optimality conditions via norm scalarization in vector optimization an orthogonality concept in normed spaces is defined and used to obtain sufficient and necessary conditions for efficiency weak efficiency and proper efficiency via norm scalarization for the case of general nonpointed cones as an application a control approximation problem with a nonpointed ordering cone is considered

a fuzzy reliability assessment of basic events of fault trees through qualitative data processing abstract probabilistic approaches are common in the analysis of reliability of complex engineering systems however they require quantitative historical failure data for determining reliability characteristics in many real world areas such as e g nuclear engineering quantitative historical failure data are unavailable or become inadequate and only qualitative data such as expert opinions which are described in linguistic terms can be collected and then used to assess system reliability moreover experts are more comfortable justifying event failure likelihood using linguistic terms which capture uncertainties rather than by expressing judgments in a quantitative manner new techniques are therefore needed that will help construct models of reliability of complex engineering system without being confined to quantitative historical failure data the objective of this study is to develop a fuzzy reliability algorithm to effectively generate basic event failure probabilities without reliance on quantitative historical failure data through qualitative data processing the originality of this study comes with an introduction of linguistic values articulated in terms of component failure possibilities in order to qualitatively assess basic event failure possibilities treated as inputs of the proposed model and generate basic event failure probabilities as its outputs to demonstrate the feasibility and effectiveness of the proposed algorithm actual basic event failure probabilities collected from nuclear power plant operating experiences are compared with the failure probabilities generated by the algorithm the results demonstrate that the proposed fuzzy reliability algorithm arises as a suitable alternative for the probabilistic reliability approach when quantitative historical failure data are unavailable

steady state shear bands in thermo plasticity i vanishing yield stress abstract this paper concerns the construction and stability properties of steady state solutions of a system of partial differential equations that model simple shearing of a slab of thermo plastic material the class of constitutive laws that give rise to a variational formulation of the steady state problem is identified and a phase plane argument is used to construct time independent solutions that may be interpreted as steady state shear bands our variational framework captures several commonly adopted constitutive laws techniques from bifurcation theory for variational problems arc applied to classify stable and unstable solutions merely in terms of the shape of the solution branch in the distinguished bifurcation diagram that arises when average strain rate is plotted against shearing force there are two novel features to our approach first the two problems in which loading is imposed by either stress boundary conditions or velocity boundary conditions are treated by one analysis and the differing stability properties of solutions are explained naturally second the stability analysis is based upon a symmetric eigenvalue problem arising from the appropriate second variation the link with dynamic behavior is made through a lyapunov functional and the linearized dynamics are not considered directly provided the proper existence theorems for the time dependent problem can be proven or are assumed our lyapunov approach yields the appropriate nonlinear dynamic stability properties of steady state solutions in this paper we shall consider the case in which vanishing strain rate implies zero stress i e there is no residual or yield stress present in our model but our analysis can be extended to encompass constitutive laws modelling nonzero yield stress

a sum of disjoint products algorithm for reliability evaluation of flow networks abstract this paper proposes a revised algorithm to evaluate the unreliability of a flow network in which capacities of arcs are assumed to be independent binary valued random variables such a problem is a generalization of the well known np hard two terminal reliability problem which evaluates the probability of the connection from a source node to a sink node the proposed algorithm is motivated by rueger both in a branching manner the proposed and rueger s algorithms express the system unreliability in terms of a sum of disjoint products where each product is derived from a branching condition b via a d cutb in o m log m time and via the first system failure under b in o d n2 2m time respectively where d is the demand n and m are the numbers of nodes and arcs in the network respectively experimental experiences show that the proposed algorithm drastically reduces the execution time and performs more robustly when compare to rueger s algorithm but the number of disjoint products derived by it will be a little bit larger

a fuzzy universal generating function based method for the reliability evaluation of series systems with performance sharing between adjacent units under parametric uncertainty abstract this paper considers fuzzy multi state systems msss with performance sharing between adjacent units in which each fuzzy multi state unit has a random performance and a random demand if the performance of a unit exceeds its individual demand performance demand its surplus performance can be transmitted to its adjacent unit that experiences performance deficiency performance

use of fuzzy set theory for level i studies in probabilistic risk assessment at a post chernobyl conference on probabilistic safety assessment and risk management psa 87 held in september 1987 the inadequacies of the current probabilistic risk assessment psa came into sharp focus highlighting the importance of improvements in the current psa professor rasmussen a pioneer in the psa methodology made a strong plea for reduction of rather large uncertainties in the results of current psa obviously amongst the ways to achieve this one of the approaches would be to encourage collection and use of accurate failure data however as the state of affairs is a better alternative would be to develop a methodology which could handle imprecision of data and uncertainties of models which are existence in the current psa fuzzy set theory fst provides a natural framework to achieve the above goal and therefore the present paper is intended to emphasize and explore the possibility of the use of such a theory to develop a methodology which is computationally simple and easy to use in the quantitative assessment of failure probability of catastrophic events in psa particularly in level i studies some illustrative examples are provided to demonstrate the feasibility and effectiveness of such an approach it is demonstrated that a general purpose computer code can be developed without much difficulty to recast the pra studies to incorporate fuzzy probabilities

the method of generalized generating sequences abstract the method of generalized generating sequences ggs is based on some modifications of the standard generating function this method is convenient for a computerized calculation of enumeration problems that arise in discrete optimization this method will be described below in the context of optimal redundancy problems

fuzzy system reliability analysis by interval of confidence abstract the use of fuzzy number over interval of confidence instead of probability and possibilitic considerations for evaluating the range value and interval of the fuzzy reliability is proposed this approach of evaluating fuzzy system reliability by interval arithmetic and cuts has a considerable advantage we can calculate reliability problems easily by the use of derive and mathcad packages through theoretical analysis an illustrative example and computational results we show that the proposed approach is more general and simplified

finite element approximation of an evolution problem modeling shear band formation abstract an error analysis is provided for the spatial approximation by the finite element method of a nonlinear time dependent problem which models the antiplane shear deformations of a thermoplastic material this problem consists of a system of two coupled partial differential equations with velocity and temperature unknowns optimal order error estimates in the l 2 norm are given for each of these

computation of several power indices by generating functions abstract in this paper we propose methods to compute the deegan packel the public good and the shift power indices by generating functions for the particular case of weighted voting games furthermore we define a new power index which combines the ideas of the shift and the deegan packel power indices and also propose a method to compute it with generating functions we conclude by some comments about the complexity to compute these power indices

distribution and reliability evaluation of max flow in dynamic multi state flow networks abstract in this article each arc in multi state flow networks in addition to multi valued capacities and associated operation probabilities is weighted with a transit time as a result the value of max flow from source to sink within specified time horizon is multi valued existing literature evaluates the transit time integrated reliability with a restriction that data is transmitted through k disjoint minimal paths this article considers the same reliability problem however the transmission of data is extended from k disjoint minimal paths to a flow that includes all disjoint and non disjoint minimal paths simultaneously this paper presents an algorithm to evaluate the probability distribution of the values of dynamic max flow the expectation of dynamic max flow as a representation of the distribution can be induced directly the transit time integrated reliability r d t is then computed which is the probability that at least d unit of data can be transmitted from source to sink within time horizon t this study is the first that discusses transit time integrated reliability in terms of flow finally computational experiments are conducted on a benchmark network to explore the properties of the proposed algorithms

fuzzy reliability assessment of systems with multiple dependent competing degradation processes components are often subject to multiple competing degradation processes for multicomponent systems the degradation dependence within one component or and among components need to be considered physics based models and multistate models are often used for component degradation processes particularly when statistical data are limited in this paper we treat dependence between degradation processes within a piecewise deterministic markov process pdmp modeling framework epistemic subjective uncertainty can arise due to the incomplete or imprecise knowledge about the degradation processes and the governing parameters to take this into account we describe the parameters of the pdmp model as fuzzy numbers then we extend the finite volume method to quantify the fuzzy reliability of the system the proposed method is tested on one subsystem of the residual heat removal system of a nuclear power plant and a comparison is offered with a monte carlo simulation solution the results show that our method can be most efficient

fuzzy system reliability analysis using fuzzy number arithmetic operations abstract this paper presents a new method to analyze fuzzy system reliability using fuzzy number arithmetic operations where the reliability of each system component is represented by a triangular fuzzy number because the proposed method uses simplified fuzzy arithmetic operations of fuzzy numbers rather than the complicated interval arithmetic operations of fuzzy numbers mentioned by cheng and mon in fuzzy sets and systems 56 1993 29 35 or the complicated extended algebraic operations of fuzzy numbers mentioned by singer in fuzzy sets and systems 34 1990 145 155 its execution is faster than the ones presented by cheng and mon and singer

a fuzzy set approach to fault tree and reliability analysis abstract conventional fault tree and reliability analysis does not give a picture concerning the tolerances of the probability values of hazards to overcome this shortcoming the relative frequencies of the basic envents are considered as fuzzy numbers using standard approximations for the membership functions n ary possibilistic and or and neg operators are derived allowing a straightforward evaluation of the frequencies of hazard events in complex systems simultaneously with their tolerances the paper shows the use of these operators for constructing possibilistic fault trees the use of the method for numerical calculation is demonstrated on a real like safety problem

numerical methods for a model for compressible miscible displacement in porous media a nonlinear parabolic system is derived to describe compressible miscible displace ment in a porous medium the system is consistent with the usual model for incompressible miscible displacement two finite element procedures are introduced to approximate the concentration of one of the fluids and the pressure of the mixture the concentration is treated by a galerkin method in both procedures while the pressure is treated by either a lalerkin method or by a parabolic mixed finite element method optimal order estimates in l2 and essentially optimal order estimates in lx are derived for the errors in the approximate solutions for both methods introduction we shall consider the single phase miscible displacement of one compressible fluid by another in a porous medium under the assumptions that no volume change results from the mixing of the components and that a pressure den sity relation exists for each component in a form that is independent of the mixing these equations of state will imply that the fluids are in the liquid state our model will represent a direct generalization of the model 3 4 7 that has been treated extensively for incompressible miscible displacement the reservoir s will be taken to be of unit thickness and will be identified with a bounded domain in r2 we shall omit gravitational terms for simplicity of exposi tion no significant mathematical questions arise when the lower order terms are included

practical sequential bounds for approximating two terminal reliability with increasing emphases on better and more reliable services network systems have incorporated reliability analysis as an integral part in their planning design and operation this article first presents a simple exact decomposition algorithm for computing the np hard two terminal reliability which measures the probability of successful communication from specified source node to sink node in the network then a practical bounding algorithm which is indispensable for large networks is presented by modifying the exact algorithm for obtaining sequential lower and upper bounds on two terminal reliability based on randomly generated large networks computational experiments are conducted to compare the proposed algorithm to the well known and widely used edge packing approximation model and to explore the performance of the proposed bounding algorithm computational results reveal that the proposed bounding algorithm is superior to the edge packing model and the trade off of accuracy for execution time ensures that an exact difference between upper and lower bounds on two terminal reliability can be obtained within an acceptable time

higher order radial derivatives and optimality conditions in nonsmooth vector optimization abstract we propose notions of higher order outer and inner radial derivatives of set valued maps and obtain main calculus rules some direct applications of these rules in proving optimality conditions for particular optimization problems are provided then we establish higher order optimality necessary conditions and sufficient ones for a general set valued vector optimization problem with inequality constraints a number of examples illustrate both the calculus rules and the optimality conditions in particular they explain some advantages of our results over earlier existing ones and why we need higher order radial derivatives

degrees of efficiency and degrees of minimality in this work we characterize different types of solutions of a vector optimization problem by means of a scalarization procedure usually different scalarizing functions are used in order to obtain the various solutions of the vector problem here we consider different kinds of solutions of the same scalarized problem our results allow us to establish a parallelism between the solutions of the scalarized problem and the various efficient frontiers stronger solution concepts of the scalar problem correspond to more restrictive notions of efficiency besides the usual notions of weakly efficient and efficient points which are characterized as global and strict global solutions of the scalarized problem we also consider some restricted notions of efficiency such as strict and proper efficiency which are characterized as tikhonov well posed minima and sharp minima for the scalarized problem

nonparametric predictive reliability of series of voting systems abstract nonparametric predictive inference npi for system reliability reflects the dependence of reliabilities of similar components due to limited knowledge from testing npi has recently been presented for reliability of a single voting system consisting of multiple types of components the components are all assumed to play the same role within the system but with regard to their reliability components of different types are assumed to be independent the information from tests is available per type of component this paper presents npi for systems with subsystems in a series structure where all subsystems are voting systems and components of the same type can be in different subsystems as npi uses only few modelling assumptions system reliability is quantified by lower and upper probabilities reflecting the limited information in the test data the results are illustrated by examples which also illustrate important aspects of redundancy and diversity for system reliability

reliability analysis and optimization of weighted voting systems with continuous states input weighted voting systems are widely used in many practical fields such as target detection human organization pattern recognition etc in this paper a new model for weighted voting systems with continuous state inputs is formulated we derive the analytical expression for the reliability of the entire system under certain distribution assumptions a more general monte carlo algorithm is also given to numerically analyze the model and evaluate the reliability this paper further proposes a reliability optimization problem of weighted voting systems under cost constraints a genetic algorithm is introduced and applied as the optimization technique for the model formulated a numerical example is then presented to illustrate the ideas

a dynamic bounding algorithm for approximating multi state two terminal reliability abstract this paper modifies jane and laih s 2008 exact and direct algorithm to provide sequences of upper bounds and lower bounds that converge to the np hard multi state two terminal reliability advantages of the modified algorithm include 1 it does not require a priori the lower and or upper boundary points of the network 2 it derives a series of increasing lower bounds and a series of decreasing upper bounds simultaneously guaranteed to enclose the exact reliability value and 3 trade off between accuracy and execution time can be made to ensure an exact difference between the upper and lower bounds within an acceptable time examples are analyzed to illustrate the bounding algorithm and to compare the bounding algorithm with existing algorithms computational experiments on a large network are conducted to realize the performance of the bounding algorithm

fuzzy universal generating functions for multi state system reliability assessment the paper considers a multi state system mss where performance rates or and corresponding state probabilities are presented as fuzzy values in many real world msss it is difficult to estimate precise values of performance rates and their probabilities because of two main reasons the first reason is inaccuracy and insufficiency of data the second one is based on the fact that msss are often used as the approximation for continuous state systems in order to simplify computational burden to overcome these deficiencies performance rates levels or and corresponding probabilities are considered as fuzzy values in this paper the fuzzy universal generating function fugf is developed to extend the universal generating function with crisp sets the composition operators are extended for fugfs and introduced in more general forms based on this a special technique for reliability assessment of such msss is developed illustrative examples are presented to demonstrate the technique

on advanced computing with words using the generalized extension principle for type 1 fuzzy sets in this paper we propose and demonstrate an effective methodology for implementing the generalized extension principle to solve advanced computing with words acww problems such problems involve implicit assignments of linguistic truth probability and possibility to begin we establish the vocabularies of the words involved in the problems and then collect data from subjects about the words after which fuzzy set models for the words are obtained by using the interval approach ia or the enhanced interval approach eia next the solutions of the acww problems which involve the fuzzy set models of the words are formulated using the generalized extension principle because the solutions to those problems involve complicated functional optimization problems that cannot be solved analytically we then develop a numerical method for their solution finally the resulting fuzzy set solutions are decoded into natural language words using jaccard s similarity measure we explain how acww problems can solve some potential prototype engineering problems and connect the methodology of this paper with perceptual computing

reliability and covariance estimation of weighted k out of n multi state systems abstract in the literature of reliability engineering reliability of the weighted k out of n system can be calculated using component reliability based on the structure function the calculation usually assumes that the true component reliability is completely known however this is not the case in practical applications instead component reliability has to be estimated using empirical sample data uncertainty arises during this estimation process and propagates to the system level this paper studies the propagation mechanism of estimation uncertainty through the universal generating function method equations of the complete solution including the unbiased system reliability estimator and the corresponding unbiased covariance estimator are derived this is a unified approach it can be applied to weighted k out of n systems with multi state components to weighted k out of n systems with binary components and to simple series and parallel systems it may also serve as building blocks to derive estimators of system reliability and uncertainty measures for more complicated systems

optimum attributes component test plans for k out of n f weibull systems using prior information abstract assuming that the proportion defective in a production process p is variable and the component lifetimes are weibull distributed integer nonlinear programming problems are formulated and solved in order to determine the optimum component inspection scheme by attributes for k out of n f system reliability demonstration using available prior knowledge a limited beta prior model is adopted to reflect the random fluctuations on p the required quantity of components to test and the permissible number of component failures up to a specified censoring time are found by solving a minimisation problem with nonlinear constraints which are related to the tolerable average producer and consumer risks first order taylor polynomials of the operating characteristic function are used to derive a quite accurate approximate solution lower and upper bounds are also deduced optimal solutions are usually robust to small variations in the weibull parameters and prior information existing technical knowledge and experience are shown to be of great practical value in designing optimal sampling plans for lot acceptance purposes the proposed approach generalises the classical viewpoint to those cases in which appreciable prior information on the fraction of defective systems exists and also allows the analyst to determine the acceptability of a k out of n f system before assembly and to limit the range of p moreover the practitioners may attain substantial savings in sample size and improved assessments of the true producer and consumer risks a 4 out of 5 f system of independent water pumps for cooling a reactor is considered to illustrate the suggested component test plans

a model for two coupled turbulent fluids part ii numerical analysis of a spectral discretization we consider a system of equations that models the stationary flow of two immiscible turbulent fluids on adjacent subdomains the equations are coupled by nonlinear boundary conditions on the interface which is here a fixed given surface we propose a spectral discretization of this problem and perform its numerical analysis the convergence of the method is proven in the two dimensional case together with optimal error estimates

optimality conditions under relaxed quasiconvexity assumptions using star and adjusted subdifferentials a set constrained optimization problem and a mathematical programming problem are considered we assume that the sublevel sets of the involving functions are convex only at the point under question and hence these functions are not assumed quasiconvex using the two star subdifferentials and the adjusted subdifferential we establish optimality conditions for usual minima and strict minima our results contain and improve some recent ones in the literature examples are provided to explain the advantages of each of our results

ritz volterra projections to finite element spaces and applications to integrodifferential and related equations the object of this paper is to investigate the convergence of finite element approximations to solutions of parabolic and hyperbolic integrodifferential equations and also of equations of sobolev and viscoelasticity type the concept of ritz volterra projection will be seen to unify much of the analysis for the different types of problems optimal order error estimates are obtained in l p for 2 leqq p infty and almost optimal order pointwise results given

on the numerical approximation of an evolution problem in nonlinear viscoelasticity abstract an error analysis is furnished for the spatial approximation via the finite element method of certain nonlinear time dependent problems emanating in the theory of viscoelastic solids numerical examples are given first for a model equation and then for numerical equilibrium solutions in cases of a nonconvex double well potential and a convex potential the latter derived from the nonconvex one via relaxation by an equal area construction

repairable consecutive k out of n f system with fuzzy states in this paper we study a repairable consecutive k out of n f system with fuzzy states the maintenance of the system is carried out by r repairmen or repair facilities the system is either circular or linear it is assumed that the working time and the repair time of each component in the system are both exponentially distributed and every component after repair is as same as new each component is classified as either a key component or an ordinary one according to its priority role to the system s repair when the system displays a gradual degradation of its performance its reliability is then analyzed in terms of fuzzy failure and success states the difference between fuzzy reliability theory and the conventional reliability theory is highlighted

fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context abstract conventional reliability theory is based on the binary state assumption and the probability assumption namely 1 the systems are precisely defined as functioning or failed 2 the system behavior is fully characterized in the context of probability measures however the probability assumption is no longer reasonable in the case of small size of samples since the term probability stems from the sample generality in this way possibility measures should be used to characterize the sample particularity in this paper the binary state assumption is reserved and the possibility assumption is taken in place of the probability assumption thus a concept of fuzzy reliability i e posbist reliability is introduced and a theory of fuzzy reliability i e posbist reliability theory is established various conclusions which are contrary to statements in conventional reliability theory i e probist reliability theory are then drawn

a general formal approach for fuzzy reliability analysis in the possibility context abstract in this paper we focus on the fuzzy reliability analysis in the posbist reliability theory in accordance with this theory the system failure state is defined precisely and the system failure and repair behaviour is fully characterized in the context of possibility measures to formalize the reliability analysis in the posbist theory we propose a general approach on the basis of a system of functional equations the solution of the system allows us to obtain fuzzy reliability characteristics of the arbitrary repairable and unrepairable systems to illustrate the construction and application of the system of functional equations various examples are given

merit functions in vector optimization we study the weak domination property and weakly efficient solutions in vector optimization problems in particular scalarization of these problems is obtained by virtue of some suitable merit functions some natural conditions to ensure the existence of error bounds for merit functions are also given