We study the conditions for unimodality of the lifetime distribution of a coherent system when the ordered component lifetimes in the system are described by generalized order statistics. Results for systems with independent and identically distributed lifetimes of components are included in this setting. The findings are illustrated with some examples for different types of systems. In particular, coherent systems with strictly bimodal density functions are presented in the case of independent standard uniform distributed lifetimes of components. Furthermore, we use the results to derive a sharp upper bound on the expected system lifetime in terms of the mean and the standard deviation of the underlying distribution.

The karyotype of a recently described species of Galtonia (Hyacinthaceae), G. regalis, is described and its cytotaxonomic relationship to other members of the genus examined. Since conflicting cytological patterns for the genus exist in the literature, the chromosome compositions of the three other species, G. candicans, G. princeps and G. viridiflora, are re-investigated. This study demonstrates that the karyotype of Galtonia is uniformly asymmetrical and distinctively trimodal, with 2n=16. Also included in this investigation is the allied monotypic genus Pseudogaltonia. Its karyotype is also asymmetrical, but differs from Galtonia in its chromosome number of 2n=18, and in certain other features.