ABSTRACT
This chapter devotes to the application of the methods of asymptotic theory of random summation to the solution of an important problem of reliability prediction of complex systems during testing or adjustment when changes are brought into the system being tested. A perculiarity of this problem is that after every modification the system changes and therefore the data for its statistical reliability analysis, i.e., time intervals between the system failures, cannot be interpreted as identically distributed random variables or which is the same, as a homogeneous sample which is characteristic for the classical problems of reliability theory and quality control. The use of the Bayesian ideology for solving the problems of reliability prediction turns out to be very fruitful and has quite a reasonable basis, since within testing complex systems we can distinguish two sources of randomness in the functioning of the system then it reacts identically each time it is fed with the same input.
