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: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland,xspace}\usepackage{amsmath,amsxtra}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document}$$M=1+\{(1/2)[1-L_{R}(\lambda)]\},$$\end{document} 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 λ R (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.