Inspection and maintenance of a system with a bypass component

We present an inspection and maintenance model for a two-component lubrication system, filter and bypass valve, with applications to centralized lubrication systems. It presents significant differences from redundant systems in previous studies on cold, warm or hot stand-by components. These are the dissimilarity between the filter and the bypass, as the latter can induce catastrophic damage after a long working period, and the stochastic dependence between the filter and the bypass valve. Inspection and testing is focused on the valve, and only if it fails to open on inspection, or it is found to be open, is the filter inspection triggered. Preventive maintenance is mainly concerned with the filter, which is replaced periodically and also when an inspection detects an open valve or a clogged filter. The sensitivity analysis reveals that the optimum policy depends more on the parameters defining the lifetime of the filter than on those of the valve.