A counting process approach to replacement models

Abstract

In this paper we present a common set-up for a large class of replacement models for stochastically failing systems. The set-up is based on the theory of counting processes, The replacement rule which minimizes "the total expected discounted cost" is determined. Several shock models are included as special eases, for example a shock model for a system which is repaired (and not replaced) at failures, and a shock model for a coherent system.

Keywords:

• Replacement
• counting process
• martingales
• conerent systems
• minmiax repair
• shock models
• minimum expected discounted cost

AMS Subject Classifications:

• Primary: 60 K 20
• Secondary: 90 B 25