Extended Periodic Inspection Policies for a Single Unit System Subject to Shocks

In this paper, two types of failures are taken into account to extend the classical periodic inspection policy for a single unit system when it has failed, in which type I failure can be rectified by a minimal repair and type II failure should be removed by a corrective replacement. More specifically, we investigate three extended periodic inspection models for a system subject to two kinds of distinctive shocks, i.e., a general periodic inspection model where the system is checked at periodic time epochs over an infinite time span (Policy A), a periodic inspection model with the consideration of quality warranty where the system is periodically checked within a maximal inspection number (Policy B), and a random periodic inspection model where the system is either periodically checked or randomly checked, whichever takes place first (Policy C). For each extended model, the average maintenance cost in one renewal cycle under special conditions is minimized to seek the optimal inspection interval theoretically and the numerical example is arranged to authenticate it analytically. Last but not least, comparisons are made among the extended models, indicating that the optimum solution varies from policy to policy.