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     

Optimal maintenance policies for a safety‐critical system and its deteriorating sensor

We consider the integrated problem of optimally maintaining an imperfect, deteriorating sensor and the safety‐critical system it monitors. The sensor's costless observations of the binary state of the system become less informative over time. A costly full inspection may be conducted to perfectly discern the state of the system, after which the system is replaced if it is in the out‐of‐control state. In addition, a full inspection provides the opportunity to replace the sensor. We formulate the problem of adaptively scheduling full inspections and sensor replacements using a partially observable Markov decision process (POMDP) model. The objective is to minimize the total expected discounted costs associated with system operation, full inspection, system replacement, and sensor replacement. We show that the optimal policy has a threshold structure and demonstrate the value of coordinating system and sensor maintenance via numerical examples. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 399–417, 2017     

Economic Losses From a Fire in a Dense-Packed U.S. Spent Fuel Pool

In 2013, the staff of the U.S. Nuclear Regulatory Commission estimated the reduction of the off-site economic losses from a fire in a drained U.S. spent fuel pool if fuel that had cooled for more than five years were transferred to dry cask storage—an option it called “expedited transfer.” In this article, it is shown that the savings would be much higher than the NRC estimated. Savings increase to about $2 trillion if: losses beyond 50 miles are included; the land-contamination threshold for long-term population relocation is changed to that used for the Chernobyl and Fukushima accidents and recommended by the U.S. Environmental Protection Agency; and, based on the experience of Japan, decontamination of land areas to levels acceptable for population return is assumed to take at least four years. If expedited transfer were implemented, the off-site economic losses would be reduced by about 98%.     

Parallel machine scheduling with eligibility constraints: A composite dispatching rule to minimize total weighted tardiness

We study a parallel machine scheduling problem, where a job j can only be processed on a specific subset of machines M_j, and the M_j subsets of the n jobs are nested. We develop a two‐phase heuristic for minimizing the total weighted tardiness subject to the machine eligibility constraints. In the first phase, we compute the factors and statistics that characterize a problem instance. In the second phase, we propose a new composite dispatching rule, the Apparent Tardiness Cost with Flexibility considerations (ATCF) rule, which is governed by several scaling parameters of which the values are determined by the factors obtained in the first phase. The ATCF rule is a generalization of the well‐known ATC rule which is very widely used in practice. We further discuss how to improve the dispatching rule using some simple but powerful properties without requiring additional computation time, and the improvement is quite satisfactory. We apply the Sequential Uniform Design Method to design our experiments and conduct an extensive computational study, and we perform tests on the performance of the ATCF rule using a real data set from a large hospital in China. We further compare its performance with that of the classical ATC rule. We also compare the schedules improved by the ATCF rule with what we believe are Near Optimal schedules generated by a general search procedure. The computational results show that especially with a low due date tightness, the ATCF rule performs significantly better than the well‐known ATC rule generating much improved schedules that are close to the Near Optimal schedules. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 249–267, 2017     

Layers of Experiments with Adaptive Combined Design

In the field of nanofabrication, engineers often face unique challenges in resource‐limited experimental budgets, the sensitive nature of process behavior with respect to controllable variables, and highly demanding tolerance requirements. To effectively overcome these challenges, this article proposes a methodology for a sequential design of experiments through batches of experimental runs, aptly named Layers of Experiments with Adaptive Combined Design (LoE/ACD). In higher layers, where process behavior is less understood, experimental regions cover more design space and data points are more spread out. In lower layers, experimental regions are more focused to improve understanding of process sensitivities in a local, data‐rich environment. The experimental design is a combination of a space‐filling and an optimal design with a tuning parameter that is dependent on the amount of information accumulated over the various layers. The proposed LoE/ACD method is applied to optimize a carbon dioxide (epet‐CO2) assisted deposition process for fabricating silver nanoparticles with pressure and temperature variables. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 127–142, 2015     

Effects of lethality in naval combat models

In the context of both discrete time salvo models and continuous time Lanchester models we examine the effect on naval combat of lethality: that is, the relative balance between the offensive and defensive attributes of the units involved. We define three distinct levels of lethality and describe the distinguishing features of combat for each level. We discuss the implications of these characteristics for naval decision‐makers; in particular, we show that the usefulness of the intuitive concept “more is better” varies greatly depending on the lethality level. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Higher‐order Markov chain models for categorical data sequences*

In this paper we study higher‐order Markov chain models for analyzing categorical data sequences. We propose an efficient estimation method for the model parameters. Data sequences such as DNA and sales demand are used to illustrate the predicting power of our proposed models. In particular, we apply the developed higher‐order Markov chain model to the server logs data. The objective here is to model the users' behavior in accessing information and to predict their behavior in the future. Our tests are based on a realistic web log and our model shows an improvement in prediction. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

An algorithm for the solution of a location problem with metric constraints

In many location problems, the solution is constrained to lie within a closed set. In this paper, optimal solutions to a special type of constrained location problem are characterized. In particular, the location problem with the solution constrained to be within a maximum distance of each demand point is considered, and an algorithm for its solution is developed and discussed.     

Covariance of weibull order statistics

Let X₁ < X₂ <… < X_n denote an ordered sample of size n from a Weibull population with cdf F(x) = 1 - exp (?x^p), x > 0. Formulae for computing Cov (X_i, X_j) are well known, but they are difficult to use in practice. A simple approximation to Cov(X_i, X_j) is presented here, and its accuracy is discussed.