Allocation strategies of standby redundancies in series/parallel system

ABSTRACT

This article deals with the topic of optimal allocation of two standby redundancies in a two-component series/parallel system. There are two original components C₁ and C₂ which can be used to construct a series/parallel system, and two spares R₁ (same as C₁) and R₂ (different from both C₁ and C₂) at hand with them being standby redundancies so as to enhance the reliability level of the system. The goal for an engineer is to seek after the optimal allocation policy in this framework. It is shown that, for the series structure, the engineer should allocate R₂ to C₁ and R₁ to C₂ provided that C₁ (or R₁) performs either the best or worst among all the units; otherwise, the allocation policy should be reversed. For the parallel structure, the optimal allocation strategy is just opposed to that of series case. We also provide some numerical examples for illustrating the theoretical results.

KEYWORDS:

• Hazard rate order
• Parallel system
• series system
• Standby redundancies
• Usual stochastic order

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 90B25
• Secondary: 60E15, 60K10

Acknowledgments

The authors thank the referees for the insight comments and suggestions, which resulted in an improvement in the presentation of this manuscript.

Funding

This work was supported by the Hong Kong PhD Fellowship Scheme (PF14-13413) of Hong Kong Research Grants Council, National Natural Science Foundation of China (11401266, 11422109), Natural Science Foundation of Jiangsu Province (BK20141145), Qing Lan Project and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.