Markov Approach to Finding Failure Times of Repairable Systems

In analyzing repairable systems it is often necessary to determine such parameters as availability, mean cycle time, and mean time to first failure. These and other failure time measures are defined, and methods of calculating them using a Markov approach are developed. Although conceptually simple, these methods are often not practically feasible because of the large number of possible system states. Various special techniques such as lumping states or decomposing the system into independent subsystems are discussed. These techniques, if applicable, can simplify the analysis considerably.     

Quantitative Reliability Evaluation of Repairable Phased-Mission Systems Using Markov Approach

A quantitative reliability model for a phased mission system is developed using a Markov process. Two cases for the mission-phase change times are assumed: 1) to be known in advance and 2) to be random variables. A method of solution is presented and illustrated by examples. The solution of phased-mission systems is equivalent to solving a sequence of uni-phase systems with appropriate initial conditions.     

Generalized Linear Mixed Models for Reliability Analysis of Multi-Copy Repairable Systems

The power law process (PLP) is usually applied to failure data from a single repairable system. When a system has a number of copies for analysis, the usual approach is to assume homogeneity among all system copies, and then to pool data from these copies. In the real world, however, it may be more reasonable to assume heterogeneity among the system copies. Therefore, this paper proposes a new generalized linear mixed model (GLMM), called PLP-GLMM, to analyse failure data from multi-copy repairable systems. In the PLP-GLMM, the underlying model for each system copy is assumed to be a PLP at Stage 1, and parameters vary among copies at Stage 2. The PLP-GLMM can make inferences about both the population, and each system copy when accounting for copy-to-copy variance. A modified Anderson-Darling test is adapted to the goodness-of-fit test of the PLP-GLMM. A numerical application is given to show the effectiveness of the model     

Limitations of Minimal Cut-Set Approach in Evaluating Reliability of Systems with Repairable Components

This work shows that, when system components are repairable, system reliability cannot be evaluated exactly by means of the fault tree approach; only a system reliability lower bound can be obtained.     

The Reliability of Repairable Complex Systems Part B: The Dissimilar Machine Case

A generalization of the reliability model given in Part A of this reliability study is made. The failure and repair rates are assumed to be exponential as in Part A, but the model equations are changed so that the following ramifications are possible. 1) The label case: it is necessary to know which of the similar machines are broken down in order to decide if a system failure has occurred. 2) The parameter case: the values of the failure and repair rates are not the same on each machine. 3) The type of failure case: the system goes from state i to i + j after a failure, j ? 1, and to i - k after a repair, k ? 1, whereas in Part A j = k = 1 only. A procedure for finding dissimilar machine model equations with time delays before failure and time restoration constraints after repair are given.     

Burn-In Programs for Repairable Systems

Burn-in programs are often used for automotive or airplane engines in order to eliminate early failures due to ineffective adjustments and similar repairable sources of failure. We assume that there are two operating states: Good and Poor. Each has its own reliability characteristic, and neither necessarily has any statistical property that improves with bum-in. The purpose of the bum-in program is to uncover the Poor engines and then to repair them to the Good state. We calculate the mean time to failure of such engines when a burn-in program is used and derive conditions under which a burn-in program is justified.     

Evaluation of Repairable System Reliability Using the ``Bad-As-Old' Concept

It is usually assumed that the underlying distribution of times to failure of systems is the exponential distribution. This is justified on the basis of the bathtub curve or Drenick's theorem, but the bathtub curve is merely a statement of plausibility and conflicts with Drenick's theorem. Even if exponentiality is not assumed, it is usually assumed that a system under study is as-good-as-new after repair. This is not a plausible assumption to make for a complex system. If failure data are available they should be tested for trend among successive failure times. If a trend exists, a time dependent (nonhomogeneous) Poisson process (called bad-as-old model in this paper) should be fitted and tested for adequacy. This paper is not intended to provide a rigorous, definitive treatment of bad-as-old models. Rather, it has three main purposes: 1) to point out the glaring, but somehow usually overlooked, inconsistency between the commonly accepted concept of wearout of repairable systems and the a priori use of renewal processes for modeling these systems; 2) to outline basic procedures for evaluating data from repairable systems and for formulating bad-as-old probabilistic models; and 3) to present the results of Monte Carlo simulations, which illustrate the grossly misleading results which can occur if independence of successive failure times is invalidly assumed.     

Availability of Some Repairable Computer Systems

A mathematical model is established for the availability of a modularly redundant repairable system which consists of many active units and one standby; coverage is considered. The hazard rates for an active unit and for the standby unit are different and are assumed to be constant. Repair time distributions are general. Availability for the system, mean system up-time, and mean system down-time are derived.     

A Squeeze Response Surface Methodology for Finding Symbolic Network Reliability Functions

A new response surface methodology (RSM) called the squeeze response surface methodology (SRSM) is proposed to gain the approximate symbolic network reliability function (SNRF). The proposed SRSM can be used to solve not only complicated system configurations, but also help decision makers gain greater understanding for the structure of the system. The response value is the value of the Bonferroni bounds (using by-products of cellular automata (CA) Monte Carlo simulation (MCS), and min-cuts) minus the simulation value (obtained from CA-MCS). SRSM squeezes the range of response values to improve solution quality. Our results compare favorably with previously developed algorithms in the literature from the experiment of the benchmark example.      

On Reliability Prediction of Repairable Redundant Digital Structures

Taking into account the real characteristics of redundant digital structures leads to neglect of failures occuring during the repair instants. The formal definition of the corresponding hypotheses leads to a simplified Markov model which a) is homogenous and b) has instantaneous repairs. At last, the paper describes the way by which the validity of the hypotheses can be judged.     

A Technique for the Analysis of Repairable Redundant Systems

A new analytical technique is presented for evaluating the steady-state performance of large repairable systems which cannot be described in terms of series-parallel subsystems. The method, which is based on a novel combinatorial algorithm, is used to calculate the frequency of failures and expected failure durations at each node in networks of repairable devices. The networks may have multiple input and output nodes, but the uptimes and downtimes of the devices in the network are assumed to be exponentially distributed and independent. To demonstrate the usefulness of the technique for large-scale networks of general configuration, the solution of a sample problem using a pilot computer program is also included.     

可修复网络稳态可用度分析

本文提出了可修复网络稳态可用度的数学分析方法。通过证明得出不可修复网络的可靠性多项式适用于可修复网络的可用度，只需相应地把部件的可靠度改为部件的可用度，把部件的不可靠度改为部件的不可用度     

可修排队系统中可靠性指标的分解

本文提出了一种分析可修排队系统的新信息处理－分解法，应用该方法我们重新讨论了服务器可修的Ｍ／Ｇ／１排队系统，获得服务器在时刻ｔ失效的概率和在（０，ｔ］中失效的平均次数这两个主要可靠性指标的分解结果，而且进一步分析了服务器可修的ＧＩ／Ｇ１排队系统。值得注意的是本文提出的解解法新颖、简洁。     

Optimum Preventive Maintenance Policies for Repairable Systems

This paper summarizes my recent work in analyzing preventive maintenance of the following kinds of repairable systems: 1-unit systems, 2-unit standby systems, and a system with unrepairable spare units. Some appropriate reliability measures of such systems are given, and optimum preventive maintenance policies which maximize or minimize these measures are derived under suitable conditions.     

Cost-Optimized Burn-In Duration for Repairable Electronic Systems

A mathematical model permits determining the duration of cost-optimized burn-in and evaluating the resultant saving for repairable electronics systems. Infant mortality failures occur according to a nonhomogeneous Poisson Process; repair actions restore the system to a bad-as-old condition. The s-expected costs associated with factory and field failures are traded-off with the costs of implementing a burn-in program. Under the constraints of the model, the optimum burn-in duration and consequent cost saving are independent of the eventual life of the system in the field. A numerical example illustrates these concepts.     

提高粒子碰撞噪声检测试验可靠性的途径

文章从粒子碰撞噪声检测(PIND)试验的原理入手，着重阐述了影构PIND试验的因素和提高PIND试验可靠性的途径。通过对PIND试验的波形分析来提高PIND试验的可靠性，使试验数据更客观、准确，以此来保证和提高产品质量。     

证券交易网络系统的可靠性与硬件实现

证券交易网络系统的主要功能是进行证券交易数据的传输、维护和计算,要求具备很高的实时性和可靠性。文章介绍了该系统的组成结构和技术特点,并从提高系统可靠性的角度出发,提出了具体的解决途径,实践证明方法是行之有效的。     

Reliability of a Repairable Multicomponent System with Redundancy in Parallel

Consider a multicomponent system consisting of two series subsystems. One contains identical components connected in parallel, while the other has nonalike components connected in series. Each component has constant hazard rate, while the subsequent repairs follow some general distributions. The supplementary variable technique developed by Kielson and Kooharian [1] and the phase technique are used to obtain the various time-dependent and steady-state solutions for the system. A numerical illustration compares the effect of two repair policies on the behavior of the system. The optimum number of components connected in parallel is obtained.     

State-Transition Monte Carlo for Evaluating Large, Repairable Systems

This paper presents a new Monte Carlo method to estimate unreliabilities of large, repairable systems which can be modeled by a stationary Markov transition diagram. Sequences of state transitions ending at absorbing states are generated, using random numbers. Times to transitions related to the state-sequences are not generated. Next, the probability of system failure occurring in a mission time along each state-sequence is calculated. Finally, the arithmetic mean of these probabilities estimates the system unreliability. This state transition Monte Carlo method yields better estimates in fewer trials than direct Monte Carlo methods. A cold-standby problem with non-identical units is also solved as a by-product of this paper.     

一种计算可修复网络可用度的快速算法

对于可修复系统,其状态数随系统规模呈指数增长。文中在系统元件类型相同的假设条件下,以维修顺序为突破口剖析马尔可夫模型,证明在某几种维修顺序条件下,可由类状态概率来计算类状态中单个状态的概率;并以可修复网络系统为例提出了从类状态到不交和状态的映射算法,从而使计算网络可用度的复杂度大大降低。仿真结果表明合并策略和映射算法的正确。