Stochastic programming models for general redundancy-optimization problems

This paper provides a unified modeling idea for both parallel and standby redundancy optimization problems. A spectrum of redundancy stochastic programming models is constructed to maximize the mean system-lifetime, /spl alpha/-system lifetime, or system reliability. To solve these models, a hybrid intelligent algorithm is presented. Some numerical examples illustrate the effectiveness of the proposed algorithm. This paper considers both parallel redundant systems and standby redundant systems whose components are connected with each other in a logical configuration with a known system structure function. Three types of system performance-expected system lifetime, /spl alpha/-system lifetime and system reliability-are introduced. A stochastic simulation is designed to estimate these system performances. In order to model general redundant systems, a spectrum of redundancy stochastic programming models is established. Stochastic simulation, NN and GA are integrated to produce a hybrid intelligent algorithm for solving the proposed models. Finally, the effectiveness of the hybrid intelligent algorithm is illustrated by some numerical examples.     

Fuzzy states as a basis for a theory of fuzzy reliability

Various engineering backgrounds have shown that the binary state assumption in probist (i.e., conventional) reliability theory, i.e. defining a system as fully failed or functioning, is not extensively acceptable, and thus the fuzzy state assumption should be used to replace the binary state assumption. As a result, the concept of profust reliability is introduced and a conceptual framework of profust reliability theory is developed on the basis of the fuzzy state assumption and the probability assumption. Profust reliability function, profust lifetime function and profust failure rate function and the mathematically rigorous relationships among them, lay a solid foundation for profust reliability theory. On the other hand, the concept of the virtual random lifetime builds a bridge linking profust reliability theory with probist reliability theory. In addition, in this paper, typical systems including the series system, parallel system, Markov model, mixture model and coherent system are briefly discussed within the conceptual framework of profust reliability theory.     

Reliability Bounds for Multi-State $k$-out-of- $n$ Systems

Algorithms have been available for exact performance evaluation of multi-state k-out-of-n systems. However, especially for complex systems with a large number of components, and a large number of possible states, obtaining "reliability bounds" would be an interesting, significant issue. Reliability bounds will give us a range of the system reliability in a much shorter computation time, which allow us to make decisions more efficiently. The systems under consideration are multi-state k-out-of-n systems with i.i.d. components. We will focus on the probability of the system in states below a certain state d, denoted by Q_sd. Based on the recursive algorithm proposed by Zuo & Tian [14] for performance evaluation of multi-state k-out-of-n systems with i.i.d. components, a reliability bounding approach is developed in this paper. The upper, and lower bounds of Q_sd are calculated by reducing the length of the k vector when using the recursive algorithm. Using the bounding approach, we can obtain a good estimate of the exact Q_sd value while significantly reducing the computation time. This approach is attractive, especially to complex systems with a large number of components, and a large number of possible states. A numerical example is used to illustrate the significance of the proposed bounding approach.     

Mixture models in profust reliability theory

Conventional (i.e. probist) reliability theory is based on the probability assumption and the binary-state assumption, whereas profust reliability theory is based on the probability assumption and the fuzzy-state assumption. The mixture model is an important form of typical systems in profust reliability theory. In this paper we show that a mixture model can be converted into a series system, and study the IFR and DFR preservabilities for mixture models. Various profust reliability bounds are given for the mixture model. In addition, we also show how to construct typical profust lifetime distributions for mixture models.     

Maximum Likelihood Estimation of Compound-Gaussian Clutter and Target Parameters

Compound-Gaussian models are used in radar signal processing to describe heavy-tailed clutter distributions. The important problems in compound-Gaussian clutter modeling are choosing the texture distribution, and estimating its parameters. Many texture distributions have been studied, and their parameters are typically estimated using statistically suboptimal approaches. We develop maximum likelihood (ML) methods for jointly estimating the target and clutter parameters in compound-Gaussian clutter using radar array measurements. In particular, we estimate i) the complex target amplitudes, ii) a spatial and temporal covariance matrix of the speckle component, and iii) texture distribution parameters. Parameter-expanded expectation–maximization (PX-EM) algorithms are developed to compute the ML estimates of the unknown parameters. We also derived the CramÉr–Rao bounds (CRBs) and related bounds for these parameters. We first derive general CRB expressions under an arbitrary texture model then simplify them for specific texture distributions. We consider the widely used gamma texture model, and propose an inverse-gamma texture model, leading to a complex multivariate$t$clutter distribution and closed-form expressions of the CRB. We study the performance of the proposed methods via numerical simulations.     

A new method for system reliability bounds

It has been established that symbolic reliability evaluation problem is an N.P. complete problem and as such is computationally infeasible for large networks. This has led to increased efforts in search for more fast exact techniques as well as better approximate methods.This paper proposes an algorithm for determining improved (tighter) upper and lower bounds on system reliability of general (i.e. non-series-parallel) systems. The proposed algorithm, like most existing methods, requires the knowledge of all simple paths and minimal cutsets of the system. The system success (failure) function is the union of all simple paths (minimal cutsets). The system success and failure functions are then modified to multinominal form and these expressions are interpreted as proper probability expressions using some approximations. The proposed algorithm gives better bounds as compared to the min-max method, the method of successive bounds, Esary-Proschan bounds and Shogan bounds and is illustrated by an example.     

System availability with non-exponentially distributed outages

This paper studies the steady-state availability of systems with times to outages and recoveries that are generally distributed. Availability bounds are derived for systems with limited information about the distributions. Also investigated are the applicability of convenient exponential models in evaluating availability for systems that have two-sided bounded distributions of times to planned outages. A general closed-form formula is derived for the steady-state availability of a system with multiple outage types of arbitrary distributions. The formula shows that only the mean values of times to repair (TTR_i , i = 1, 2,..., n) affect the steady-state availability; i.e., distributions of TTR_i with the same mean value have the same effect in determining the steady-state system availability. However, the distributions of times to outages, (TTO_i, i = 1, 2,..., n), have an important impact on the steady-state system availability. Bounds are provided for the steady-state availability for a system subject to unplanned outages, for which times-to-outages are exponentially distributed and planned outages for which times-to-outages have bounded distributions. In practice, the distribution of time to planned outages is generally bounded due to economic constraints and industrial competition. The bounds derived here are good estimates of the system's steady-state availability, if the only known information of time-to-planned-outage is its two-sided bounds. Popular all-exponential models that assume that all times to outages and recoveries are exponentially distributed can under-estimate or over-estimate system availability if used for a system with generally distributed times to outages, of which limited information is known. Therefore explicit criteria are presented for determining when an all-exponential model, if applied to systems with outages of two-sided bounded general distributions, is a good approximation     

The effect of compensating faults models on NMR system reliability

Realistic estimates of the reliability of systems with N-tuple modular redundancy (NMR), must consider the effect of compensation of logic faults. Earlier analyses that include compensating faults are impractical to use, yield very complex mathematical formulas for reliability indices, and/or concern the simplest triple modular redundancy (TMR) system only. This paper gives a general approach to the problem. Two models of compensating faults are considered. For either model the lower and upper bounds on frequency of compensating faults are found. By applying some results of NMR system evaluation, the new estimates of upper and lower bounds of NMR system reliability with respect to compensating faults are derived. A simple algebraic form of the final results makes them useful     

Reliability and component importance of a consecutive-k-out-of-n system

This paper explores the duality between the consecutive-k-out-of-n F and G systems, studies the Birnbaum reliability importance of the components in an i.i.d. system, and reviews the research in uniform treatment of the linear and circular consecutive-k-out-of-n:F systems. Upper and lower bounds for the reliability of a linear consecutive-k-out-of-n system are developed by constructing k-fold series and parallel redundant systems from the linear system.     

Nonparametric estimation of mean time to failure with unknown stochastic censoring

In this note we study a nonparametric estimator of the mean time to failure within the model of random censorship, provided only failures are recorded, and censoring times are not available. The s-bias of this estimator is of order O(1) and does not vanish with increasing sample size. We present bounds for the main term of the s-bias under additional assumptions such as the Koziol-Green model of random censoring and lifetime distributions belonging to the IFRA or DFRA classes. A corrected estimator s-bias is proposed for use in reliability practice, provided that the underlying lifetime distribution is IFRA or DFRA. This is a valuable tool if one is able to observe only failure times.     

Analysis of Multiple-Antenna Systems With Finite-Rate Feedback Using High-Resolution Quantization Theory

This paper considers the development of a general framework for the analysis of transmit beamforming methods in multiple-antenna systems with finite-rate feedback. Inspired by the results of classical high-resolution quantization theory, the problem of finite-rate quantized communication system is formulated as a general fixed-rate vector quantization problem with side information available at the encoder (or the quantizer) but unavailable at the decoder. The framework of the quantization problem is sufficiently general to include quantization schemes with general non-mean-squared distortion functions and constrained source vectors. Asymptotic distortion analysis of the proposed general quantization problem is provided by extending the vector version of the Bennett's integral. Specifically, tight lower and upper bounds of the average asymptotic distortion are proposed. Sufficient conditions for the achievability of the distortion bounds are also provided and related to corresponding classical fixed-rate quantization problems. The proposed general methodology provides a powerful analytical tool to study a wide range of finite-rate feedback systems. To illustrate the utility of the framework, we consider the analysis of a finite-rate feedback multiple-input single-output (MISO) beamforming system over independent and identically distributed (i.i.d.) Rayleigh flat-fading channels. Numerical and simulation results are presented that further confirm the accuracy of the analytical results     

Delay-limited capacity: multiple antennas, moment constraints, and fading statistics

Different performance measures are an important mean in order to analyze and design wireless communications systems. Examples of common performance measures are the ergodic capacity, the outage capacity, and the average mean-square error (MSE). In this work, we study the delay-limited capacity (DLC). The DLC depends on the properties of the fading channel, e.g. on the spatial correlation and on the line-of-sight (LOS) component. In this letter, we derive the DLC for the general class of parallel fading channels, including the multiple antenna channels under moment and long-term power constraint. We prove that the DLC is Schur-concave with respect to the spatial correlation in single-input multiple-output (SIMO), and multiple-input single-output (MISO). Bounds for the DLC of multiple-input multiple-output (MIMO) and parallel fading channels are derived and the impact of the the mean component and spatial correlation on these bounds is characterized.     

Optimising CDMA Cell Planning with Soft Handover

Soft handover (SHO) is one of the fundamental features of code division multiple access (CDMA) systems such as universal mobile telecommunication system (UMTS), and it is affected by the placement and density of cells. Inclusion of soft handover in optimization models for UMTS and CDMA cell site selection and configuration has previously been very limited but it is important for coverage because it can provide gain to the user. Some authors have excluded SHO on the basis of tractability while others have found that omitting SHO in planning gives adequate solutions. As such the incorporation of SHO remains an important component for definitive investigation in optimisation models for cell planning. In this paper we focus on the problem and effect of including SHO in cell planning optimisation. We introduce a new cell planning optimisation model that explicitly incorporates SHO and reduces computational complexity. Exact results can be obtained when the orthogonality factor is zero, while a conservative approximation of interference is used to generate lower bounds on coverage in the general case. We demonstrate the tractability of this model and show that it leads to improved lower bounds for coverage maximisation in network planning.     

Coding for Parallel Channels: Gallager Bounds and Applications to Turbo-Like Codes

The transmission of coded communication systems is widely modeled to take place over a set of parallel channels. This model is used for transmission over block-fading channels, rate-compatible puncturing of turbo-like codes, multicarrier signaling, multilevel coding, etc. New upper bounds on the maximum-likelihood (ML) decoding error probability are derived in the parallel-channel setting. We focus on the generalization of the Gallager-type bounds and discuss the connections between some versions of these bounds. The tightness of these bounds for parallel channels is exemplified for structured ensembles of turbo codes, repeat-accumulate (RA) codes, and some of their recent variations (e.g., punctured accumulate-repeat-accumulate codes). The bounds on the decoding error probability of an ML decoder are compared to computer simulations of iterative decoding. The new bounds show a remarkable improvement over the union bound and some other previously reported bounds for independent parallel channels. This improvement is exemplified for relatively short block lengths, and it is pronounced when the block length is increased. In the asymptotic case, where we let the block length tend to infinity, inner bounds on the attainable channel regions of modern coding techniques under ML decoding are obtained, based solely on the asymptotic growth rates of the average distance spectra of these code ensembles.     

An extended combinatorial analysis framework for discrete-time queueing systems with general sources

The paper considers a general class of discrete time systems with batch arrivals and departures. Such models appear frequently in the teletraffic analysis of computer and communications networks. Our arrival models are assumed to be quite general. They could be independent and identically distributed (i.i.d.) in successive slots, periodic, Markovian, or described by the moving average time-series model, etc. Our solution framework is novel and unifying and it uses a combination of multidimensional generating functions and combinatorial analysis utilizing extensions of classical ballot theorems. In general, we provide an explicit analytical expression as an infinite sum to obtain the system stationary probability distribution avoiding classical root-finding methods, matrix analytical methodologies, and spectral decomposition approaches. We provide a number of analytical and numerical examples including: i.i.d. models with Poisson and Binomial arrivals; multiserver queueing systems fed by Markovian sources; queues fed with a discrete moving average source of the first and second order; an i.i.d. discrete Pareto batch arrival model. Closed-form analytical expressions are obtained for the stationary distribution of the system queue lengths and numerical examples are also provided when appropriate.     

Design and analysis of very high-speed network architectures

Communication architectures for very-high-speed networks are dealt with. The use of high communication speed increases the ratio between the end-to-end propagation delay and the packet transmission time. This increase restricts the utilization of the high system bandwidth in broadcast channel-based systems, causing a rapid performance deterioration. A communication system architecture characterized by the use of several parallel channels and design of the nodes' channel interface is presented. The channel-division approach is introduced, showing that for a given system bandwidth the total system capacity will be increased by bandwidth division and parallel communication. An analytic model of this system is developed, from which the proposed system's performance is obtained and performance bounds determined for multichannel slotted finite systems. The results show that the architecture has a potential to improve significantly the system performance compared to conventional single-channel-based systems. Furthermore, for a given network configuration an optimal architecture can be found which simultaneously maximizes the system throughput and minimizes the average packet delay     

Stability results for decomposable multidimensional digital systems based on the lyapunov equation

Lower bounds for the stability margins of 2-D digital systems are extended to n-D systems. These bounds are then improved for n-D (including 2-D) systems which have characteristic polynomials with 1-D factor polynomials. Stability analysis of n-D systems due to finite wordlength is considered, some tight lower bounds on coefficient wordlength which guarantee the n-D system to be stable and/or globally asymptotically stable are presented. Improved and/or extended criteria for absence of overflow oscillations and global asymptotic stability of n-D systems are proposed as well. An example is presented to illustrate the theoretical results, and it is shown that the lower bound on coefficient wordlength could be considerably improved for the (partial) factorable denominator n-D digital systems. All the discussions are based on the n-D Lyapunov equation.     

Reliability bounds for some static system models using lifetime data on their components

It has become increasingly difficult to obtain a sampling distribution of the reliability function of a system. Therefore, reliability bounds have been studied to facilitate the analysis of reliability characteristics. The bounds for the reliability of the system depend on the mean and variance of the lifetimes recorded on the system. However, in the early stages of design, the lifetime data on a system may either be costly or non-existent. Thus, by using lifetime data on the components of the system, the present study deals with the analysis of reliability bounds for some static system models.     

Improved upper bounds on error-probability for biorthogonal trellis-coded CDMA systems

We employ the transfer function approach to obtain error-probability upper bounds for asynchronous trellis-coded CDMA systems based on biorthogonal signature sequences. The technique provides uniformly tight bounds for the biorthogonal sequence based trellis codes, both with and without parallel transitions, in contrast to previously published results.     

A hierarchical model for estimating the early reliability of complex systems

We describe a hierarchical Bayesian model for assessing the early reliability of complex systems, for which sparse or no system level failure data are available, except that which exists for comparable systems developed by different categories of manufacturers. Novel features of the model are the inclusion of a "quality" index to allow separate treatment for systems produced by "experienced" & "inexperienced" manufacturers. We show how this index can be employed to distinguish the behavior of systems produced by each category of manufacturer for the first few applications, with later pooling of outcomes from both categories of manufacturers after the first few uses (i.e., after inexperienced manufacturers gain experience). We demonstrate how this model, together with suitable informative priors, can reproduce the reliability growth in the modeled systems. Estimation of failure probabilities (and associated uncertainties) for early launches of new space vehicles is used to illustrate the methodology. Disclaimer-This paper is provided solely to illustrate how hierarchical Bayesian methods can be applied to estimate systems reliability (including uncertainties) for newly introduced complex systems with sparse or nonexistent system level test data. The example problem considered (i.e. estimating failure probabilities of new launch vehicles) is employed solely for illustrative purposes. The authors have made numerous assumptions & approximations throughout the document in order to demonstrate the central techniques. The specific methodologies, results, and conclusions presented in this paper are neither approved nor endorsed by the United States Air Force or the Federal Aviation Administration.