joint reliability and weighted importance measures of a k out of n system with random weights for components abstract in this paper the joint importance of two components in a k out of n system with random weights for components is studied rahmani et al 2016 introduced the weighted importance wi measure corresponding to component i and investigated its properties we generalize this measure for two components i and j and its relation with joint reliability importance is studied finally the stochastic behavior of this measure is discussed

identification of an infinite dimensional parameter for stochastic diffusion equations this paper concerns the control of diffusions under partial observations part i studies the control of the signal process dx t b t x t u t dt sigma t x t u t db t when the observation is dy t h t x t dt dw t and when the objective is to maximize a reward function e int r t k s x s u s ds g x t the existence of an optimal relaxed control is proved part ii studies the separated problem and proves the existence of an optimal markovian filter then the authors compare the two problems and prove under mild conditions that the value functions for the two problems are equal

optimal control for partially observed diffusions stochastic control problems are considered in which a state process x t and an observation process y t are governed by ito sense stochastic differential equations driven by independent brownian motions the control u t enters linearly in the dynamics of x t a separated control problem is introduced in which the state at any time t is a measure lambda t representing an unnormalized conditional distribution for x t given y s u s for s leqq t the method depends on introducing a pathwise version of lambda t which depends continuously on observation and control trajectories y u existence of an optimal control is obtained in a suitable class larger than the usual class of controls admissible in the strict sense that u t is measurable on the sigma algebra mathcal f t y generated by observations y s s leqq t the dynamics of lambda t are studied using a method of forward and backward partial differential equations under a suitable nondegeneracy condition the m

dynamic modeling of general three state k out of n g systems permanent based computational results this paper is concerned with dynamic reliability analysis of three state k out of n g systems it is assumed that the components and the systems can be in three states perfect functioning partial performance and complete failure using the concept of permanent we study marginal and joint survival functions for the lifetime of two different three state k out of n g systems that consist of independent and nonidentical components illustrative examples are also provided for the components which follow the markov degradation process

k1 k2 km out of n system and its reliability abstract this paper is concerned with a system consisting of multiple types of components and having k 1 k 2 k m out of n structure the k 1 k 2 k m out of n system is a system consisting of n i components of type i i 1 2 m and functions if at least k 1 components of type 1 k 2 components of type 2 k m components of type m work n i 1 n n i the exact and approximate expressions are obtained for the survival function of the system under concern the weighted k 1 k 2 k m out of n system is also defined and studied this weighted model is applied to evaluate the wind power system that consists of two wind plants

on average cost stopping time problems we consider the stopping time problems whose costs are given by time average forms a generalization of the gittins index we show the existence of the optimal solutions and give their approximation to these stopping time problems

probabilistic analysis of mean field games the purpose of this paper is to provide a complete probabilistic analysis of a large class of stochastic differential games with mean field interactions we implement the mean field game strategy developed analytically by lasry and lions in a purely probabilistic framework relying on tailor made forms of the stochastic maximum principle while we assume that the state dynamics are affine in the states and the controls and the costs are convex our assumptions on the nature of the dependence of all the coefficients upon the statistical distribution of the states of the individual players remains of a rather general nature our probabilistic approach calls for the solution of systems of forward backward stochastic differential equations of a mckean vlasov type for which no existence result is known and for which we prove existence and regularity of the corresponding value function finally we prove that a solution of the mean field game problem as formulated by lasry and lions does indeed provide appr

stress strength reliability analysis of system with multiple types of components using survival signature abstract in this paper we study the estimation for stress strength reliability of the system with multiple types of components based on survival signature in the situation that different types of components are subjected to different types of random stresses the maximum likelihood estimator maximum spacing estimator bootstrap p confidence interval two point estimators and generalized confidence interval using generalized pivotal quantity for system stress strength reliability are derived under the assumption that the stresses and strengths variables follow the gompertz distributions with common or unequal scale parameters additionally when the stresses and strengths variables follow the gompertz distributions with unequal scale parameters a modified generalized confidence interval for the system stress strength reliability based on the fisher z transformation is also proposed in the situation that the system is subjected to the common stress the above point estimators and confidence intervals for the system stress strength reliability are also developed monte carlo simulations are performed to compare the performance of these point estimators and confidence intervals a real data analysis is presented for an illustration of the findings

singular stochastic control and optimal stopping with partial information of ito levy processes we study partial information possibly non markovian singular stochastic control of ito levy processes and obtain general maximum principles the results are used to find connections between singular stochastic control reflected backward stochastic differential equations and optimal stopping in the partial information case as an application we give an explicit solution to a class of optimal stopping problems with finite horizon and partial information

fibered threefolds and lang vojta s conjecture over function fields using the techniques introduced by corvaja and zannier in 2008 we solve the non split case of the geometric lang vojta conjecture for affine surfaces isomorphic to the complement of a conic and two lines in the projective plane in this situation we deal with sections of an affine threefold fibered over a curve whose boundary in the natural projective completion is a quartic bundle over the base whose fibers have three irreducible components we prove that the image of each section has bounded degree in terms of the euler characteristic of the base curve

stress strength reliability analysis of multi state system based on generalized survival signature abstract the stress strength model has been widely used in reliability design of system in the traditional stress strength reliability theory the system and each component are assumed to be only in one of two possible states being either working or failed and the notion of stress strength reliability is the probability that the strength is larger than the stress in this paper we study the stress strength reliability of multi state system based on generalized survival signature it is supposed that the state of multi state system is defined by using the ratio between strength and stress random variables the definitions of generalized survival signature for a certain class of multi state systems with multi state components in both discrete and continuous cases are given in addition the expressions of stress strength reliability in both discrete and continuous situations are derived in the case of continuous multi state system it is assumed that the random strength and stress are both from the weibull distributions with different scale parameters and the two different continuous kernel functions are pareto and generalized half logistic distribution functions respectively based on the assumptions the stress strength reliability is estimated by using both classical and bayesian statistical theories the uniformly minimum variance unbiased estimator and maximum likelihood estimator for the stress strength reliability of the continuous multi state system are derived under the squared error loss function the exact expression of bayes estimator for the stress strength reliability of the continuous multi state system is developed by using gauss hypergeometric function finally the monte carlo simulations are performed to compare the performances of the proposed stress strength reliability estimators and a real data set is also analyzed for an illustration of the findings

algebraic hyperbolicity of ramified covers of mathbb g 2_m and integrap points on affine subsets of mathbb p _2 let x be a smooth affine surface x to mathbb g 2 m be a finite morphism we study the affine curves on x with bounded genus and number of points at infinity obtaining bounds for their degree in terms of euler characteristic a typical example where these bounds hold is represented by the complement of a three component curve in the projective plane of total degree at least 4 the corresponding results may be interpreted as bounding the height of integral points on x over a function field in the language of diophantine equations our results may be rephrased in terms of bounding the height of the solutions of f u v y 0 with u v y over a function field u v s units it turns out that all of this contain some cases of a strong version of a conjecture of vojta over function fields in the split case moreover our method would apply also to the nonsplit case we remark that special cases of our results in the holomorphic context were studied by m green already in the seventies and recently in greater generality by noguchi winkelmann and yamanoi however the algebraic context was left open and seems not to fall in the existing techniques

the relaxed general maximum principle for singular optimal control of diffusions in this paper we study optimality in stochastic control problems where the state process is a stochastic differential equation sde and the control variable has two components the first being abs

a separation principle for partially observed control of singular stochastic processes abstract the analysis of partially observed stochastic control problems often replaces the unknown state process with its conditional distribution given the observations this technique rewrites the dynamics in terms of knowable processes whose costs coincide with the original processes this paper considers stochastic processes having singular behavior and presents an approach which separates the determination of the optimal control from the task of estimating the conditional distribution of the unknown process it involves using a martingale problem characterization for the dynamics followed by a further characterization using occupation measures this final characterization forms the basis for an equivalent linear programming formulation of the problem over the space of occupation measures

stress strength reliability in the presence of fuzziness this paper investigates the stress strength reliability in the presence of fuzziness the fuzzy membership function is defined as a function of the difference between stress and strength values and the fuzzy reliability of single unit and multicomponent systems are calculated the inclusion of fuzziness in the stress strength interference enables the user to make more sensitive analysis illustrations are presented for various stress and strength distributions

scheduling continuous time kalman filters a set of n independent gaussian linear time in variant systems is observed by m sensors whose task is to provide a steady state causal estimate minimizing the mean square error on the system states subject to additional measurement costs the sensors can switch between systems instantaneously and there are additional resource constraints for example on the number of sensors that can observe a given system simultaneously we first derive a tractable relaxation of the problem which provides a bound on the achievable performance this bound can be computed by solving a convex program involving linear matrix inequalities and moreover this program can be decomposed into coupled smaller dimensional problems in the scalar case with identical sensors we give an analytical expression of an index policy proposed in a more general context by whittle in the general case we develop open loop periodic switching policies whose performance matches the bound arbitrarily closely

optimality in accelerated life tests we formulate a stochastic control problem arising from the optimal design of accelerated life tests the model is obtained in a natural way in the setup of point processes the cost functional depends on the total number of items under test at time t the observed number of items failed up to time t and the stress level applied to the items under test at time t the optimal policy minimizing the cost functional is characterized via the dynamic programming equation after a further specification of the model we prove that the solution is of bang bang type in some specific cases we also prove that the control problem is equivalent to an optimal stopping problem this amounts to simply running the test with the number of items and the stress level at their highest available value up to the exit time of the state process from a given region in this special case we exhibit an explicit solution and give a criterion in order to decide whether to let the experiment run or to stop it

the nonstochastic multiarmed bandit problem in the multiarmed bandit problem a gambler must decide which arm of k nonidentical slot machines to play in a sequence of trials so as to maximize his reward this classical problem has received much attention because of the simple model it provides of the trade off between exploration trying out each arm to find the best one and exploitation playing the arm believed to give the best payoff past solutions for the bandit problem have almost always relied on assumptions about the statistics of the slot machines in this work we make no statistical assumptions whatsoever about the nature of the process generating the payoffs of the slot machines we give a solution to the bandit problem in which an adversary rather than a well behaved stochastic process has complete control over the payoffs in a sequence of t plays we prove that the per round payoff of our algorithm approaches that of the best arm at the rate o t 1 2 we show by a matching lower bound that this is the best possible we also prove that our algorithm approaches the per round payoff of any set of strategies at a similar rate if the best strategy is chosen from a pool of n strategies then our algorithm approaches the per round payoff of the strategy at the rate o log n1 2 t 1 2 finally we apply our results to the problem of playing an unknown repeated matrix game we show that our algorithm approaches the minimax payoff of the unknown game at the rate o t 1 2

reliability of coherent systems with a single cold standby component in this paper the influence of a cold standby component on a coherent system is studied a method for computing the system reliability of coherent systems with a cold standby component based on signature is presented numerical examples are presented reliability and mean time to failure of different systems are computed

on the existence of optimal controls the optimal control problem where the state is governed by an ito stochastic differential equation possibly just an ordinary differential equation is formulated in martingale terms under a coercivity condition which is weaker than compactness of the control set a convexity condition and mild continuity hypotheses on the data it is shown by the direct method that optimal controls exist hard and soft constraints are allowed in the absence of soft constraints it is shown that there exists an optimal control that is a function only of the present time and state i e the synthesis problem has a solution the main tool here is krylov s markovian selection theorem

singular optimal stochastic controls i existence we apply the compactification method to study the control problem where the state is governed by an ito stochastic differential equation allowing both classical and singular control the problem is reformulated as a martingale problem on an appropriate canonical space after the relaxed form of the classical control is introduced under some mild continuity hypotheses on the data it is shown by purely probabilistic arguments that an optimal control for the problem exists the value function is shown to be borel measurable

importance of components in k out of n system with components having random weights the purpose of this paper is to study the component importance in k out of n system with components having random weights the system works if at least k components work and the total weight of all working components is above the required level c a new measure of component importance called weighted importance for such a system is introduced and its relation with birnbaum reliability measure of importance is studied it is shown that the larger weight stochastically implies the larger weighted measure of importance it is also shown that if two components are identically distributed then the larger weight stochastically implies the larger birnbaum reliability measure of importance finally it is proved that if the weight of a component is stochastically increased then the weighted and birnbaum reliability measures of importance are increased accordingly

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

a general stochastic maximum principle for optimal control problems the maximum principle for nonlinear stochastic optimal control problems in the general case is proved the control domain need not be convex and the diffusion coefficient can contain a control variable

on the comparison of reliability experiments based on the convolution order in this article we study the comparison of experiments in system reliability theory when the component lifetimes are independent and identically distributed random variables that have a common two parameter exponential distribution with a location parameter for this purpose we define a new stochastic order which we call the convolution order and study some basic properties of it we then focus our attention on the family of distribution functions that are mixtures of distributions of partial sums of independent exponential random variables and derive results that identify several conditions under which members of this family are ordered in the convolution stochastic order we apply the results to order lifetimes of coherent systems and as a consequence we obtain information inequalities among various lifetimes of coherent systems we find situations wherein high reliability decreases statistical information

continuous multi armed bandits and multiparameter processes a general framework is proposed for continuous time dynamic allocation models of a scarce resource among competing projects the allocation model is formulated as a multi armed bandit model and solved as a control problem of a multiparameter process in contrast to discrete time bandits where only one arm can be pulled at a time the continuous time bandit must allow simultaneous pulls the multiparameter approach allows a strong solution of diffusion type bandits here the main problem is to define precisely how to switch among arms and the solution involves local times

an approximation method for controlled discrete jump processes under partial observations the paper is concerned with control and filtering of a discrete jump markov process when only the total number of jumps is observed a partially observable control problem is considered and equivalence between this problem and the separated one is proved a technique to approximate the value function under some suitable assumptions is presented

martingale measures and stochastic calculus in this paper martingale measures introduced by j b walsh are investigated we prove with techniques of stochastic calculus that each continuous orthogonal martingale measure is the time changed image martingale measure of a white noise

unique characterization of conditional distributions in nonlinear filtering on definit un probleme de martingale filtree pour un generateur a et on montre etant donne des hypotheses appropriees sur a que la distribution conditionnelle est la solution unique au probleme

a general characterization of the mean field limit for stochastic differential games the mean field limit of large population symmetric stochastic differential games is derived in a general setting with and without common noise on a finite time horizon minimal assumptions are imposed on equilibrium strategies which may be asymmetric and based on full information it is shown that approximate nash equilibria in the n player games admit certain weak limits as n tends to infinity and every limit is a weak solution of the mean field game mfg conversely every weak mfg solution can be obtained as the limit of a sequence of approximate nash equilibria in the n player games thus the mfg precisely characterizes the possible limiting equilibrium behavior of the n player games even in the setting without common noise the empirical state distributions may admit stochastic limits which cannot be described by the usual notion of mfg solution

indexability of restless bandit problems and optimality of whittle index for dynamic multichannel access in this paper we consider a class of restless multiarmed bandit processes rmabs that arises in dynamic multichannel access user server scheduling and optimal activation in multiagent systems for this class of rmabs we establish the indexability and obtain whittle index in closed form for both discounted and average reward criteria these results lead to a direct implementation of whittle index policy with remarkably low complexity when arms are stochastically identical we show that whittle index policy is optimal under certain conditions furthermore it has a semiuniversal structure that obviates the need to know the markov transition probabilities the optimality and the semiuniversal structure result from the equivalence between whittle index policy and the myopic policy established in this work for nonidentical arms we develop efficient algorithms for computing a performance upper bound given by lagrangian relaxation the tightness of the upper bound and the near optimal performance of whittle index policy are illustrated with simulation examples

whittle index for partially observed binary markov decision processes we consider the problem of dynamically scheduling m out of n binary markov chains when only noisy observations of state are available with ergodic equivalently long run average reward by passing on to the equivalent problem of controlling the conditional distribution of state given observations and controls it is cast as a restless bandit problem and its whittle indexability is established

predicting monthly streamflow using data driven models coupled with data preprocessing techniques 1 in this paper the accuracy performance of monthly streamflow forecasts is discussed when using data driven modeling techniques on the streamflow series a crisp distributed support vectors regression cdsvr model was proposed for monthly streamflow prediction in comparison with four other models autoregressive moving average arma k nearest neighbors knn artificial neural networks anns and crisp distributed artificial neural networks cdann with respect to distributed models of cdsvr and cdann the fuzzy c means fcm clustering technique first split the flow data into three subsets low medium and high levels according to the magnitudes of the data and then three single svrs or anns were fitted to three subsets this paper gives a detailed analysis on reconstruction of dynamics that was used to identify the configuration of all models except for arma to improve the model performance the data preprocessing techniques of singular spectrum analysis ssa and or moving average ma were coupled with all five models some discussions were presented 1 on the number of neighbors in knn 2 on the configuration of ann and 3 on the investigation of effects of ma and ssa two streamflow series from different locations in china xiangjiaba and danjiangkou were applied for the analysis of forecasting forecasts were conducted at four different horizons 1 3 6 and 1 2 month ahead forecasts the results showed that models fed by preprocessed data performed better than models fed by original data and cdsvr outperformed other models except for at a 6 month ahead horizon for danjiangkou for the perspective of streamflow series the ssa exhibited better effects on danjingkou data because its raw discharge series was more complex than the discharge of xiangjiaba the ma considerably improved the performance of ann cdann and cdsvr by adjusting the correlation relationship between input components and output of models it was also found that the performance of cdsvr deteriorated with the increase of the forecast horizon

a new image thresholding method based on gaussian mixture model in this paper an efficient approach to search for the global threshold of image using gaussian mixture model is proposed firstly a gray level histogram of an image is represented as a function of the frequencies of gray level then to fit the gaussian mixtures to the histogram of image the expectation maximization em algorithm is developed to estimate the number of gaussian mixture of such histograms and their corresponding parameterization finally the optimal threshold which is the average of these gaussian mixture means is chosen and the experimental results show that the new algorithm performs better

stochastic near optimal controls necessary and sufficient conditions for near optimality near optimization is as sensible and important as optimization for both theory and applications this paper concerns dynamic near optimization or near optimal controls for systems governed by the ito stochastic differential equations sdes where both the drift and diffusion terms are allowed to depend on controls and the systems are allowed to be degenerate necessary and sufficient conditions for a control to be near optimal are studied it is shown that any near optimal control nearly maximizes the hh function which is a generalization of the usual hamiltonian and is quadratic with respect to the diffusion coefficients in some integral sense and vice versa if certain additional concavity conditions are imposed error estimates for both the near optimality of the controls and the near maximum of the hh function are obtained based on some delicate estimates of the adjoint processes examples are presented to demonstrate the results

singular control and optimal stopping of spdes and backward spdes with reflection we consider general singular control problems for random fields given by a stochastic partial differential equation spde we show that under some conditions the optimal singular control can be identified with the solution of a coupled system of spde and a reflected backward spde rbspde as an illustration we apply the result to a singular optimal harvesting problem from a population whose density is modeled as a stochastic reaction diffusion equation existence and uniqueness of solutions of rbspdes are established as well as comparison theorems we then establish a relation between rbspdes and optimal stopping of spdes and apply the result to a risk minimizing stopping problem

the relaxed stochastic maximum principle in singular optimal control of diffusions this paper studies optimal control of systems driven by stochastic differential equations where the control variable has two components the first being absolutely continuous and the second singular our main result is a stochastic maximum principle for relaxed controls where the first part of the control is a measure valued process to achieve this result we establish first order optimality necessary conditions for strict controls by using strong perturbation on the absolutely continuous component of the control and a convex perturbation on the singular one the proof of the main result is based on the strict maximum principle ekeland s variational principle and some stability properties of the trajectories and adjoint processes with respect to the control variable

existence of markov controls and characterization of optimal markov controls given a solution of a controlled martingale problem it is shown under general conditions that there exists a solution having markov controls which has the same cost as the original solution this result is then used to show that the original stochastic control problem is equivalent to a linear program over a space of measures under a variety of optimality criteria existence and characterization of optimal markov controls then follows an extension of echeverria s theorem characterizing stationary distributions for uncontrolled markov processes is obtained as a corollary in particular this extension covers diffusion processes with discontinuous drift and diffusion coefficients

order statistics from mixed exchangeable random variables two different exchangeable samples are considered and these two samples are assumed to be independent of each other from these two samples a new sample is combined and treated as a single set of observations the distribution of a single order statistic and the joint distribution of two order statistics for a new mixed sample are derived and expressed in terms of joint distribution functions as a special case the distribution of a single order statistic and the joint distribution of two nonadjacent order statistics from exchangeable random variables are obtained the results presented in this paper allows widespread applications in modelling of various lifetime data biomedical sciences reliability and survival analysis actuarial sciences etc where the assumption of independence of data cannot be accepted and the exchangeability is a more realistic assumption

two armed restless bandits with imperfect information stochastic control and indexability we present a two armed bandit model of decision making under uncertainty where the expected return to investing in the risky arm increases when choosing that arm and decreases when choosing the safe arm these dynamics are natural in applications such as human capital development job search and occupational choice using new insights from stochastic control along with a monotonicity condition on the payoff dynamics we show that optimal strategies in our model are stopping rules that can be characterized by an index which formally coincides with gittins index our result implies the indexability of a new class of restless bandit models

generalizations of siegel s and picard s theorems we prove new theorems that are higher dimensional generalizations of the classical theorems of siegel on integral points on affine curves and of picard on holomorphic maps from c to affine curves these include results on integral points over varying number fields of bounded degree and results on kobayashi hyperbolicity we give a number of new conjectures describing from our point of view how we expect siegel s and picard s theorems to optimally generalize to higher dimensions in this article we prove new theorems that are higher dimensional generaliza tions of the classical theorems of siegel on integral points on affine curves and of picard on holomorphic maps from c to affine curves in section 2 we will give the statements of siegel s and picard s theorems and we will recall how these two theorems from such seemingly different areas of mathematics are related we will then proceed to give a number of new conjectures describing from our point of view how we expect siegel s and picard s theorems to optimally generalize to higher dimensions these include conjectures on integral points over varying number fields of bounded degree and conjectures addressing hyperbolic questions these conjectures appear to be fundamentally new we will then summarize our progress on these conjectures we have been able to get results in all dimensions with best possible results in many cases for surfaces

on surfaces of general type with maximal albanese dimension abstractgiven a minimal surface s equipped with a generically nite map to an abelianvariety and c s a rational or an elliptic curve we show that the canonical degreeof c is bounded by four times the self intersection of the canonical divisor of s asa corollary we obtain the niteness of rational and elliptic curves with an optimaluniform bound on their canonical degrees on any surface of general type with twolinearly independent regular one forms 1 1 introduction the object of this paper is to give an e ective bound on the canonical degrees of rationaland elliptic curves on a minimal surface of general type with generically nite albanese maplinearly in terms of the canonical volume of the surface here the canonical degree is thedegree with respect to the canonical polarization of the surface and the self intersection ofthis polarization is the canonical volume we will work in the complex analytic setting so that all varieties are complex analytic wewill assume the rudiments from the the theory of classi cation of complex projective surfacesas found for example in 3 we call a smooth projective surface to be of maximal albanesedimension if its albanese map is generically nite n b this terminology is di erent fromthat introduced in 21 we recall that any smooth projective surface s of maximal albanesedimension admits a morphism to a minimal one whose canonical divisor pulls back to thepositive part p of the zariski decomposition of the canonical divisor k of s and the canonicalvolume of s is by de nition vol k p

greatest common divisors and vojta s conjecture for blowups of algebraic tori we give results and inequalities bounding the greatest common divisor of multivariable polynomials evaluated at s unit arguments generalizing to an arbitrary number of variables results of bugeaud corvaja zannier hernandez luca and corvaja zannier in closely related results and in line with observations of silverman we prove special cases of vojta s conjecture for blowups of toric varieties as an application we classify when terms from simple linear recurrence sequences can have a large greatest common divisor in an appropriate sense the primary tool used in the proofs is schmidt s subspace theorem from diophantine approximation

improved time censored reliability test plans for k out of n gamma systems abstract relevant prior knowledge supported by historical data and expert judgments is common in many manufacturing processes the classical viewpoint to the determination of acceptance sampling plans for k out of n gamma systems is generalized to those situations in which the available previous information is appreciable a beta distribution with a reduced parameter space is adopted to describe the stochastic behavior of the fraction of defective systems an integer nonlinear programming problem is stated to find the inspection scheme that minimizes the required number of components to test and keeps the average producer and consumer risks below specified thresholds first lower and upper bounds as well as an approximate solution are derived then an efficient step by step procedure which finds the best acceptance sampling plan in a finite number of iterations is provided the inclusion of prior information into the decision process provides substantial savings in the sample size required for demonstrating system reliability and also more accurate assessments of the actual producer and consumer risks a system of five water pumps for cooling a reactor is analyzed for illustrative and comparative purposes

computing reliability indices of repairable systems via signature the purpose of this paper is to show the usefulness of system signature for computing some important reliability indices of repairable systems in particular we obtain signature based expressions for stationary availability rate of occurrence of failure and mean time to the first failure of repairable systems using these expressions we compute corresponding reliability indices of all systems with three and four components computational results are also presented for consecutive k within m out of n f and m consecutive k out of n f systems

bandit problems with levy processes bandit problems model the trade off between exploration and exploitation in various decision problems we study two armed bandit problems in continuous time where the risky arm can have two types high or low both types yield stochastic payoffs generated by a levy process we show that the optimal strategy is a cut off strategy and we provide an explicit expression for the cut off and for the optimal payoff

switching costs and the gittins index the theorem of gittins and jones 1974 is perhaps the single most powerful result in the literature on bandit problems this result establishes that in independent armed bandit problems with geometric discounting over an infinite horizon all optimal strategies may be obtained by solving a family of simple optimal stopping problems that associate with each arm an index known as the dynamic allocation index or more popularly as the gittins index importantly the gittins index of an arm depends solely on the characteristics of that arm and the rate of discounting and is otherwise completely independent of the problem under consideration these features simplify significantly the task of characterizing optimal strategies in this class of problems

denumerable armed bandits this paper studies the class of denumerable armed i e finite or countably infinitearmed bandit problems with independent arms and geometric discounting over an infinite horizon in which each arm generates rewards according to one of a finite number of distributions or types the number of types in the support of an arm as also the types themselves are allowed to vary across the arms we derive certain continuity and curvature properties of the dynamic allocation or gittins index of gittins and jones 1974 and provide necessary and sufficient conditions under which the gittins jones result identifying all optimal strategies for finite armed bandits may be extended to infinite armed bandits we then establish our central result at each point in time the arm selected by an optimal strategy will with strictly positive probability remain an optimal selection forever more specifically for every such arm there exists at least one type of that arm such that when conditioned on that type being the arm s true type the arm will survive forever and continuously with nonzero probability when the reward distributions of an arm satisfy the monotone likelihood ratio property mlrp the survival prospects of an arm improve when conditioned on types generating higher expected rewards however we show how this need not be the case in the absence of mlrp implications of these results are derived for the theories of job search and matching as well as other applications of the bandit paradigm

on fewnomials integral points and a toric version of bertini s theorem an old conjecture of erd s and renyi proved by schinzel predicted a bound for the number of terms of a polynomial g x x when its square g x has a given number of terms further conjectures and results arose but some fundamental questions remained open in this paper with methods which appear to be new we achieve a final result in this direction for completely general algebraic equations f x g x 0 where f x y is monic of arbitrary degree in y and has boundedly many terms in x we prove that the number of terms of such a g x is necessarily bounded this includes the previous results as extremely special cases we shall interpret polynomials with boundedly many terms as the restrictions to 1 parameter subgroups or cosets of regular functions of bounded degree on a given torus glm such a viewpoint shall lead to some best possible corollaries in the context of finite covers of glm concerning the structure of their integral points over function fields in the spirit of conjectures of vojta and a bertini type irreducibility theorem above algebraic multiplicative cosets a further natural reading occurs in non standard arithmetic where our result translates into an algebraic and integral closedness statement inside the ring of non standard polynomials