Continuous inspection with memory

In this article we consider continuous inspection plans (inspection stopping plans) as recurrent events in the sequence of investigation outcomes (steps of inspection). Along with traditional continuous inspection plans, it is the first time we consider plans of continuous inspection with memory which memorize the result of the last step of inspection after the inspection is stopped. For a wide range of plans of both traditional continuous inspection and continuous inspection with memory, we have obtained the main characteristics, i.e. mathematical expectation of the number of inspected objects before the inspection is stopped and variance.