System availability in a shock model under preventive repair and phase-type distributions

✍ Scribed by Delia Montoro-Cazorla; Rafael Pérez-Ocón

• Publisher: John Wiley and Sons
• Year: 2010
• Tongue: English
• Weight: 120 KB
• Volume: 26
• Category: Article
• ISSN: 1524-1904
• DOI: 10.1002/asmb.811

✦ Synopsis

Abstract

A device that can fail by shocks or ageing under policy N of maintenance is presented. The interarrival times between shocks follow phase‐type distributions depending on the number of cumulated shocks. The successive shocks deteriorate the system, and some of them can be fatal. After a prefixed number k of nonfatal shocks, the device is preventively repaired. After a fatal shock the device is correctively repaired. Repairs are as good as new, and follow phase‐type distributions. The system is governed by a Markov process whose infinitesimal generator, stationary probability vector, and availability are calculated, obtaining well‐structured expressions due to the use of phase‐type distributions. The availability is optimized in terms of the number k of preventive repairs. Copyright © 2009 John Wiley & Sons, Ltd.