The maintenance of equipment has been an important issue for companies for many years. For systems with hidden or unrevealed failures (i.e., failures are not self-announcing), a common practice is to regularly inspect the system looking for such failures. Examples of these systems include protective devices, emergency devices, standby units, underwater devices etc. If no periodical inspection is scheduled, and a hidden failure has already occurred, severe consequences may result. Research on periodical inspection seeks to establish the optimal inspection interval (Failure Finding Interval) of systems to maximize availability and/or minimize expected cost. Research also focuses on important system parameters such as unavailability. Most research in this area considers non-negligible downtime due to repair/replacement but ignores the downtime caused by inspections. In many situations, however, inspection time is non-negligible. We address this gap by proposing an optimal failure finding interval (FFI) considering both non-negligible inspection time and repair/replacement time. A novel feature of this work is the development of models for both age-based and calendar-based inspection policies with random/constant inspection time and random/constant repair/replacement time. More specifically, we first study instantaneous availability for constant inspection and repair/replacement times. We start with the assumption of renewal of the system at each inspection. We then consider models with the assumption of renewal only after failure. We also develop limiting average availability models for random inspection and repair/replacement times, considering both age-based and calendar-based inspection policies. We optimize these availability models to obtain an optimal FFI in order to maximize the system’s availability. Finally, we develop several cost models for both age-based and calendar-based inspection policies with random inspection time and repair/replacement time. We formulate the model for constant inspection time and repair/replacement time as a special case. We investigate the optimization of cost models for each case to obtain optimal FFI in order to minimize the expected cost. The numerical examples and case study presented in the dissertation demonstrate the importance of considering non-negligible downtime due to inspection.

The maintenance of equipment has been an important issue for companies for many years. For systems with hidden or unrevealed failures (i.e., failures are not self-announcing), a common practice is to regularly inspect the system looking for such failures. Examples of these systems include protective devices, emergency devices, standby units, underwater devices etc. If no periodical inspection is scheduled, and a hidden failure has already occurred, severe consequences may result. Research on periodical inspection seeks to establish the optimal inspection interval (Failure Finding Interval) of systems to maximize availability and/or minimize expected cost. Research also focuses on important system parameters such as unavailability. Most research in this area considers non-negligible downtime due to repair/replacement but ignores the downtime caused by inspections. In many situations, however, inspection time is non-negligible. We address this gap by proposing an optimal failure finding interval (FFI) considering both non-negligible inspection time and repair/replacement time. A novel feature of this work is the development of models for both age-based and calendar-based inspection policies with random/constant inspection time and random/constant repair/replacement time. More specifically, we first study instantaneous availability for constant inspection and repair/replacement times. We start with the assumption of renewal of the system at each inspection. We then consider models with the assumption of renewal only after failure. We also develop limiting average availability models for random inspection and repair/replacement times, considering both age-based and calendar-based inspection policies. We optimize these availability models to obtain an optimal FFI in order to maximize the system’s availability. Finally, we develop several cost models for both age-based and calendar-based inspection policies with random inspection time and repair/replacement time. We formulate the model for constant inspection time and repair/replacement time as a special case. We investigate the optimization of cost models for each case to obtain optimal FFI in order to minimize the expected cost. The numerical examples and case study presented in the dissertation demonstrate the importance of considering non-negligible downtime due to inspection.