Models to consider load-sharing in reliability calculation and simulation of systems consisting of mechanical components

The load-sharing case occurs in systems, if a load is shared by several components. Then the failure of a component results in a higher load share for the surviving components. This paper places emphasis on the analytic description of systems with load-sharing, the algebraic calculation and the simulative solution of their reliability. The capacity flow model, the Freund model and the state-graph method are presented as models for the analytic description. The state-graph method is the most general model: systems with individual failure behavior of the components, individual load steps as well as complex system structures can be considered. All three models are restricted to components with constant failure rates in the corresponding load level. However, in most mechanical systems the failure rates of components are not constant due to aging and wear-out. A more adequate method for the load-sharing case in mechanical systems is the application of simulation techniques. In this paper the general simulation algorithms are presented for 1-out-of-n systems consisting of components with constant failure rates and of components with time-dependent failure rates. In the case of constant failure rates, the failure times in the load levels can be sampled directly from the failure distributions due to the memory-less property of the exponential distribution. The simulation results are shown for both a 1-out-of-2 and a 1-out-of-3 system. For verification purpose the results of the simulation are compared with the analytic solution of the Freund model. In the case of time-dependent failure rates a dynamic modification of the failure distribution of the components is necessary. This is done by a time shift of the distributions and transformed random numbers. The simulation results are presented for a 1-out-of-2 and a 1-out-of-3 system. The failure behavior of the mechanical components is described by a Weibull distribution in each load level. In order to verify the simulation results the analytic bounds of the corresponding system with no increased load and maximum load are calculated.