Reliability Evaluation for a Multi-State System Under Stress-Strength Setup

Abstract

The two most commonly used reliability models in engineering applications are binary k-out-of-n:G and consecutive k-out-of-n:G systems. Multi-state k-out-of-n:G and multi-state consecutive k-out-of-n:G systems have been proposed as an extension of these systems and they have been found to be more flexible tool for modeling engineering systems. In this article, multi-state systems, in particular, multi-state k-out-of-n:G and multi-state consecutive k-out-of-n:G, are considered in a stress-strength setup. The states of the system are classified considering the number of components whose strengths above (below) the multiple stresses available in an environment. The exact state probabilities are provided and the results are illustrated for various stress-strength distributions. Maximum likelihood estimators of state probabilities are also presented.

Keywords:

• Exponential distribution
• Maximum likelihood estimate
• Multi-state k-out-of-n:G system
• Order statistics
• Pareto distribution
• Stress-strength reliability

Mathematics Subject Classification:

• 90B25
• 62F10

Acknowledgment

The authors would like to express gratitude to the referee for a thorough review and valuable comments that led to some improvements in this article.