In this paper, we consider series and parallel systems composed of n independent items drawn from a population consisting of m different substocks/subpopulations. We show that for a series system, the optimal (maximal) reliability is achieved by drawing all items from one substock, whereas, for a parallel system, the optimal solution results in an independent drawing of all items from the whole mixed population. We use the theory of stochastic orders and majorization orders to prove these and more general results. We also discuss possible applications and extensions.
Bibliographical noteFunding Information:
The authors are thankful to the Editor-in-Chief, the Associate Editor and the anonymous reviewers for their valuable constructive comments which led to an improved version of the manuscript. The first author sincerely acknowledges the financial support from the Claude Leon Foundation, South Africa. Research of the second author was supported by the NRF (National Research Foundation of South Africa), Grant No 103613. The work of the third author was supported by Priority Research Centers Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2009–0093827). The work of the third author was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2016R1A2B2014211).
© 2017 Elsevier Inc.
- Majorization order
- Parallel system
- Schur-convex/concave function
- Series system
- Stochastic orders