Answer to an open problem about stochastic comparison of parallel systems with geometric components. (English) Zbl 1525.60027
Summary: T. Mao and T. Hu [Probab. Eng. Inf. Sci. 24, No. 2, 245–262 (2010; Zbl 1193.60025)] left an open problem about the hazard rate order between two parallel systems of \(n\) geometric components. B. Du et al. [ibid. 26, No. 3, 375–391 (2012; Zbl 1271.60031)] solved the problem for \(n=2\). J. Wang [Stat. Probab. Lett. 106, 86–90 (2015; Zbl 1397.60058)] gave the answer to the problem for \(n\) up to 9. In this short note, we solve the open problem for any \(n\).
MSC:
| 60E15 | Inequalities; stochastic orderings |
| 62N05 | Reliability and life testing |
| 90B25 | Reliability, availability, maintenance, inspection in operations research |
References:
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