Reliability of recoverable objects under continuous control

A key feature of the reliability of recoverable objects is the possibility for functioning without failure at any given time. The recoverable objects have the reliability characteristics of the non-recoverable objects only until the first failure. After first the first failure two parallel processes take place: failures of the objects; recovery of the objects. The superimposition of the two processes forms the actual behaviour of the objects. The main objective of the study is to determine the quantitative probability of the reliable operation of the recoverable objects under the assumption that the distribution function of the failures of non-recoverable objects is known. Next goal is the search for an analytical expression for this probability and for cases when it is not possible - to find methods for numerical solution. In solving the problem two approaches are used: The first approach is to formulate the process in Markov terms i.e. to prove that it meets the relevant criteria. The second approach is to solve so called recovery equation and, as a result, to determine the density of the probability distribution of failures i.e. the failure flow density. In the present study it is attempted to determine directly the probability of reliable operation based on a mathematical model of the behaviour. The model of the process of recovery is based on the following assumptions: known function of the probability of reliable operation until the first failure; the density distribution of the recovery function - g (t) is known; control of the functional status of objects is continuous and the recovery begins at the moment of identification of the failure