A theorem that gives the optimal control of Gaussian processes using the mathematical expectation of a function of the time and the place where the uncontrolled processes hit the boundary of the stopping region for the first time is proved. The result obtained in this note is an extension of a theorem due to Whittle.

Characterizations of a multivariate extreme value distribution in terms of its marginals are established.

A new concept of ageing distribution, namely new better than used in failure rate (NBUFR), is introduced. Different properties of the NBUFR class and its dual class are presented. Its relations to other classes of life distributions are investigated. Finally, NBUFR survival under shock models is discussed.

An expression for the asymptotic or steady-state performance function is derived for a multistate coherent system when each component changes states in time according to a semi-Markov process, the stochastic processes being mutually independent. This generalizes the expression for system availability of a binary coherent system when the components are governed by mutually independent alternating renewal processes.