Maintaining Systems With Dependent Failure Modes and Resource Constraints

Abstract

Many works on preventive maintenance (PM) of systems only consider either a single failure mode, or statistically independent failure modes. Here, we study the maintenance policy for systems with two statistically dependent failure modes (namely maintainable, and nonmaintainable), and resource constraints. Assume (i) the nonmaintainable failures unidirectionally affect the maintainable failure rate; (ii) due to the constrained resource, only a limited number of imperfect PM actions are performed to reduce the maintainable failure; and (iii) the improvement factor due to each imperfect PM is fixed, and the maximal number before replacement is fixed. By combining a Castro model for statistically dependent failure modes with a Zhang-Jardine model for a single failure mode and imperfect PM, we propose a hybrid maintenance model for systems with statistically dependent failure modes and limited imperfect PM. To examine the maintenance policy, assume that both the nonmaintainable failures and the maintainable failures follow the same type of failure rate functions such as the increasing power law failure rate function. We discuss the relation between expected cost rate per unit-time and each decision variable, and then give a solution to a constrained optimization problem provided that the length of the interval between two successive maintenance actions cannot be too small. Numerical simulations for the increasing power law failure rate fully verify the proposed maintenance policy, which can be also extended to other increasing failure rate functions such as an exponential failure rate function.