Implicit vector equilibrium problems with applications

Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C: K--> 2(Y) a point-to-set mapping such that for any x is an element of K, C(x) is a pointed, closed, and convex cone in Y and int C(x) not equal 0. Given a mapping g : K --> K and a vector valued bifunction f : K x K - Y, we consider the implicit vector equilibrium problem (IVEP) of finding x* is an element of K such that f (g(x*), y) is not an element of - int C(x) for all y is an element of K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. (C) 2003 Elsevier Science Ltd. All rights reserved.

Model-based clustering in gene expression microarrays: An application to breast cancer data

In microarray studies, the application of clustering techniques is often used to derive meaningful insights into the data. In the past, hierarchical methods have been the primary clustering tool employed to perform this task. The hierarchical algorithms have been mainly applied heuristically to these cluster analysis problems. Further, a major limitation of these methods is their inability to determine the number of clusters. Thus there is a need for a model-based approach to these. clustering problems. To this end, McLachlan et al. [7] developed a mixture model-based algorithm (EMMIX-GENE) for the clustering of tissue samples. To further investigate the EMMIX-GENE procedure as a model-based -approach, we present a case study involving the application of EMMIX-GENE to the breast cancer data as studied recently in van 't Veer et al. [10]. Our analysis considers the problem of clustering the tissue samples on the basis of the genes which is a non-standard problem because the number of genes greatly exceed the number of tissue samples. We demonstrate how EMMIX-GENE can be useful in reducing the initial set of genes down to a more computationally manageable size. The results from this analysis also emphasise the difficulty associated with the task of separating two tissue groups on the basis of a particular subset of genes. These results also shed light on why supervised methods have such a high misallocation error rate for the breast cancer data.

A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type I extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.

Warranty and optimal reliability improvement through product development

For products sold with warranty, the warranty servicing cost can be reduced by improving product reliability through a development process. However, this increases the unit manufacturing cost. Optimal development must achieve a trade-off between these two costs. The outcome of the development process is uncertain and needs to be taken into account in the determination of the optimal development effort. The paper develops a model where this uncertainty is taken into account. (C) 2003 Elsevier Ltd. All rights reserved.

Repair-replace strategies for two-dimensional warranty policies

For repairable items sold with free replacement warranty, the actions available to the manufacturer to rectify failures under warranty are to (1) repair the failed item or (2) replace it with a new one. A proper repair-replace strategy can reduce the expected cost of servicing the warranty. In this paper, we study repair-replace strategies for items sold with a two-dimensional free replacement warranty. (C) 2003 Elsevier Ltd. All rights reserved.

Study of n-fold Weibull competing risk model

This paper deals with an n-fold Weibull competing risk model. A characterisation of the WPP plot is given along with estimation of model parameters when modelling a given data set. These are illustrated through two examples. A study of the different possible shapes for the density and failure rate functions is also presented. (C) 2003 Elsevier Ltd. All rights reserved.

Tool support for testing concurrent Java components

Concurrent programs are hard to test due to the inherent nondeterminism. This paper presents a method and tool support for testing concurrent Java components. Too[ support is offered through ConAn (Concurrency Analyser), a too] for generating drivers for unit testing Java classes that are used in a multithreaded context. To obtain adequate controllability over the interactions between Java threads, the generated driver contains threads that are synchronized by a clock. The driver automatically executes the calls in the test sequence in the prescribed order and compares the outputs against the expected outputs specified in the test sequence. The method and tool are illustrated in detail on an asymmetric producer-consumer monitor. Their application to testing over 20 concurrent components, a number of which are sourced from industry and were found to contain faults, is presented and discussed.

API documentation with executable examples

The rise of component-based software development has created an urgent need for effective application program interface (API) documentation. Experience has shown that it is hard to create precise and readable documentation. Prose documentation can provide a good overview but lacks precision. Formal methods offer precision but the resulting documentation is expensive to develop. Worse, few developers have the skill or inclination to read formal documentation. We present a pragmatic solution to the problem of API documentation. We augment the prose documentation with executable test cases, including expected outputs, and use the prose plus the test cases as the documentation. With appropriate tool support, the test cases are easy to develop and read. Such test cases constitute a completely formal, albeit partial, specification of input/output behavior. Equally important, consistency between code and documentation is demonstrated by running the test cases. This approach provides an attractive bridge between formal and informal documentation. We also present a tool that supports compact and readable test cases; and generation of test drivers and documentation, and illustrate the approach with detailed case studies. (C) 2002 Elsevier Science Inc. All rights reserved.

Genetic algorithms in statistical tolerancing

An important aspect in manufacturing design is the distribution of geometrical tolerances so that an assembly functions with given probability, while minimising the manufacturing cost. This requires a complex search over a multidimensional domain, much of which leads to infeasible solutions and which can have many local minima. As well, Monte-Carlo methods are often required to determine the probability that the assembly functions as designed. This paper describes a genetic algorithm for carrying out this search and successfully applies it to two specific mechanical designs, enabling comparisons of a new statistical tolerancing design method with existing methods. (C) 2003 Elsevier Ltd. All rights reserved.

Modelling inpatient length of stay by a hierarchical mixture regression via the EM algorithm

The modelling of inpatient length of stay (LOS) has important implications in health care studies. Finite mixture distributions are usually used to model the heterogeneous LOS distribution, due to a certain proportion of patients sustaining-a longer stay. However, the morbidity data are collected from hospitals, observations clustered within the same hospital are often correlated. The generalized linear mixed model approach is adopted to accommodate the inherent correlation via unobservable random effects. An EM algorithm is developed to obtain residual maximum quasi-likelihood estimation. The proposed hierarchical mixture regression approach enables the identification and assessment of factors influencing the long-stay proportion and the LOS for the long-stay patient subgroup. A neonatal LOS data set is used for illustration, (C) 2003 Elsevier Science Ltd. All rights reserved.

Dynamic multi-resolution spatial object derivation for mobile and WWW applications

Online geographic information systems provide the means to extract a subset of desired spatial information from a larger remote repository. Data retrieved representing real-world geographic phenomena are then manipulated to suit the specific needs of an end-user. Often this extraction requires the derivation of representations of objects specific to a particular resolution or scale from a single original stored version. Currently standard spatial data handling techniques cannot support the multi-resolution representation of such features in a database. In this paper a methodology to store and retrieve versions of spatial objects at, different resolutions with respect to scale using standard database primitives and SQL is presented. The technique involves heavy fragmentation of spatial features that allows dynamic simplification into scale-specific object representations customised to the display resolution of the end-user's device. Experimental results comparing the new approach to traditional R-Tree indexing and external object simplification reveal the former performs notably better for mobile and WWW applications where client-side resources are limited and retrieved data loads are kept relatively small.

A framework and tool support for the systematic testing of model-based specifications

Formal specifications can precisely and unambiguously define the required behavior of a software system or component. However, formal specifications are complex artifacts that need to be verified to ensure that they are consistent, complete, and validated against the requirements. Specification testing or animation tools exist to assist with this by allowing the specifier to interpret or execute the specification. However, currently little is known about how to do this effectively. This article presents a framework and tool support for the systematic testing of formal, model-based specifications. Several important generic properties that should be satisfied by model-based specifications are first identified. Following the idea of mutation analysis, we then use variants or mutants of the specification to check that these properties are satisfied. The framework also allows the specifier to test application-specific properties. All properties are tested for a range of states that are defined by the tester in the form of a testgraph, which is a directed graph that partially models the states and transitions of the specification being tested. Tool support is provided for the generation of the mutants, for automatically traversing the testgraph and executing the test cases, and for reporting any errors. The framework is demonstrated on a small specification and its application to three larger specifications is discussed. Experience indicates that the framework can be used effectively to test small to medium-sized specifications and that it can reveal a significant number of problems in these specifications.

Applying ontologies to business and systems modelling techniques and perspectives: Lessons learned

For many years in the area of business systems analysis and design, practitioners and researchers alike have been searching for some comprehensive basis on which to evaluate, compare, and engineer techniques that are promoted for use in the modelling of systems' requirements. To date, while many frameworks, factors, and facets have been forthcoming, none appear to be based on a sound theory. In light of this dilemma, over the last 10 years, attention has been devoted by researchers to the use of ontology to provide some theoretical basis for the advancement of the business systems modelling discipline. This paper outlines how we have used a particular ontology for this purpose over the last five years. In particular we have learned that the understandability and the applicability of the selected ontology must be clear for IS professionals, the results of any ontological evaluation must be tempered by economic efficiency considerations of the stakeholders involved, and ontologies may have to be focused for the business purpose and type of user involved in the modelling situation.