Optimal allocation of two redundancies in a n-component series system with proportional hazard rates lifetimes

Abstract

In this paper, we deal with the problem of optimally allocating two active [standby] redundancies in a series system consisting of n-components ($n\ge 2$) in the sense of the stochastic ordering. For the case of active redundancy, we establish two results associated with the likelihood ratio and reserved hazard rate orders in the setting of proportional hazard rates (PHR) model. For the case of standby redundancy, we also present some new ordering results under the exponential or PHR framework. The results established here generalize and strengthen corresponding ones in the recent literature. Numerical examples are also provided to explicate the theoretic results.

Keywords:

• Stochastic order
• active redundancy
• standby redundancy
• series system
• PHR model
• likelihood ratio order
• reversed hazard rate order

Additional information

Funding

We thank the referees for the constructive suggestions. This work was supported by National Natural Science Foundation of China (11871252, 11771220, 51961145106), and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions. The authorship is listed in alphabetic order.