Reliability of a Coherent System in a Multicomponent Stress-Strength Model

SYNOPTIC ABSTRACT

The problem of finding system reliability is difficult in a multicomponent stress-strength model because the strengths of different components may be different, and they may experience the same or different stress levels. In a single-component stress-strength model, reliability of a component is the probability of its strength being greater than the stress imposed on it. In a multicomponent stress-strength model, we must take into account the structure function of the system and respective stress and strength levels of the components while determining the system reliability. In this article we show how the stress-strength reliability of a multicomponent system, at least its lower bound, can be derived. The stress-strength reliability of a system is expressed here as a function of the stress-strength reliabilities of its individual components. This generalized expression helps evaluate the stress-strength reliability of different coherent systems, regardless of the dependent or independent nature of the stress and strength variables.

Key Words and Phrases::

• coherent system
• invariance principle
• minimal cut set
• stress-strength reliability
• structure function

Acknowledgment

•	This work was done when the authors were visiting the Department of Statistics, University of California, Davis, USA, as Visiting Professors.
•	The authors are thankful to the anonymous referee for some constructive comments.