Studies on Optimal Maintenance Policies for Extended Inspection Models

Abstract

The thesis studies optimal inspection and maintenance policies for high reliable systems. Some modified and extended inspection models from the viewpoint of actual models are considered. Using the reliability theory, such models are mathematically analyzed and useful inspection schedules are determined. Reasonable costs of inspections and failures for each model are introduced, and the expected costs until the detection of failures are obtained. Optimal inspection policies which minimize these expccted costs are derived analytically and numerically. In particular, these results would be practically applied to determine inspection schedules for systems such as digital control devices. Further, optimal maintenance and inspection policies for a finite interval are similarly considered and are analytically discussed. This thesis is divided into 7 chapters. An initial chapter gives the introduction which is constructed by the review of literatures and the organization of this thesis. Chapters 2 to 4 consider the modified inspection models and discuss these optimal policies: Chapter 2 studies optimal inspection policies for a two-unit system. First, the system operates as a two-unit system, and when one unit fails, it operates as a single-unit system. The system is checked continuously or periodically while it operates as a two-unit system, and is checked periodically by self-diagnosis after a failed unit is detached from the system. Chapter 3 studies optimal inspection policies for a system with self-testing which can detect some failures without performing external inspection. However, the failure might not be detected rapidly by self-testing, and so, it would be necessary to check the system periodically by inspection. This chapter considers the model where a failure is detected by either self-testing or periodic inspection. Then, optimal inspection policies which minimize the expected costs are analytically derived. Chapter 4 studies optimal maintenance and inspection policies for a finite interval. Optimal policies which minimize the expected costs of periodic replacement with minimal repair, block replacement, simple replacement and inspection policy are derived for a finite interval. Chapter 5 studies optimal inspection policies for a system with two types of inspection: There might exist some failures which can not be detected by type-1 inspection and can be detected only by type-2 inspection, however, type-1 inspection has a lower cost than that of type-2 inspection. An optimal number to perform type-1 inspection until the next type-2 inspection is analytically derived. Chapter 6 considers an extended model in Chapter 5, where the system is replaced at the specified N-th type-2 inspection. The expected cost per unit of time is analytically obtained, and an optimal number to perform type-1 inspection until the next type-2 inspection is numerically derived. Finally, in Chapter 7, the results are summarized.