Optimal allocation of elements in a complex of renewable standby systems

The importance of eliminating randomness in insuring that renewable systems satisfy all necessary conditions is well known. In this paper, groups of standby renewable systems with a repair facility (RF) which form a symmetric “complex-RF” are considered. Return rules are obtained which maximize (in probability) the time up to the first failure of the complex over the class of rules of returns of the element to the complex which depend on the state of the complex and the failure times of the elements renewed at the RF. If the renewal is carried out by a sequential and monotone RF, then in this subclass of return rules, the maximum of the mean number of renewed elements is obtained for any finite time interval. In the case of the ordinary flow of element failures and ergodicity of the random process indicating the number of working elements in the complex, it is proved that the subclass of return rules obtained maximizes the steady-state mean of the working systems.