ABSTRACT
This chapter provides an example of an important practical problem that is successfully solved with the help of the apparatus of random summation. This example is of great interest since it has generated a whole sequence of asymptotic problems of the theory of random summation that were completely solved just recently. To increase the reliability of technical systems additional (reserve) elements are used, that accept loading in the case of the main element failure. Depending on the condition of the reserve element, three types of reservation are considered: loaded (hot), unloaded (cold) and light-weight (warm). Under hot reservation the element stays in the same condition as the main one. The reliability of technical systems can also be increased by repair of troubled elements.
