Sharp upper and lower reliability bounds for the ℒ- and -classes of life distributions with a given mean are provided. Bounds are also given for a distribution which is related to a known distribution (not necessarily exponential) through the Laplace order.

A new stochastic predator-prey model is introduced. The predator population X(t) is described by a linear birth-and-death process with birth rate λ1X and death rate μ1X. The prey population Y(t) is described by a linear birth-and-death process in which the birth rate is λ2Y and the death rate is . It is proven that and iff

In this paper we establish a characterization theorem for a general class of life-testing models based on a relationship between conditional expectation and the failure rate function. As a simple application of the theorem, we characterize the gamma, Weibull, and Gompertz distributions, since they have many probabilistic and statistical properties useful in both biometry and engineering reliability.

The statistical properties of a population of immigrant pairs of individuals subject to loss through emigration are calculated. Exact analytical results are obtained which exhibit characteristic even–odd effects. The population is monitored externally by counting the number of emigrants leaving in a fixed time interval. The integrated statistics for this process are evaluated and it is shown that under certain conditions only even numbers of individuals will be observed.

Exact reliability formulas for linear and circular consecutive-k-of-n: F systems are derived in the case of equal component reliabilities.

The computer age and the phenomenological complexity of the AIDS/HIV epidemic have engendered a rich profusion of deterministic and stochastic time series models for the development of an epidemic. The present study examines the reliability of deterministic approximations of fundamentally random processes. Through numerical analysis and probabilistic considerations, we derive absolute and simultaneous confidence interval bounding techniques, and offer a practical procedure based on these developments. A heartening aspect of the computational study presented at the close of this paper indicates that when the population size is in the thousands, the deterministic version to the classical logistic epidemic is a good approximation.

This paper approaches the problem of computing the price of an Asian option in two different ways. Firstly, exploiting a scaling property, we reduce the problem to the problem of solving a parabolic PDE in two variables. Secondly, we provide a lower bound which is so accurate that it is essentially the true price.

The move-to-front scheme is studied taking into account some forms of Markov dependence for the way items are requested. One of the dependences specifically rules out two consecutive requests for the same item. The other is the so-called p-correlation. An expression for the stationary distribution of the sequence of arrangements of items is given in each case. A necessary and sufficient condition for these distributions to belong to a particular class of distributions is also given. The mean search time for an item is calculated for each form of dependence and these are compared with the value obtained in the case of independent requests. Some properties of the sequence of requests are given. Finally, an expression for the variance of the search time is obtained.

Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i = 1, 2, 3) is exponentially distributed with rate cα i. The arrival rate at level i is λ i and the service time is exponentially distributed with rate μ i. In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.

We consider a family of M(t)/M(t)/1/1 loss systems with arrival and service intensities (λt (c), μt (c)) = (λct, μct), where (λt, μt) are governed by an irreducible Markov process with infinitesimal generator Q = (qij)m × m such that (λt, μt) = (λi, μi) when the Markov process is in state i. Based on matrix analysis we show that the blocking probability is decreasing in c in the interval [0, c∗], where c∗ = 1/maxi Σj≠iqij/(λi + μi). Two special cases are studied for which the result can be extended to all c. These results support Ross's conjecture that a more regular arrival (and service) process leads to a smaller blocking probability.