Modeling and analysis for a repairable system with multi-state components under K-mixed redundancy strategy

Abstract

In this paper, a three components repairable system with K-mixed redundancy strategy is proposed, in which the lifetimes of components, the repair time of failure components and the vacation time are distributed with different phase-type (PH) distributions. The different phases can represent different operational levels, repair levels and vacation levels. The multiple vacation policy is also adopted so that the human resources can be fully utilized. The repairable system is studied in both transient and stationary regimes with the matrix-analytic method, and not only some traditional reliability indexes are obtained, but also several new reliability indexes are obtained by employing Kronecker operator theory and aggregated stochastic theory. Finally, a numerical example is implemented to illustrate the results obtained in the paper.

Keywords:

• PH distribution
• K-mixed redundancy strategy
• reliability
• multiple vacation

Acknowledgments

The authors are very grateful to comments and suggestions of two anonymous referees that improved the previous version of the article.

Additional information

Funding

This research is supported by the National Natural Science of China under Grant No. 71601101, Fundamental Research Program of Shanxi Province Scientific No. 20210302124310, and Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (No. 2022L415).