Reliability of structural systems with correlated elements

Calculation of the probability of failure of a system with correlation members is usually a difficult and time-consuming numerical problem. However, for some types of systems with equally correlated elements this calculation can be performed in a simple way. This has suggested two new methods based on so-called average and equivalent correlation coefficients. By using these methods approximate values for the probability of failure can easily be calculated. The accuracy of these methods is illustrated with examples.     

Reliability of a multi-state system subject to shocks using phase-type distributions

The reliability of a multi-state system is considered. The system is subject to both internal wear-out and external shocks causing damage that cumulates as shocks follow one another. As a consequence of this cumulating damage, the system wear-out process can be affected.     

有优先权且有两不同修理设备的两部件冷贮备可修系统的可靠性分析

在开关不完全可靠的情况下,研究了两个不同型部件和两个修理设备组成的冷贮备系统.在部件1有工作和修理优先权的条件下,建立了在部件和开关工作寿命及修理时间均服从指数分布的可修系统模型,利用Markov理论和Laplace变换,给出了系统可靠度的Laplace表达式及系统的稳态指标.     

On waiting time distributions associated with compound patterns in a sequence of multi-state trials

In this article, waiting time distributions of compound patterns are considered in terms of the generating function of the numbers of occurrences of the compound patterns. Formulae for the evaluation of the generating functions of waiting time are given, which are very effective computational tools. We provide several viewpoints on waiting time problems associated with compound patterns and develop a general workable framework for the study of the corresponding distributions. The general theory is employed for the investigation of some examples in order to illustrate how the distributions of waiting time can be derived through our theoretical results. This research was partially supported by the ISM Cooperative Research Program (2006-ISM·CRP-2007).     

Normality of meromorphic functions with multiple zeros and shared values

In this paper, we study the normality of a family of meromorphic functions and general criteria for normality of families of meromorphic functions with multiple zeros concerning shared values are obtained.     

Robustness of perturbation analysis estimators for queueing systems with unknown distributions

Sample-path-based stochastic gradient estimators for performance measures of queueing systems rely on the assumption that a probability distribution of the random vector of interest (e.g., a service or interarrival time sequence) is given. In this paper, we address the issue of dealing with unknown probability distributions and investigate the robustness of such estimators with respect to possibly erroneous distribution choices. We show that infinitesimal perturbation analysis (IPA) can be robust in this sense and, in some cases, provides distribution-independent estimates. Comparisons with other gradient estimators are provided, including experimental results. We also show that finite perturbation analysis (FPA), though only providing gradient approximations, possesses some attractive robustness properties with respect to unknown distribution parameters. An application of FPA estimation is included for a queueing system performance optimization problem involving customers with real-time constraints.This work was supported in part by the National Science Foundation Grant ECS-88-01912 and by the Office of Naval Research Contract N00014-87-K-0304.The authors wish to thank Dr. Jack Holtzman for several useful comments and suggestions.     

Generating function analysis of some joint distributions for Poisson loss systems

We present a new approach to derive joint distributions for stationary Poisson loss systems. In particular, for M/M/m/0 and M/M/1/n we find the Laplace transforms (with respect to time t) of the probability that at time t there are i customers in the system and during [0,t], j customers are refused admission; for M/M/m/0 we further determine the LT of the probability that the system was full for less than s time units during [0,t] and serves i customers at time t. Explicit formulas for the corresponding moments are also given.     

Reliability analysis of a renewable multiple cold standby system

We present a general reliability analysis of the basic multiple cold standby system attended by a single repair facility. The particular case of deterministic repair provides some explicit results for the survival function illustrated by computer-plotted graphs.     

Reliability analysis of an Attitude Determination and Control System (ADCS) through the RAMSAS method

Reliability analysis of modern large-scale systems is a challenging task which could benefit from the jointly exploitation of recent model-based approaches and simulation techniques to flexibly evaluate the system reliability performances and compare different design choices. In this context, RAMSAS, a model-based method which supports the reliability analysis of systems through simulation by combining the benefits of popular OMG modeling languages with wide adopted simulation and analysis environments, has been recently proposed. This paper shows the effectiveness of RAMSAS through a real case study concerning the reliability analysis of an Attitude Determination and Control System (ADCS) of a satellite.     

STRUCTURES OF SYSTEMS WITH EXPONENTIAL LIFE DISTRIBUTIONS

Abstract. Structures of monotone systems and cold standby systems with     

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.     

APPROXIMATING ANALYSIS OF A KIND OF REPAIRABLE STANDBY SYSTEMS

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Group classification of systems of non-linear reaction-diffusion equations with general diffusion matrix. II. Generalized Turing systems

Group classification of systems of two coupled non-linear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.     

A general method for writing the dynamical equations of nonholonomic systems with ideal constraints

The basic notions of the dynamics of nonholonomic systems are revisited in order to give a general and simple method for writing the dynamical equations for linear as well as non-linear kinematical constraints. The method is based on the representation of the constraints by parametric equations, which are interpreted as dynamical equations, and leads to first-order differential equations in normal form, involving the Lagrangian coordinates and auxiliary variables (the use of Lagrangian multipliers is avoided). Various examples are illustrated.      

Reliability of fault-tolerant systems with parallel task processing

The paper considers performance and reliability of fault-tolerant software running on a hardware system that consists of multiple processing units. The software consists of functionally equivalent but independently developed versions that start execution simultaneously. The computational complexity and reliability of different versions are different. The system completes the task execution when the outputs of a pre-specified number of versions coincide. The processing units are characterized by different availability and processing speed. It is assumed that they are able to share the computational burden perfectly and that execution of each version can be fully parallelized.     

Global fixed-time stabilization for a class of switched nonlinear systems with general powers and its application

This paper investigates the problem of global fixed-time stabilization for a class of uncertain switched nonlinear systems with the general powers, namely, the powers of the considered systems can be different odd rational numbers, even rational numbers or both odd and even rational numbers. By skillfully using the common Lyapunov function method and the adding a power integrator technique, a common state feedback control strategy is developed. It is proved that the proposed controller can guarantee that the state of the resulting closed-loop system converges to zero for any given fixed time under arbitrary switchings. Simulation results of the liquid-level system are provided to show the effectiveness of the proposed method.     

M/M/1 Queueing systems with inventory

We derive stationary distributions of joint queue length and inventory processes in explicit product form for various M/M/1-systems with inventory under continuous review and different inventory management policies, and with lost sales. Demand is Poisson, service times and lead times are exponentially distributed. These distributions are used to calculate performance measures of the respective systems. In case of infinite waiting room the key result is that the limiting distributions of the queue length processes are the same as in the classical M/M/1/∞-system. All authors were supported by DAAD/KBN grant number D/02/32206.     

Queue-length and waiting-time distributions of discrete-time GI X/Geom/ 1 queueing systems with early and late arrivals

In this paper, we give a unified approach to solving discrete-time GI ^X/Geom/ 1 queues with batch arrivals. The analysis has been carried out for early- and late-arrival systems using the supplementary variable technique. The distributions of numbers in systems at prearrival epochs have been expressed in terms of roots of associated characteristic equations. Furthermore, distributions at arbitrary as well as outside observer's observation epochs have been obtained using the relation derived in this paper. We also present delay analyses for both the systems. Numerical results are presented for various interarrival-time and batch-size distributions. This revised version was published online in June 2006 with corrections to the Cover Date.