Generalized multi-state k-out-of-n:G systems

In a binary k-out-of-n:G system, k is the minimum number of components that must work for the system to work. Let 1 represent the working state and 0 the failure state, k then indicates the minimum number of components that must be in state 1 for the system to be in state 1. This paper defines the multi-state k-out-of-n:G system: each component and the system can be in 1 of M+1 possible states: 0, 1, ..., M. In Case I, the system is in state ⩾j iff at least k_j components are in state ⩾j. The value of k_j I 1 can be different for different required minimum system-state level j. Examples illustrate applications of this definition. Algorithms for reliability evaluation of such systems are presented     

Reliability analysis of k-out-of-n systems with partially repairable multi-state components

In some environments the components might not fail fully, but can lead to degradation and the efficiency of the system may decreases. However, the degraded components can be restored back through a proper repair mechanism. In this paper, we present a model to perform reliability analysis of k-out-of-n systems assuming that components are subjected to three states such as good, degraded, and catastrophic failure. We also present expressions for reliability and mean time to failure (MTTF) of k-out-of-n systems. Simple reliability and MTTF expressions for the triple-modular redundant (TMR) system, and numerical examples are also presented in this study.     

Performance utility-analysis of multi-state systems

This paper defines a new utility importance of a state of a component in multi-state systems. This utility importance overcomes some drawbacks of a well-known importance measure suggested by William S. Griffith (J. Applied Probability, 1980). The relationship between this new utility importance and the Griffith importance is studied and their difference is illustrated with examples. The contribution of an individual component to the performance utility of a multi-state system is discussed. Examples show that a meaningful index for measuring the performance of individual components in a multi-state system can hardly be defined in general, without considering the actual values of the utility levels and the distributions of the component-states in the system. An example illustrates how genetic algorithm, simulated annealing, and tabu search can be used in selecting components and defining the position order of components so that the performance utility of a multi-state system is optimized.     

一类多状态连续n中取k(G)系统的可靠性计算

为了计算多状态连续厅中取后（G）系统的可靠性,引入4个定理,将满足引理的多状态系统转换为二元状态系统。分别推导了多状态线形连续k／n（G）系统和环形连续k／n（G）系统的可靠性计算公式。证明了固定k值增加一个新部件,若部件可靠性独立同分布,线形和环形系统可靠性均增加;若部件可靠性独立但不同分布,环形系统存在一个极值,新增加部件可靠性大于这个极值时得到的新系统可靠性增加,反之系统可靠性下降。     

Dominant multi-state systems

In this paper, we propose a definition of the dominant multi-state system. Under the proposed definition, multi-state systems are divided into two groups without reference to component relevancy conditions: dominant systems, and nondominant systems. Dominant systems can be further divided into two groups: with binary image, and without binary image. A multi-state system with binary image implies that its structure function can be expressed in terms of binary structure functions such that it can be treated as a binary system structure, and existing algorithms for reliability evaluation of binary systems can be applied for system performance evaluation. A technique is provided for establishing the bounds of performance distribution of dominant systems without binary image. The properties of dominant systems are studied. Examples are given to illustrate applications of the proposed definitions and methods.     

Composite importance measures for multi-state systems with multi-state components

This paper presents & evaluates composite importance measures (CIM) for multi-state systems with multi-state components (MSMC). Importance measures are important tools to evaluate & rank the impact of individual components within a system. For multi-state systems, previously developed measures do not meet all user needs. The major focus of the study is to distinguish between two types of importance measures which can be used for evaluating the criticality of components in MSMC with respect to multi-state system reliability. This paper presents Type 1 importance measures that are involved in measuring how a specific component affects multi-state system reliability. A Monte Carlo (MC) simulation methodology for estimating the reliability of a MSMC is used for computing the proposed CIM metrics. Previous approaches (Type 2) have focused on investigating how a particular component state or set of states affects multi-state system reliability. For some systems, it is not clear how to prioritize system component importance, collectively considering all of its states, using the previously developed importance measures. That detracts from those measures. Experimental results show that the proposed CIM can be used as an effective tool to assess component criticality for MSMC. Examples are used to illustrate & compare the proposed CIM with previous multi-state importance measures.     

Linear multi-state sliding-window systems

This paper proposes a new model that generalizes the consecutive k-out-of-r-from-n:F system to the multi-state case. In this model (linear multi-state sliding window system), the system consists of n linearly ordered multi-state elements. Each element can have various states: from complete-failure up to perfect-functioning. A performance rate is associated with each state. The sliding window system fails if the sum of the performance rates of any r consecutive multi-state elements is lower than a minimum allowable level. An algorithm for system reliability evaluation is based on an extended universal moment-generating function. Examples of system reliability evaluation are presented.     

Performance evaluation of generalized selection diversity systems over Nakagami‐m fading channels

The generalized selection combining (GSC) scheme that adaptively combines a subset of M strongest paths out of L available diversity paths finds applications in several wideband receivers and broadband wireless communications. In this paper, exact closed‐form expressions for the moment generating function (MGF), the probability density function (PDF) and the cumulative density function (CDF) of the GSC(M, L) output signal‐to‐noise ratio (SNR) in independent and identically distributed (i.i.d) Nakagami‐m fading channels are derived while the fading index is a positive integer. These expressions hold for any M and L and provide a comprehensive framework for performance analysis including the derivation of closed‐form formulas for the average symbol error probability (ASEP) of a broad class of binary and M‐ary modulations, mean combined SNR and the outage probability of GSC(M, L) receiver structures. When the Nakagami‐m fading index is not an integer, the MGF of GSC(M, L) output SNR is derived as an (M − 1)‐fold infinite series. With this MGF, analytical expressions for both the outage probability and error rates can be readily obtained. An easily programmable recursive solution of the MGF of GSC(M, L) output SNR is also outlined for both the positive integer and noninteger fading severity index cases. Copyright © 2002 John Wiley & Sons, Ltd.     

Redundancy optimization for series-parallel multi-state systems

This paper generalizes a redundancy optimization problem to multi-state systems, where the system and its components have a range of performance levels-from perfect functioning to complete failure. The components are: (1) chosen from a list of products available in the market; and (2) characterized by their nominal performance level, availability and cost. System availability is represented by a multi-state availability function, which extends the binary-state availability. To satisfy the required multi-state system availability, the redundancy for each component can be used. A procedure which determines the minimal-cost series-parallel system structure subject to a multi-state availability constraint is proposed. A fast procedure is developed, based on a universal generating function, to evaluate the multi-state system availability. Two important types of systems are considered and special operators for the universal generating function determination are introduced. A genetic algorithm is used as an optimization technique. Examples are given     

Reliability of multi-state systems with two failure-modes

Systems with two failure modes (STFM) consist of devices, which can fail in either of two modes. For example, switching systems can not only fail to close when commanded to close but can also fail to open when commanded to open. This paper considers systems consisting of different elements characterized by nominal performance level in each mode. Such systems are multi-state because they have multiple performance levels in both modes, depending on the combination of elements available at the moment. The system availability is defined as the probability of satisfaction of given constraints imposed on system performance in both modes. The paper suggests reliability measures for multi-state systems with 2 failure modes, and presents a procedure for evaluating these measures. The procedure is based on the use of a universal moment generating function (UMGF). It allows one to estimate availability and s-expected performance of complex systems with series-parallel and bridge topology. Basic UMGF technique operators are developed for two types of systems, based on transmitting-capacity and on operation-time.     

Reliability of k-out-of-n:G systems with imperfect fault-coverage

k-out-of-n:G systems are modeled to determine their reliability and availability. Markov models are obtained to examine the fault-tolerant operation of the system. From the Markov chains, reliability and availability measures are found as state probabilities. Recursive expressions for mean time-between-failures and mean time-to-failure are obtained for repairable systems, considering perfect and imperfect fault-coverage     

Stochastic ordering results for consecutive k-out-of-n:F systems

A linear (circular) consecutive k-out-of-n:F system is a system of n linearly (circularly) ordered components which fails if and only if at least k consecutive components fail. We use recursive relationships on the reliability of such systems with independent identically distributed components to show that for any fixed k, the lifetime of a (linear or circular) consecutive k-out-of-n:F system is stochastically decreasing in n. This result also holds for linear systems when the components are independent and not necessarily identically distributed, but not in general for circular systems.     

Performance evaluation of data communication systems

This paper is a tutorial and a survey of analytical methods in the evaluation of data communication networks. The major mathematical methods are Markov chains applied to discrete time systems and queueing theory. Emphasis is placed on the applications of the mathematical tools. The discussion follows the framework of the layered architecture. In the section on data link control, rigorous as well as "engineering" approaches are highlighted. In this area, models of great accuracy have been developed. In the path-control or routing layer, the major model is provided by Kleinrock's delay analysis of packet networks. Finite buffer pools still pose many problems. The method of the homogeneous network is introduced, a method which reduces complexity originating from the network topology in favor of more realistic protocol features. This thought is expanded into the layer of end-to-end protocols where the tandem-queue model is introduced and its application to the flow-control problem discussed.     

Markov model for k-out-of-n:G systems with built-in-test

This paper considers some new variations when the Built-In-Test technique is applied to k-out-of-n:G systems. A complete Markov model for the reliability and availability analysis of k-out-of-n:G systems with BIT is developed. Both fault coverage and false alarm are considered. A new inverse Laplace transform formula is derived to solve the differential simultaneous equations. Finally, generalized analytical functions for system reliability and availability are obtained. Our approach and solution are helpful and applicable for analyzing the impact of BIT design parameters on k-out-of-n:G system RAM and optimizing the redundancy management strategy.     

Fast optimal diagnosis procedures for k-out-of-n:G systems

A k-out-of-n:G system consists of a set of components, where each component is either faulty or fault-free. The system is working if at least k components are fault-free. The problem of finding an optimal diagnosis procedure for a given k-out-of-n:G system has been considered in several research fields including medical diagnosis, redundant-system testing, and searching data-files. A polynomial-time algorithm for this problem was presented first by Salloum, and later by Salloum and Breuer, and independently by Ben-Dov. This paper implements the Salloum-Breuer-Ben-Dov algorithm, leading to an optimal diagnosis procedure that can determine the state of any given system in O(n·log(n)) time complexity and O(n) space complexity. The efficiency is achieved by using a generalized radix sorting procedure that uses a heap data structure. For some k-out-of-n:G systems, including those with equal testing costs for all components, the components along the leftmost and rightmost paths in the optimal diagnostic tree uniquely determine the other components in the tree. This property is used to devise a faster optimal diagnosis procedure than the one for the general k-out-of-n:G system. With regard to complexity, these procedures are the best solutions for the problem under consideration. This conjecture is supported by the fact that all these procedures require a sorting operation which has O(n·log(n)) as a lower bound on its time complexity     

Performance evaluation of optical fiber transmission systems

A method is presented for evaluating of error probability for optical-fiber communication systems in the present of intersymbol interference and additive noise. It is based on deriving a best approximation, in a minimax sense, for the cumulative distribution function of the additive noise. The method takes into account the avalanche photodetector's non-Gaussian shot noise statistics. The additive noise is also not constrained to be Gaussian. Examples are presented for comparison to previously published techniques     

Performance evaluation of ASK phase-diversity lightwave systems

Phase diversity coherent systems are gaining increasing interest with the increase of the bit rate in optical transmissions. In this work, an accurate approach for the evaluation of the error probability in ASK phase-diversity lightwave systems is presented. The approach is based on a Gaussian quadrature rule integration, which takes into account the exact characterization of the filtered phase noise through its moments. The effects of the laser linewidth on the error probability for hybrid circuits with different number of ports are derived and discussed. Also, the effects of the frequency offset are considered     

Performance evaluation of optically pre-amplified PPM systems

An original analysis is presented for an optical fiber n-ary pulse position modulation (PPM) system employing optical preamplification. The theoretical results, from calculations performed at a bit-rate of 622 Mbit/s and a wavelength of 1.53 μm, demonstrate that the PPM system offers a 7.5 dB sensitivity benefit in comparison with an equivalent PCM system. Furthermore the results illustrate that optically preamplified PPM offers sensitivities significantly better than the fundamental limit of an optically preamplified PCM system and in fact approaches that of coherent detection