A poissonian binomial model with constrained parameters

The article examines ways of computing cumulative probabilities for a constrained Poissonian binomial distribution arising from a model of a weapon defense system.     

A general age replacement model with minimal repair

A general age replacement is introduced which incorporates minimal repair, planned and unplanned replacements, and costs which depend on time. Finite and infinite horizon results are obtained. Various special cases are considered. Furthermore, a shock model with general cost structure is considered.     

Clinical Characterization of Insomnia among Veterans with PTSD: Identifying Risk Factors for Diagnosis and Treatment with Sedative-Hypnotics

Abstract

Insomnia is prevalent among Veterans with post-traumatic stress disorder (PTSD), it exacerbates PTSD symptoms, and it contributes to impaired functioning and quality of life. To improve treatment outcomes, it is important to identify risk factors for insomnia and sedative-hypnotic use. Classification and regression trees and logistic regression models were used to identify variables associated with insomnia or sedative-hypnotic use. Key findings include low insomnia diagnosis rates (3.5–5.6%) and high rates of sedative-hypnotics (44.2–49.0%). Younger Veterans and those without a breathing-related sleep disorder (BRSD) were more likely to receive an insomnia diagnosis. Veterans with greater service connection and those with an alcohol/substance use disorder were more likely to be prescribed sedative-hypnotics. Interaction terms may have identified potential groups at risk of being under-diagnosed with insomnia (i.e. non-black Veterans with psychiatric co-morbidity, black Veterans without psychiatric co-morbidity) as well as groups at risk for sedative-hypnotic use (i.e. younger Veterans without BRSD). In sum, Veterans with PTSD have high rates of sedative-hypnotic use despite minimal evidence they are effective. This is counter to recommendations indicating behavioral interventions are the first-line treatment. Policy changes are needed to reduce use of sedative-hypnotics and increase access to behavioral insomnia interventions.     

The effects of model parameter deviations on the variance of a linearly filtered time series

We consider a general linear filtering operation on an autoregressive moving average (ARMA) time series. The variance of the filter output, which is an important quantity in many applications, is not known with certainty because it depends on the true ARMA parameters. We derive an expression for the sensitivity (i.e., the partial derivative) of the output variance with respect to deviations in the model parameters. The results provide insight into the robustness of many common statistical methods that are based on linear filtering and also yield approximate confidence intervals for the output variance. We discuss applications to time series forecasting, statistical process control, and automatic feedback control of industrial processes. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

A dual criteria sequencing problem with earliness and tardiness penalties

We consider the problem of sequencing n jobs on a single machine, with each job having a processing time and a common due date. The common due date is assumed to be so large that all jobs can complete by the due date. It is known that there is an O(n log n)‐time algorithm for finding a schedule with minimum total earliness and tardiness. In this article, we consider finding a schedule with dual criteria. The primary goal is to minimize the total earliness and tardiness. The secondary goals are to minimize: (1) the maximum earliness and tardiness; (2) the sum of the maximum of the squares of earliness and tardiness; (3) the sum of the squares of earliness and tardiness. For the first two criteria, we show that the problems are NP‐hard and we give a fully polynomial time approximation scheme for both of them. For the last two criteria, we show that the ratio of the worst schedule versus the best schedule is no more than . © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 422–431, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10020     

On labeling the vertices of products of complete graphs with distance constraints

Variations of Hale's channel assignment problem, the L(j, k)‐labeling problem and the radio labeling problem require the assignment of integers to the vertices of a graph G subject to various distance constraints. The λ_j,k‐number of G and the radio number of G are respectively the minimum span among all L(j, k)‐labelings, and the minimum span plus 1 of all radio labelings of G (defined in the Introduction). In this paper, we establish the λ_j,k‐number of ∏ K for pairwise relatively prime integers t₁ < t₂ < … < t_q, t₁ ≥ 2. We also show the existence of an infinite class of graphs G with radio number |V(G)| for any diameter d(G). © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Polynomial‐time approximation scheme for concurrent open shop scheduling with a fixed number of machines to minimize the total weighted completion time

In this article, we consider the concurrent open shop scheduling problem to minimize the total weighted completion time. When the number of machines is arbitrary, the problem has been shown to be inapproximable within a factor of 4/3 ‐ ε for any ε > 0 if the unique games conjecture is true in the literature. We propose a polynomial time approximation scheme for the problem under the restriction that the number of machines is fixed. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Optimal sample size allocation for tests with multiple levels of stress with extreme value regression

In this article, we discuss the optimal allocation problem in a multiple stress levels life‐testing experiment when an extreme value regression model is used for statistical analysis. We derive the maximum likelihood estimators, the Fisher information, and the asymptotic variance–covariance matrix of the maximum likelihood estimators. Three optimality criteria are defined and the optimal allocation of units for two‐ and k‐stress level situations are determined. We demonstrate the efficiency of the optimal allocation of units in a multiple stress levels life‐testing experiment by using real experimental situations discussed earlier by McCool and Nelson and Meeker. Monte Carlo simulations are used to show that the optimality results hold for small sample sizes as well. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Untruthful probabilistic demand forecasts in vendor‐managed revenue‐sharing contracts: Coordinating the chain

Vendor‐managed revenue‐sharing arrangements are common in the newspaper and other industries. Under such arrangements, the supplier decides on the level of inventory while the retailer effectively operates under consignment, sharing the sales revenue with his supplier. We consider the case where the supplier is unable to predict demand, and must base her decisions on the retailer‐supplied probabilistic forecast for demand. We show that the retailer's best choice of a distribution to report to his supplier will not be the true demand distribution, but instead will be a degenerate distribution that surprisingly induces the supplier to provide the system‐optimal inventory quantity. (To maintain credibility, the retailer's reports of daily sales must then be consistent with his supplied forecast.) This result is robust under nonlinear production costs and nonlinear revenue‐sharing. However, if the retailer does not know the supplier's production cost, the forecast “improves” and could even be truthful. That, however, causes the supplier's order quantity to be suboptimal for the overall system. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007