Reliability Considerations for a Two Element Redundant System with Generalized Repair Times

The mean time to failure for a two element, redundant repairable system is derived. The system consists of identical elements each having a constant failure rate λ and a general repair time distribution, f_R(x). The increase in expected time to failure of the system over a single nonrepairable element is calculated and found to be:

where L_R(λ) is the Laplace transform of the probability density function of f_R(x), with s equal to λ. M is plotted for elements having several different repair time distributions. For these cases M is found to be relatively independent of the distributions and primarily a function of the product λR (where R is the mean time to repair for a single element). The conclusion is drawn that redundancy and repair can greatly increase the operating time of the system described in this paper.