Stergios B. Fotopoulos

Stochastic Modeling and Analysis of Manufacturing Systems

Manufacturing systems have become increasingly complex over recent years. This volume presents a collection of chapters which reflect the recent development of probabilistic models and methodologies that have either been motivated by manufacturing systems research or been demonstrated to have significant potential in such research. The editor has invited a number of leading experts to present detailed expositions of specific topics. These include: Jackson networks, fluid models, diffusion and strong approximations, to GSMP framework, stochastic convexity and majorization, perturbation, scheduling via Brownian models, and re-entrant lines and dynamic scheduling. Each chapter has been written with graduate students in mind, and several have been used in graduate courses that teach the modeling and analysis of manufacturing systems.

A Comment on the Relationship between Coefficient Alpha and Scale Characteristics

To date, three major articles have analyzed the use of coefficient alpha on scales published in the marketing literature. These studies have improved our understanding of the scale development process and the behavior of coefficient alpha. One consistent result is that coefficient alpha produces an R-square of approximately .10 when regressed against scale length. In the most recent of these three meta-analyses, Peterson (1994) suggested that alpha does not behave as suggested by theory. We reexamine the behavior of alpha in relation to scale length, scale width, and response centrality. Our results suggest different conclusions from those previously reached.

Optimization Techniques in Statistics

Synopsis: Classical Optimisation Techniques, Optimisation and Inequalities, Numerical Methods of Optimisation, Linear Programming Techniques, Non-linear Programming Techniques, Dynamic Programming Methods, Variational Methods, Stochastic Approximation Procedures, Optimisation in Simulation, Optimisation in Function Spaces Classical Optimisation Techniques: Preliminaries, Necessary and Sufficient Conditions for an Extremum, Constrained Optimisation - Lagrange Multipliers, Statistical Applications Optimisation and Inequalities: Classical Inequalities, Matrix Inequalities, Applications Numerical Methods of Optimisation: Numerical Evaluation of Roots of Equations, Direct Search Methods, Gradient Methods, Convergence of Numerical Procedures, Non-linear Regression and Other Statistical Algorithms Linear Programming Techniques: Linear Programming Problem, Standard Form of the Linear Programming Problem, Simplex Method, Karmarkars Algorithm, Zero-Sum Two Person Finite-Games and Linear Programming, Integer Programming, Statistical Applications Non-linear Programming Methods: Statistical Examples, Kuhn-Tucker Conditions, Quadratic Programming, Convex Programming, Applications, Statistical Control of Optimisation, Stochastic Programming, Geometric Programming Dynamic Programming Methods: Regulation and Control, Functional Equation and Principles of Optimality, Dynamic Programming and Approximation, Patent Care through Dynamic Programming, Pontryagin Maximum Principle, Miscellaneous Applications Variational Methods: Statistical Applications, Euler-Lagrange Equations, Neyman-Pearson Technique, Robust Statistics and Variational Methods, Penalised Maximum Likelihood Estimates Stochastic Approximation Procedures: Robbins-Monro Procedure, General Case, Kiefer-Wolfowitz Procedure, Applications, Stochastic Approximation and Filtering Optimisation in Simulation: Optimisation Criteria, Optimality of Regression Experiments, Response Surface Methods, Miscellaneous Stochastic Methods, Application Optimisation in Function Spaces: Preliminaries, Optimisation Results, Splines in Statistics, Chapter Exercises, Bibliography Index.

Inference for single and multiple change-points in time series

The article reviews methods of inference for single and multiple change‐points in time series, when data are of retrospective (off‐line) type. The inferential methods reviewed for a single change‐point in time series include likelihood, Bayes, Bayes‐type and some relevant non‐parametric methods. Inference for multiple change‐points requires methods that can handle large data sets and can be implemented efficiently for estimating the number of change‐points as well as their locations. Our review in this important area focuses on some of the recent advances in this direction. Greater emphasis is placed on multivariate data while reviewing inferential methods for a single change‐point in time series. Throughout the article, more attention is paid to estimation of unknown change‐point(s) in time series, and this is especially true in the case of multiple change‐points. Some specific data sets for which change‐point modelling has been carried out in the literature are provided as illustrative examples under both single and multiple change‐point scenarios.

Safety stock determination with correlated demands and arbitrary lead times

Abstract In this new paper a new method is proposed for determining the safety stock when daily demands are autocorrelated and lead times follow an arbitrary distribution. The method is then used as a basis for examining effects on the safety stock when the usual assumptions, namely, independence and normality of daily demand and normality of lead times, are violated. The new method is derived by using inequalities on the basis of probability arguments. It is simple to use and provides an upper bound of the safety stock. Further numerical investigation based on the new method shows that the effect of autocorrelation is more pronounced than departure from normality in determining the safety stock. Substantial error may be incurred if such autocorrelation is ignored in the test cases.

Maximum likelihood estimation of a change-point for exponentially distributed random variables

We consider the problem of estimating the unknown change-point in the parameter of a sequence of independent and exponentially distributed random variables. An exact expression for the asymptotic distribution of the maximum likelihood estimate of the change-point is derived. The analysis is based on the application of Weiner-Hopf factorization identity involving the distribution of ascending and descending ladder heights, and the renewal measure in random walks.

Exact asymptotic distribution of change-point mle for change in the mean of Gaussian sequences

We derive exact computable expressions for the asymptotic distribution of the change-point mle when a change in the mean occurred at an unknown point of a sequence of time-ordered independent Gaussian random variables. The derivation, which assumes that nuisance parameters such as the amount of change and variance are known, is based on ladder heights of Gaussian random walks hitting the half-line. We then show that the exact distribution easily extends to the distribution of the change-point mle when a change occurs in the mean vector of a multivariate Gaussian process. We perform simulations to examine the accuracy of the derived distribution when nuisance parameters have to be estimated as well as robustness of the derived distribution to deviations from Gaussianity. Through simulations, we also compare it with the well-known conditional distribution of the mle, which may be interpreted as a Bayesian solution to the change-point problem. Finally, we apply the derived methodology to monthly averages of water discharges of the Nacetinsky creek, Germany.

UNIT ROOT TESTS WITH INFINITE VARIANCE ERRORS

This paper considers the asymptotic properties of some unit root test statistics with the errors belonging to the domain of attraction of a symmetric α-stable law with 0 < α < 2. The results obtained can be viewed as a parallel extension of the asymptotic results for the finite-variance case. The test statistics considered are the Dickey-Fuller, the Lagrange multiplier, the Durbin-Watson and Phillips-type modified. Their asymptotic distributions are expressed as functionals of a standard symmetric α-stable Lévy motion. Percentiles of these test statistics are obtained by computer simulation. Asymptotic distributions of sample moments that are part of the test statistics are found to have explicit densities. A small Monte Carlo simulation study is performed to assess small-sample performance of these test statistics for heavy-tailed errors.

Flexible supply contracts under price uncertainty

This article develops supply contracts covering environments with changing prices. We investigate characterization properties of the price processes, while considering costs and discount factors. We determine expressions of the contracts expected low price and its second moment for a given horizon. We then employ these expected price and second moment values to identify an expected optimum time before the contract expires at which the lowest price occurs. Simulation experiments verify our analysis, and they illustrate how the optimum purchase time decreases as the drift term increases.

Change‐point methods for Weibull models with applications to detection of trends in extreme temperatures

We develop change-point methodology for identifying dynamic trends in the scale and shape parameters of a Weibull distribution. The methodology includes asymptotics of the likelihood ratio statistic for detecting unknown changes in the parameters as well as asymptotics of the maximum likelihood estimate of the unknown change-point. The developed methodology is applied to detect dynamic changes in the minimum temperatures of Uppsala, Sweden. Copyright