Block replacement policy with uncertain lifetimes

•Block replacement policy with uncertain lifetimes instead of random lifetimes.•Chance value model for uncertain block replacement problem.•Expected value model for uncertain block replacement problem.•Critical value model for uncertain block replacement problem.

Block replacement policy is a type of preventive replacement policies where the units are always replaced at failure or at a scheduled time periodically. Assuming that the lifetimes of the units are uncertain variables, this paper studies the block replacement policy in an uncertain environment. To deal with the different constraints a decision maker may face, three different criterions are used to build the optimization models for the uncertain block replacement problem, which are chance value, expected value and critical value. Based on these criterions, the uncertain block replacement models are transformed into some equivalent crisp models. Then the optimal scheduled replacement time under each criterion is obtained and its properties are investigated.