Optimal Inspection Models with Their Applications

Reliability engineering was established in the 1950s for the aim of maintaining the reliability of vacuum tubes, and has been widely applied mainly to space and military systems [1]. Currently, the reliability of solid-state semiconductor devices which include large-scale integrated circuits has been need in reliability engineering.

System reliability can be improved by providing some redundant and standby units. Especially, standby units play an important role in the case where failures of an operating unit are costly or dangerous. A typical example is standby electric generators in nuclear power plants, hospitals, and other public facilities.

Some units in offices and industries successively execute jobs and computer processes. It would be impossible or impractical to maintain such units in a strict periodic fashion shown in Chap. 2.

When the failure time follows an exponential distribution, the policies of inspection first, last, and overtime have been proposed, and their optimal policies have been derived and compared analytically and numerically in Sect. 3.​3 and Sect. 3.​4.

The supply of spare parts is a big issue in maintaining complex systems such as aircrafts and warships, because spare parts have a wide variety of items and are stocked at multi-echelon facilities such as bases and depots. Multi-Echelon Technique for Recoverable Item Control (METRIC) is the inventory theory of spare parts for US Air Force with multi-echelon facilities [1, 2].

Some systems might be hierarchical, i.e., a system is constituted with several subsystems, a subsystem is constituted with several sub-subsystems, and such hierarchical relations continue from a system to discrete parts in Fig. 1.​3. One typical example is a jet fighter with maintenance hatch beside its airframe: When the hatch is opened, there exist some equipment chassis which are easy to exchange at failures, and are called LRUs (Line Replacement Units). An LRU has knobs for handling easily and electric connector sockets for connecting other LRUs electrically, and can be gotten out when its connector sockets are disassembled, its fixed attachments are released, and are pulled out. In addition, this contains lots of printed card boards, and failed boards are eluted one by one, are checked by the special function tester, and are exchanged to normal ones. Such LRU repair works are undergone at military maintenance facilities and failed boards are repaired at civilian factories.

This chapter describes optimal inspection and maintenance policies for storage systems. A system such as missiles and spare parts of aircrafts is in storage for a long time from transportation to usage [1, 2], which is called a storage system.

This chapter describes optimal inspection and maintenance policies for phased array radars (PAR). A PAR is the radar which steers a directional electromagnetic wave, i.e., steers its beam electrically. Comparing with conventional radars which steer their antenna mechanically, a PAR has no mechanical portion to drive radar antenna, and hence, can steer very rapidly.

The electric power is one of important infrastructures which support our society, and its inexpensive supply is required because the power cost is reflected in product costs. Various renewable energies have great expectations for their future.

The airframe for civil aviation has to be lightweight because its weight affects the range and fuel-efficiency of aircraft and is different from military aviation. The airframe has to be tolerant for damage due to statistical and dynamic mechanical stresses produced by changes of air pressure and temperature, vibration of engine and aerodynamic turbulence and shocks when it takes off and lands. Aluminum alloys 2024 and 7075 are adopted for the principal substance of construction because its tensile strength is almost as same as that of ferrous alloy and its specific weight is from one third to one fourth of ferrous alloy. The stressed skin semi-monocoque structure is adopted and its stress is analyzed strictly utilizing a finite element method for reducing weight [1].