Maintenance modeling for balanced systems subject to two competing failure modes

Many 1-out-of n pairs: G balanced systems experience two competing failure processes, but the complex failure mechanisms present challenging issues in maintenance modeling. This paper formulates a maintenance policy optimization model for balanced systems composed of multiple functionally-exchangeable units. A unit may fail due to the hard failure caused by a self-failure mechanism, or shock failures due to abrupt or sudden stress from the external environment, whichever occurs first. Once a unit fails, the symmetric component stops working immediately to be a standby unit to keep the system balanced. When there are at least two standby units in the balanced system, dynamically reallocating the two units on positions is a feasible way to increase the probability of the system running. Moreover, the repair and replacement actions are properly performed to avoid the system being out of balance. More units on operation will increase the system operational cost, but fewer units may induce system failure. Thus, there is a trade-off between the number of working units and the system average maintenance cost. The objective of this work is to find the optimal number of operating units to minimize the maintenance cost per unit time. An illustrative example is used to demonstrate the effectiveness of the proposed policy, where a sensitivity analysis illustrates how the cost parameters affect the system maintenance cost.