Methods for Calculating the Reliability Function for Systems Subjected to Random Stresses

The reliability function is calculated for components and systems which are subjected to stresses arriving randomly in time at a given average rate. The component is assumed to exist in a finite number of states, each of which is affected differently by the applied stress. During normal operation, failure rates are assigned to each of the states of the component; when the stress is applied, the failure rates for each state change to a new value. By defining the transitions among the states as a first order Markov process, the average probability of no failure prior to and including time t is calculated for the cases where the sets of failure rates are either discrete or continuous. The solution for the average probability is given as a matrix equation and several methods for reducing the equation to a useable form are examined. In addition, the theory of failure and repair processes is reviewed and methods for simplifying the calculation of the reliability of a system are presented.