Inference from accelerated life tests using eyring type re-parameterizations

Least squares estimators of the parameters of the generalized Eyring Model are obtained by using data from censored life tests conducted at several accelerated environments. These estimators are obtained after establishing that the Gauss-Markov conditions for least squares estimation are satisfied. Confidence intervals for the hazard rate at use conditions are obtained after empirically showing that the logarithm of the estimate of the hazard rate at use conditions is approximately normally distributed. The coverage probabilities of the confidence intervals are also verified by a Monte Carlo experiment. The techniques are illustrated by an application to some real data.     

Properties of an approximate hazard transform

The calculation of the exact reliability of complex systems is a difficult and tedious task. Consequently simple approximating techniques have great practical value. The hazard transform of a system is an invertible transformation of its reliability function which is convenient and useful in both applied and theoretical reliability work. A simple calculus for finding an approximate hazard transform for systems formed by series and parallel combinations of components is extended so that it can be used for any coherent system. The extended calculus is shown to lead to conservative approximations. A first order version of the extended calculus is also discussed. This method of approximation is even more simple to use, but is not always conservative. Examples of its application indicate that it is capable of giving quite accurate results.     

Hyperbolic integer programming

The hyperbolic integer program is treated as a special case of a hyperbolic program with a finite number of feasible points. The continuous hyperbolic program also belongs to this class since its solution can be obtained by considering only the extreme points of the feasible set. A general algorithm for solving the hyperbolic integer program which reduces to solving a sequence of linear integer problems is proposed. When the integer restriction is removed, this algorithm is similar to the Isbell-Marlow procedure. The geometrical aspects of the hyperbolic problem are also discussed and several cutting plane algorithms are given.     

Stochastic duels involving reliability

The reliability of weapons in combat has been treated by Bhashyam in the context of a stochastic duel characterized by fixed ammunition supplies. negative exponentially distributed firing times and weapon lifetimes, and a fixed number of spare weapons for each duelist. The present paper takes a different approach by starting with the fundamental duel of Ancker and Williams, characterized by unlimited ammunition and by ordinary renewal firing times, and adding to it weapon lifetimes which can be functions of time or of round position in the firing sequence. Probabilities of winning and tieing are derived and it is shown that under certain conditions the weapon lifetimes are equivalent to random time and ammunition limits.     

Models for multi-item continuous review inventory policies subject to constraints

Models are formulated for determining continuous review (Q, r) policies for a multiitem inventory subject to constraints. The objective function is the minimization of total time-weighted shortages. The constraints apply to inventory investment and reorder workload. The formulations are thus independent of the normal ordering, holding, and shortage costs. Two models are presented, each representing a convex programming problem. Lagrangian techniques are employed with the first, simplified model in which only the reorder points are optimized. In the second model both the reorder points and the reorder quantities are optimized utilizing penalty function methods. An example problem is solved for each model. The final section deals with the implementation of these models in very large inventory systems.     

A branch and bound algorithm for the minimum storage‐time sequencing problem

The minimum storage‐time sequencing problem generalizes many well‐known problems in combinatorial optimization, such as the directed linear arrangement and the problem of minimizing the weighted sum of completion times, subject to precedence constraints on a single processor. In this paper we propose a new lower bound, based on a Lagrangian relaxation, which can be computed very efficiently. To improve upon this lower bound, we employ a bundle optimization algorithm. We also show that the best bound obtainable by this approach equals the one obtainable from the linear relaxation computed on a formulation whose first Chvàtal closure equals the convex hull of all the integer solutions of the problem. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 313–331, 2001     

Optimal control of an M/G/1 queue with impatient priority customers

An optimal operating policy is characterized for the infinite‐horizon average‐cost case of a single server queueing control problem. The server may be turned on at arrival epochs or off at departure epochs. Two classes of customers, each of them arriving according to an independent Poisson processes, are considered. An arriving 1‐customer enters the system if the server is turned on upon his arrival, or if the server is on and idle. In the former case, the 1‐customer is selected for service ahead of those customers waiting in the system; otherwise he leaves the system immediately. 2‐Customers remain in the system until they complete their service requirements. Under a linear cost structure, this paper shows that a stationary optimal policy exists such that either (1) leaves the server on at all times, or (2) turns the server off when the system is empty. In the latter case, we show that the stationary optimal policy is a threshold strategy, this feature being commonplace in most of priority queueing systems and inventory models. However, the optimal policy in our model is determined by two thresholds instead of one. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 201–209, 2001     

Applying a bootstrap approach for setting reorder points in military supply systems

This paper develops and applies a nonparametric bootstrap methodology for setting inventory reorder points and a simple inequality for identifying existing reorder points that are unreasonably high. We demonstrate that an empirically based bootstrap method is both feasible and calculable for large inventories by applying it to the 1st Marine Expeditionary Force General Account, an inventory consisting of $20–30 million of stock for 10–20,000 different types of items. Further, we show that the bootstrap methodology works significantly better than the existing methodology based on mean days of supply. In fact, we demonstrate performance equivalent to the existing system with a reduced inventory at one‐half to one‐third the cost; conversely, we demonstrate significant improvement in fill rates and other inventory performance measures for an inventory of the same cost. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 459–478, 2000     

Optimal scheduling of reader—systems

We consider a reader—writer system consisting of a single server and a fixed number of jobs (or customers) belonging to two classes. Class one jobs are called readers and any number of them can be processed simultaneously. Class two jobs are called writers and they have to be processed one at a time. When a writer is being processed no other writer or readers can be processed. A fixed number of readers and writers are ready for processing at time 0. Their processing times are independent random variables. Each reader and writer has a fixed waiting cost rate. We find optimal scheduling rules that minimize the expected total waiting cost (expected total weighted flowtime). We consider both nonpreemptive and preemptive scheduling. The optimal nonpreemptive schedule is derived by a variation of the usual interchange argument, while the optimal schedule in the preemptive case is given by a Gittins index policy. These index policies continue to be optimal for systems in which new writers enter the system in a Poisson fashion. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 483–495, 1998     

Scheduling to minimize the total compression and late costs

We consider a single-machine scheduling model in which the job processing times are controllable variables with linear costs. The objective is to minimize the sum of the cost incurred in compressing job processing times and the cost associated with the number of late jobs. The problem is shown to be NP-hard even when the due dates of all jobs are identical. We present a dynamic programming solution algorithm and a fully polynomial approximation scheme for the problem. Several efficient heuristics are proposed for solving the problem. Computational experiments demonstrate that the heuristics are capable of producing near-optimal solutions quickly. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 67–82, 1998