Chapter List

1. Introduction

Most systems in offices and industries are successively executing the work of jobs and the process of computers. For such systems, it would be impossible or impractical to maintain them in a strictly periodic fashion. For example, when a job has a variable working cycle and processing time, it would be better to make some maintenances after it has completed its work and process. Barlow and Proschan1 considered the random age replacement policy and obtained analytically its reliability quantities using a renewal theory. Pinedo2 summarized the various schedules of jobs which have random processing times.

This chapter proposes the random inspection policy in which a system is checked at the same random times as its working times. Many papers of inspection models have been already published and were surveyed in extensively Barlow and Proschan,1 Kaio and Osaki,3 Valdes-Flores and Feldman,4 Hariga and Al-Fawzan,5 and Nakagawa.6 However, there is no paper in the literature treating with a random inspection model.

At first, we obtain the...