System comparison procedures for automatic target recognition systems

Estimating the performance of an automatic target recognition (ATR) system in terms of its probability of successfully identifying a target involves extensive image collection and processing, which can be very time‐consuming and expensive. Therefore, we investigate the Wald sequential test for the difference in two proportions as a sample size‐reducing alternative to ranking and selection procedures and confidence intervals. An analysis of the test parameters leads to a practical methodology for implementing the Wald test for fairly comparing two systems, based on specific experimental goals. The test is also extended with the modified, sequentially rejective Bonferroni procedure for the multiple pairwise comparison of more than two systems. Two sampling schemes for different experimental goals are also discussed. The test methodology is applied to actual data to compare different configurations of a specific ATR system, with the results demonstrating that the modified Wald sequential procedure is a useful alternative to comparing proportions with confidence intervals, particularly when data are expensive. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 357–371, 1999     

On the reliability,availability and bayes confidence intervals for multicomponent systems

The problem of computing reliability and availability and their associated confidence limits for multi-component systems has appeared often in the literature. This problem arises where some or all of the component reliabilities and availabilities are statistical estimates (random variables) from test and other data. The problem of computing confidence limits has generally been considered difficult and treated only on a case-by-case basis. This paper deals with Bayes confidence limits on reliability and availability for a more general class of systems than previously considered including, as special cases, series-parallel and standby systems applications. The posterior distributions obtained are exact in theory and their numerical evaluation is limited only by computing resources, data representation and round-off in calculations. This paper collects and generalizes previous results of the authors and others. The methods presented in this paper apply both to reliability and availability analysis. The conceptual development requires only that system reliability or availability be probabilities defined in terms acceptable for a particular application. The emphasis is on Bayes Analysis and the determination of the posterior distribution functions. Having these, the calculation of point estimates and confidence limits is routine. This paper includes several examples of estimating system reliability and confidence limits based on observed component test data. Also included is an example of the numerical procedure for computing Bayes confidence limits for the reliability of a system consisting of N failure independent components connected in series. Both an exact and a new approximate numerical procedure for computing point and interval estimates of reliability are presented. A comparison is made of the results obtained from the two procedures. It is shown that the approximation is entirely sufficient for most reliability engineering analysis.     

Compound availability measures

An availability measure is the probability that a two-state system modeled by an alternating renewal process is available at one or more points or intervals. The concept of availability measures is extended to formulae for the joint prediction of availability and numbers of breakdowns (or repairs) of the system during a fixed interval.     

Scheduling customer arrivals to a stochastic service system

An efficient algorithm for determining the optimal arrival schedule for customers in a stochastic service system is developed. All customers arrive exactly when scheduled, and service times are modeled as iid Erlang random variables. Costs are incurred at a fixed rate per unit of time each customer waits for service, and an additional cost is incurred for every unit of time the server operates beyond a scheduled closing time. The objective is to minimize total operating cost. This type of problem arises in many operational contexts including transportation, manufacturing, and appointment‐based services. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 549–559, 1999     

Weibull tolerance intervals associated with moderate to small survival proportions for use in a new formulation of lanchester combat theory

Given herein is an easily implemented method for obtaining, from complete or censored data, approximate tolerance intervals associated with the upper tail of a Weibull distribution. These approximate intervals are based on point estimators that make essentially most efficient use of sample data. They agree extremely well with exact intervals (obtained by Monte Carlo simulation procedures) for sample sizes of about 10 or larger when specified survival proportions are sufficiently small. Ranges over which the error in the approximation is within 2 percent are determined. The motivation for investigation of the methodology for obtaining the approximate tolerance intervals was provided by the new formulation of Lanchester Combat Theory by Grubbs and Shuford [3], which suggests a Weibull assumption for time-to-incapacitation of key targets. With the procedures investigated herein, one can use (censored) data from battle simulations to obtain confidence intervals on battle times associated with given low survivor proportions of key targets belonging to either specified side in a future battle. It is also possible to calculate confidence intervals on a survival proportion of key targets corresponding to a given battle duration time.     

Some comparison results of system availability

System availability is a measure which is used to evaluate the performance of a system which can be in one of the two states: operational or nonoperational. It indicates the proportion of the time the system is available to perform its function. This paper discusses the concepts of stable point availability, stable interval availability, and long-run availability for the case of complete/minimal repair. Comparisons of these measures are made based on stochastic orderings and classifications of lifetime distributions. These comparisons are useful in determining policies for improving or maximizing the proportion of time the system is operational. The effect of using a burn-in procedure for maximizing these measures is also discussed. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 205–218, 1998     

The long term effects of an aging fleet on operational availability and cost: evidence from the U.S. coast guard

This paper empirically examines whether the aging of a fleet affects operational availability and operating cost using a unique data-set on the 117 47-foot Motor Lifeboats (MLBs) of the United States Coast Guard (USCG). Procured from 1997 to 2003, the 47-foot MLB is the standard lifeboat of the USCG and all 117 MLBs remain in service. The aging of the MLB fleet has resulted in higher annual operating costs and lower operational availability, although the nature of this relationship remains unclear. Our estimation strategy utilizes an error components estimator to examine these issues. We employ three variants of the dependent variables (i.e. the standard logarithmic transformation as is most commonly seen in the literature, inverse hyperbolic sine [IHS], and level outcomes). The point estimates from the standard logarithmic model finds operational availability for the MLBs decreases at a rate between 0.83 and 1.8% per year and cost increases at a rate between 0.33 and 7.81% per year. Similar effects are shown with the IHS and level outcome specifications. In terms of nonlinearity effects, we find the most pronounced changes in operational availability and cost occur for MLBs aged 15 years or more (in comparison to younger MLBs).     

Polynomial‐time approximation schemes for two‐machine open shop scheduling with nonavailability constraints

This paper addresses a two‐machine open shop scheduling problem, in which the machines are not continuously available for processing. The processing of an operation affected by a non‐availability interval can be interrupted and resumed later. The objective is to minimize the makespan. We present two polynomial‐time approximation schemes, one of which handles the problem with one non‐availability interval on each machine and the other for the problem with several non‐availability intervals on one of the machines. Problems with a more general structure of the non‐availability intervals are not approximable in polynomial time within a constant factor, unless . © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Simulating stable stochastic systems,V: Comparison of ratio estimators

The regenerative method for estimating parameters in a simulation requires the simulator to estimate the ratio of two means. Five point estimates and four confidence intervals for this ratio have been computed for three stochastic simulations. The jackknife method appears to be the most promising for both point and interval estimation.     

Approximation algorithms for the capacitated traveling salesman problem with pickups and deliveries

We consider the Capacitated Traveling Salesman Problem with Pickups and Deliveries (CTSPPD). This problem is characterized by a set of n pickup points and a set of n delivery points. A single product is available at the pickup points which must be brought to the delivery points. A vehicle of limited capacity is available to perform this task. The problem is to determine the tour the vehicle should follow so that the total distance traveled is minimized, each load at a pickup point is picked up, each delivery point receives its shipment and the vehicle capacity is not violated. We present two polynomial‐time approximation algorithms for this problem and analyze their worst‐case bounds. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 654–670, 1999     

Inventory control in divergent supply chains with time‐based dispatching and shipment consolidation

This article analyses a divergent supply chain consisting of a central warehouse and N nonidentical retailers. The focus is on joint evaluation of inventory replenishment and shipment consolidation effects. A time‐based dispatching and shipment consolidation policy is used at the warehouse in conjunction with real‐time point‐of‐sale data and centralized inventory information. This represents a common situation, for example, in various types of vendor managed inventory systems. The main contribution is the derivation of an exact recursive procedure for determining the expected inventory holding and backorder costs for the system, under the assumption of Poisson demand. Two heuristics for determining near optimal shipment intervals are also presented. The results are applicable both for single‐item and multiitem systems. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 59–71, 2011     

Statistical analysis for masked system life data from Marshall‐Olkin Weibull distribution under progressive hybrid censoring

This paper considers the statistical analysis of masked data in a series system, where the components are assumed to have Marshall‐Olkin Weibull distribution. Based on type‐I progressive hybrid censored and masked data, we derive the maximum likelihood estimates, approximate confidence intervals, and bootstrap confidence intervals of unknown parameters. As the maximum likelihood estimate does not exist for small sample size, Gibbs sampling is used to obtain the Bayesian estimates and Monte Carlo method is employed to construct the credible intervals based on Jefferys prior with partial information. Numerical simulations are performed to compare the performances of the proposed methods and one data set is analyzed.     

The impact of inventory information distortion due to customer order cancellations

In this paper we study the impact of cancellations of customer orders on an inventory system. We develop a periodic review (s, S) inventory model with Poisson demands, deterministic demand leadtimes and supply leadtimes. When no set up cost is present for replenishment, the behavior of the system cost can be studied analytically. For the case with a fixed set up cost, we derive the operating characteristics of the model via an embedded Markov chain analysis. Based on this, we formulate the total cost function and suggest a two‐phase approach to optimization. Our model can be used to compute cancellation fees and to evaluate the impacts of various conditions of cancellation. We find that cancellations, as major sources of inventory information distortion, increase total system costs, and the magnitude of the cost impact depends on the probability of cancellation and the expected cancellation time. Other relevant lessons and insights are also discussed. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 213–231, 1999     

Inference on a future reliability parameter with the weibull process model

An inferential procedure is presented which provides confidence intervals for a future reliability parameter when reliability growth testing is only partially completed. Hypothesis tests based on this method are uniformly most powerful unbiased. These results are applicable if (1) the system failure rate can be modeled as the intensity function of a Weibull process and (2) efforts to improve reliability are assumed to continue at a steady rate throughout the intervening period of testing. The usefulness of this methodology is illustrated by evaluating the risk of not reaching some future reliability milestone. If such risk is unacceptably high, program management may have time to identify problem areas and take corrective action before testing has ended. As a consequence, a more reliable system may be developed without incurring overruns in the scheduling or cost of the development program.     

Nonparametric estimation of some quantities of interest from renewal theory

In this paper, confidence intervals are given for two quantities of importance related to renewal processes. For each quantity, two confidence intervals are discussed. One confidence interval is given for general, all‐purpose use. Another confidence interval is given which is easier to compute, but not of general use. The case where data are subject to right censorship is also considered. Some numerical comparisons are made. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 638–649, 2003.     

A two-state system with partial availability in the failed state

A generalization of the alternating renewal model of a repairable system to permit partial availability in the failed state is introduced. It is shown how, by making use of an embedded alternating renewal process, we can readily derive expressions for various measures of system availability. Expressions for the point availability of the generalized process are presented.     

Analyzing availability using transfer function models and cross spectral analysis

If we look at the literature of reliability and life testing we do not see much on the use of the powerful methods of time series analysis. In this paper we show how the methods of multivariate time series analysis can be used in a novel way to investigate the interrelationships between a series of operating (running) times and a series of maintenance (down) times of a complex system. Specifically, we apply the techniques of cross spectral analysis to help us obtain a Box-Jenkins type transfer function model for the running times and the down times of a nuclear reactor. A knowledge of the interrelationships between the running times and the down times is useful for an evaluation of maintenance policies, for replacement policy decisions, and for evaluating the availability and the readiness of complex systems.     

On optimal aiming to hit a linear target

Typically weapon systems have an inherent systematic error and a random error for each round, centered around its mean point of impact. The systematic error is common to all aimings. Assume such a system for which there is a preassigned amount of ammunition of n rounds to engage a given target simultaneously, and which is capable of administering their fire with individual aiming points (allowing “offsets”). The objective is to determine the best aiming points for the system so as to maximize the probability of hitting the target by at least one of the n rounds. In this paper we focus on the special case where the target is linear (one‐dimensional) and there are no random errors. We prove that as long as the aiming error is symmetrically distributed and possesses one mode at zero, the optimal aiming is independent of the particular error distribution, and we specify the optimal aiming points. Possible extensions are further discussed, as well as civilian applications in manufacturing, radio‐electronics, and detection. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 323–333, 1999     

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.