Consider a production process where the categories of successive units form a Markov chain with known transition matrix. Whenever a unit is produced, we may, at a fixed cost, inspect it. If its value is less than maximal, we may replace it with a perfect (maximal value) unit. We obtain optimal...

Consider the stochastic processes X1, X2,... and [Lambda]1, [Lambda]2,... where the X process can be thought of as observations on the [Lambda] process. We investigate the asymptotic behavior of the conditional distributions of Xt+v given X1,..., Xt and [Lambda]t+v given X1,..., Xt with regard...

The change point problem for independent normal means is considered as a multiple testing problem. Two stepwise methods are considered. Namely, the binary segmentation method of Vostrikova (1981) [7] and the maximum residual down method of Cohen et al. (2009) [5]. Both of these methods are shown...

We consider a sequential rule, where an item is chosen into the group, such as a university faculty member, only if his score is better than the average score of those already belonging to the group. We study four variables: The average score of the members of the group after k items have been...

Let X_n,…,X₁ be i.i.d. random variables with distribution function F and finite expectation. A statistician, knowing F, observes the X values sequentially and is given two chances to choose X's using stopping rules. The statistician's goal is to select a value of X as large as possible. Let V_n²...

A new Secretary Problem is considered, where for fixed k and m one wins if at some time i = m(j .. 1) + 1 up to jm one selects one of the j best items among the first jm items, j = 1,...,k. Selection is based on relative ranks only. Interest lies in small k values, such as k = 2 or 3. This is...

The classical Bomber problem concerns properties of the optimal allocation policy of arsenal for an airplane equipped with a given number, n, of anti-aircraft missiles, at a distance t 0 from its destination, which is intercepted by enemy planes appearing according to a homogeneous Poisson...