Approximated reliability of r-out-of-n(F) system with common cause failure and maintenance

In modern industries very high reliability system are needed. To improve the reliability of system, the component redundancy and maintenance of component or system play an impotant role and must be studied. This paper presents a reliability model of a r-out-of-n(F) redundant system with maintenance and Common Cause Failure. Failed component repair times are arbitrarily distributed. The system is in a failed state when r units failed because of the combination of single element failure or CCF(Common Cause Failure). Laplace transformation of reliability is derived by using analysis of Markov state transition graph. By using the analyzed MTBF, we compute MTBF of r-out-of-n(F) system. The MTBF with CCF is saturable even if repair rate is large.Approximated reliability of the r-out-of-n(F) system with maintenance and Common Cause Failure O.SummaryThe paper presents a reliability model of a r-out-of-n(F) redundant system with maintenance and Common Cause Failure. Failed component repair times are arbitrarily distributed. The system is in a failed state when r units failed because of the combination of single element failure or Common Cause Failure. Laplace transformation of reliability is derived by using analysis of Markov state transition graph. By analyzing this mean visiting time equations, we compute MTBF and shows computational example. The MTBF with CCF is saturable even if repair rate is large. In general the maintenance overcomes MTBF bounds, But the repair method not overcome the MTBF saturation when the system has Common Cause Failure.     

Parametric Analysis of 2-Unit Redundant Computer Systems With Corrective and Preventive Maintenance

This paper shows the span of results which can be obtained by modeling a system's behavior by stochastic processes and demonstrates practical rules for employing Markov and semi-Markov models. The introduction summarizes several methods for reliability analysis and gives the advantages and drawbacks of four methods: Markov processes, semi-Markov processes, supplementary variables, the method of stages. The remainder deals with reliability and availability modeling of a 2-unit redundant computer system. There are a) two types of maintenance: corrective (c. m.) and preventive (p. m.), and b) two system parameters: coverage, and an increased failure rate when one unit is under repair or inspection. Approximate expressions for reliability, mean time to failure, and asymptotic availability show the effects of the system parameters as well as of the shapes of the Cdf's of the times related to maintenance actions. For c.m., Markov modeling is a good approximation. For p.m., Markov modeling is a rough approximation; one can go to semi-Markov models or to the method of stages. Lastly, an approximate expression is given for the mean inspection interval which maximizes reliability and availability for p.m.     

RAM analysis of a navigational system by Markov technique: A case study

An analysis is made for a typical repairable Dual-VHF Omni Range (Dual-VOR), for prediction of its reliability, availability and maintainability by adopting Markov technique. Dual-VOR is a ground based azimuth navigational system for aircraft. The failure rates of various functional blocks for the Dual-VOR have been derived from the MIL-HDBK. The repair rates have been based on maintenance practices and repair policies adopted for the system. Markov modelling for reliability involves solving a set of differential equations. Markov modelling for availability involves solving a set of linear simultaneous equations. A simple technique which involves only the availability model has been adopted for determining the mean time to repair (MTTR). RAM analysis of “hot-standby” configuration of Dual-VOR has been discussed.     

A Unified Method for Analyzing Mission Reliability for Fault Tolerant Computer Systems

A reliability model is proposed and evaluated for a fault tolerant computer system which consists of multiple classes of modules and allows for degraded modes of performance. Each module of a given class has both an active and a passive hazard rate; constant hazard rates are assumed for active and dormant failures, and the given class may operate either in N Modular Redundancy (NMR: n + 1 out of 2n + 1 = N) or as a standby sparing system. The model allows for mission-phase changes at deterministic time points when the numbers of modules per class can be changed. The analysis proceeds by generalizing the notions of standby and NMR redundancy, which for N = 3 is TMR (Triple Modular Redundancy), into a concept called hybrid-degraded redundancy. The probabilistic evaluation of the unified redundancy concept is then developed to yield, for a given modular class, the joint distribution of success and the number of nonfailed modules from that class, at special times. With this information, a Markov chain analysis gives the reliability of an entire sequence of phases (mission profile).     

Reliability & Availability of Duplex Systems: Some Simple Models

The reliability and availability of a system can be enhanced by redundancy and repair. The reliability and availability are shown for some simple models of duplex systems, by using Markov methods. All transition rates between states are constant.     

Stochastic analysis of a general standby system with constant human error and arbitrary system repair rates

This paper presents a mathematical model for performing reliability and availability analyses of a general standby system with constant human error and common-cause failure rates. In addition, system repair times are assumed arbitrarily distributed. Markov and supplementary variable techniques were used to develop equations for the model. The method of linear ordinary differential equation is developed to obtain the general expressions of the steady state availability. The Laplace transform technique was used to obtain the system time-dependent availability, reliability and mean time to failure expressions.     

Comparisons of block diagram and Markov method system reliability and mean time to failure results for constant and non-constant unit failure rates

This paper presents a comparison of system reliability and mean time to failure results obtained using two different methods (i.e. block diagram and Markov) for the same system with constant and non-constant unit failures rates. The device of stages approach is used to obtain the non-constant unit failure rate when using the Markov method.     

Comparative redundancy, an alternative to triple modular redundant system design

A new scheme for implementing highly reliable digital systems is proposed. The method has a circuitry overhead which is comparable to that of the triple modular redundancy (TMR) scheme, although it is shown to have a reliability, and more importantly a mean time to failure, improvement well beyond that expected from the standard TMR systems. The reliability and mean time to failure are both developed from a discrete state, continuous time, Markov model of the new system. The results for the reliability and mean time to failure characteristics for this new design of system, termed comparative redundancy, are compared to both TMR and a single unit.     

Solving dependability/performability irreducible Markov models using regenerative randomization

Markov models are commonly used to asses the dependability/performability of fault-tolerant systems. Computation of many dependability/performability measures for repairable fault-tolerant systems requires the transient analysis of irreducible Markov models. Examples of such measures are the unavailability at time t and the s-expected interval unavailability at time t. Randomization (also called uniformization) is a well-known Markov transient analysis method and has good properties: numerical stability, well-controlled computation error, and ability to specify the computation error in advance. However, the randomization method is computationally expensive when the model is stiff, as is the case for Markov models of repairable fault-tolerant systems when the mission time of interest is large. Steady-state detection is a technique proposed to speedup randomization when the model is irreducible. This paper points out that another method, regenerative randomization, which has the same good properties as randomization, also covers irreducible models, and compares, for the important class of irreducible failure/repair models with exponential failure and repair time distributions and repair in every state with failed components, the efficiency of the regenerative randomization method with that of randomization with steady-state detection. In the frequent case in which the initial state is the state without failed components the regenerative randomization method can be faster than randomization with steady-state detection, especially when the model is large and the failure rates are much smaller than the repair rates. For other initial probability distributions, the regenerative randomization method seems to perform worse than randomization with steady-state detection.     

Cost analysis of a two-unit standby system under the influence of earthquakes

This paper deals with two models. In model 1, which is cold standby, when an earthquake comes the operation of the unit is stopped. In model 2, which is warm standby, a medium intensity earthquake will cause a short circuit failure mode. The repair is available immediately upon calling. In model 1, the failure rate is taken to be constant whereas the repair time distribution is arbitrary. In model 2, the failure and repair time distributions are considered to be arbitrarily distributed. Applying the regenerative theory in Markov renewal processes, various reliability characteristics of interest have been explicitly obtained.     

Automated analysis of phased-mission reliability

A method for automated analysis of phased mission reliability which considers the problem in terms of the construction of a continuous-time discrete-state Markov model and uses a standard Markov-chain solution technique that is adapted to the problem of phased missions is presented. The resulting state space is the union of the states in each independent phase, rather than the sum. This results in a model that can be substantially smaller than those required by other methods. A unified framework which is used for defining the separate phases using fault trees and for constructing and solving the resulting Markov model is discussed. The usual solution technique is altered to account for the phased nature of the problem. The framework is described for a previously published, simple three-component, three-phase system. An example in which a hypothetical two-phase application involving a fault-tolerant parallel processor is considered is given. The approach applies where the transition rates (failure and repair rates) are constant and where the phase change times are deterministic     

The number of working periods of a repairable Markov system duringa finite time interval

In reliability analysis, continuous parameter homogeneous irreducible finite Markov processes are used to model repairable systems with time-independent transition rates between individual states. The state space is then partitioned into the set of up states and the set of down states. The number of completed repair events during a finite time interval is an important (undiscounted) cost measure for such a system; it can be expressed in terms of the number of working periods during the same time interval. This paper derives a closed-form expression for the PMF of this latter quantity. The tool used is a recent result on the joint distribution of sojourn times in finite Markov processes. The MatLab implementation of the Markov model of a 2-unit parallel power transmission system is used to demonstrate the utility of the formula. The quantity examined is the number of completed repairs during a finite time interval. The method is viable in this case whereas the more usual randomization technique is not     

Robust transmission of MELP-compressed speech: an illustrative example of joint source-channel decoding

A mixed-excitation linear predictive (MELP) speech coder was selected as the US federal standard for 2400 b/s speech compression. This paper examines the quality of MELP-compressed speech when transmitted over noisy communication channels in conjunction with a variety of error-control schemes. The focus is on channel decoders that exploit the "residual redundancy" inherent in the MELP bitstream. This residual redundancy, which is manifested by the correlation in time and the nonuniform distribution of various MELP parameters, can be quantified by modeling the parameters as one-step Markov chains and computing the entropy rate of the Markov chains based on the relative frequencies of transitions. Moreover, this residual redundancy can be exploited by an appropriately "tuned" channel decoder to provide substantial coding gain when compared with decoders that do not exploit it. Channel coding schemes include conventional binary convolutional codes and iteratively-decoded parallel concatenated convolutional (turbo) codes.     

A non-homogeneous Markov model for phased-mission reliabilityanalysis

Three assumptions of Markov modeling for reliability of phased-mission systems that limit flexibility of representation are identified. The proposed generalization has the ability to represent state-dependent behavior, handle phases of random duration using globally time-dependent distributions of phase change time, and model globally time-dependent failure and repair rates. The approach is based on a single nonhomogeneous Markov model in which the concept of state transition is extended to include globally time-dependent phase changes. Phase change times are specified using nonoverlapping distributions with probability distribution functions that are zero outside assigned time intervals; the time intervals are ordered according to the phases. A comparison between a numerical solution of the model and simulation demonstrates that the numerical solution can be several times faster than simulation     

Reliability analysis of interconnection networks using hierarchicalcomposition

Based on the nature of the upper- and lower-bound block diagram models of multistage interconnection networks (MINs), a series system consisting of independent subsystems is considered. To model the reliability of such a system with online repair and imperfect coverage, the usual approach is to construct and solve a large, overall Markov model. A two-level hierarchical model is instead proposed in which each subsystem is modeled as a Markov chain and the system reliability is then modeled as a series system of independent Markov components. This technique is extended to compute the instantaneous availability of the system with imperfect coverage and online repair. Extensions to allow for transient faults and phase-type repair time distributions are straightforward. It should be possible to apply this approach to other fault-tolerant MINs and to any system that can be modeled as a series system where each subsystem has a parallel-redundant structure     

Some Applications of Regenerative Stochastic Processes to Reliability Theory?Part Two: Reliability and Availability of 2-Item Redundant Systems

Part-two uses regenerative processes to develop very general expressions for the reliability and for the point-availability of a system composed of two s-identical, repairable items working in warm redundancy. It is assumed that: a) the failure rate is arbitrary in the operating state, but constant in the reserve state, b) the repair rates are arbitrary, c) the system has only one repair crew and has no preventive maintenance, d) switching is perfect. The results for this model are then successively simplified to cover some well known particular cases.     

Redundant-system demonstrated-reliability approximation usingpiece-part failure rates

A method of obtaining the reliability of a redundant system when only the part force-of-mortality estimates (hazard rates) for electronic parts are available is presented. Part failures are reported without specifying whether the parts are configured in series or in parallel. The sum of all the part failure rates in the system, recorded from the turn-on date of the system up to the present time of monitoring, and the sum of the failure rates of all the parts in the system recorded up to a certain previous time after the system turn-on date are calculated. The system reliability for a certain critical mission time, with or without redundancy, is calculated at that previous time. The method is useful in field-equipment reliability monitoring because exact computation is impossible without knowing whether the failed parts are configured in series or in parallel. Generally, Monte Carlo simulation should be used only to verify the results calculated through an analytic method, if such a method is available and is neither time consuming nor cost prohibitive. A dimensionless reliability parameter is introduced     

三余度飞控计算机架构及其可靠性研究

余度架构设计是解决飞控计算机可靠性问题的有效途径。为了满足高可靠性飞控计算机系统对可靠性和容错性的特殊要求的目的,提出一种新型三余度飞控计算机的余度架构方案,描述飞控计算机冗余设计方法,设计余度计算机软硬件的总体框架,采用马尔可夫方法对该方案进行了可靠性分析,获得了故障覆盖率和失效率对飞控计算机整体可靠性的影响结果,得到所设计余度架构方案可行的结论。     

三模冗余演化自修复系统可靠性及状态规律分析

为研究三模冗余演化自修复系统可靠性及状态规律,首先给出了系统架构及其工作 流程,继而以马尔科夫(Markov)过程理论为基础对其进行了可靠性建模,最后基于此模型对 系统可靠 性及状态规律进行了仿真研究。结果表明：修复率与故障率比值是影响系统可靠性的 主要因素;系统运作区间以可用度与可靠度差值的极值分为两大部分,极值点前,系 统主要处于状态0、1,演化修复作用对系统可靠性贡献不大;极值点后,系统在状态1、2间 转换概率提高,演化修复作用成为提高系统可靠性主要因素。所得结论对特定环境中系统的 设计、应用、评估具有一定的理论指导意义。