procedures and simulation studies used to compare two different designs of the progressive-stress test.