Renewal-type equations for a general repair process

✍ Scribed by J. S. Dagpunar

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 167 KB
• Volume: 13
• Category: Article
• ISSN: 0748-8017
• DOI: 10.1002/(sici)1099-1638(199707)13:4<235::aid-qre99>3.0.co;2-y

✦ Synopsis

We consider a component which undergoes instantaneous general repairs on failure. Suppose that

, where V i is the virtual age immediately after the ith failure, Y i is the time between the (i -1)th and ith failures, (•) is a specified repair functional, and V 0 = s. We derive integral equations for the repair density, and also for the joint density of repairs with respect to chronological age and virtual age on failure. In the asymptotic case, approximations are obtained for the mean and variance of virtual age on failure, virtual age after repair, and time between failures. Two policies are then considered. The first, an upgraded repair strategy employs minimal repairs until the component reaches a specified age, thereafter repairs restore the virtual age to that prescribed level. The second policy considered is the Kijima Type 2 model which is not amenable to the usual g-renewal analysis that is used in the Type 1 model. The repair density is obtained by numerical solution of the relevant integral equation. Finally, approximations for the asymptotic moments are found to be in close agreement with simulated results.