On estimating the reliability of a component subject to several different stresses (strengths)

This paper is concerned with estimating p = P(X₁ < Y …, X_n < Y) or q =P (X < Y₁, …, X < Y_n) where the X's and Y's are all independent random variables. Applications to estimation of the reliability p from stress-strength relationships are considered where a component is subject to several stresses X₁, X₂, …, X_N whereas its strength, Y, is a single random variable. Similarly, the reliability q is of interest where a component is made of several parts all with their individual strengths Y₁, Y₂ …, Y_N and a single stress X is applied to the component. When the X's and Y's are independent and normal, maximum likelihood estimates of p and q have been obtained. For the case N = 2 and in some special cases, minimum variance unbiased estimates have been given. When the Y's are all exponential and the X is normal with known variance, but unknown mean (or uniform between 0 and θ, θ being unknown) the minimum variance unbiased estimate of q is established in this paper.     

A note on integer linear fractional programming

This note consists of developing a method for enforcing additional constraints to linear fractional programs and showing its usefulness in solving integer linear fractional programs.     

Application of level crossing analysis to discrete state processes in queueing systems

In this paper we introduce a discrete state level crossing analysis and present some basic results and a key theorem of level crossings. We illustrate the fertility of the discrete state level crossing analysis by applying it to queueing systems with (i) bulk arrival, (ii) instantaneous feedback, (iii) limited waiting space, and (iv) to machine interference problems.     

On n/1/F̄ dynamic deterministic problems

We consider sequencing of n jobs which will arrive intermittently and are to be processed on a single machine; the arrival and the processing times of each jobs are assumed known. A schedule is to be developed that minimizes the mean flow time. Two models are considered: (i) when no pre-emption or inserted idle time is allowed in the schedule, and (ii) when pre-emption is allowed but the jobs follow a pre-empt-repeat discipline We illustrate that Cobham's and Phipp's SPT dispatching rule does not guarantee the optimum F? even for the non-preemptive model We propose a branch and bound algorithm for both models and discuss our computational experience We also examine the relative performances of the optimum nonpre-emptive sequence, and the optimum pre-empt-repeat sequence over that resulting from SPT dispatching rule on a large number of sets of jobs of varying sizes and tightness.     

Concavity and monotonicity properties in a groundwater management model

We consider a discrete‐time groundwater model in which the cost of pumping takes a slightly different form to that which has been traditional in the research literature to date. This enables us to prove that (a) the optimal pumping quantity is nondecreasing in the ground water stock, (b) the stock level remaining after each period's pumping is also nondecreasing in the groundwater stock, (c) the optimal decision is determined by maximizing a concave function, and finally (d) the optimal pumping quantity is nonincreasing in the number of periods to go. We show that (a)–(c), while intuitive, do not hold under traditional modeling assumptions. We also explain the connections between our results and similar ones for some classic problems of operations research. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 00: 000–000, 2011