The general theory of optimal confidence limits for system reliability based on results of Buehler (1957) and Sudakov and references cited there (1974) is developed. Counterexamples to some results of Sudakov (1974), Winterbottom (1974) and Harris and Soms (1980, 1981) are exhibited. Numerical...

In this paper we study a generalization of the Eulerian numbers and a class of polynomials related to them. An interesting application to probability theory is given in Section 3. There we use these extended Eulerian numbers to construct an uncountably infinite family of lattice random variables...

n balls are randomly distributed into N cells so that no cell may contain more than one ball. This process is repeated m times. In addition, balls may disappear, such disappearances are independent and identically Bernoulli distributed. Conditions are given under which the number of empty cells...