Phased-mission system reliability under Markov environment

The authors show how to determine the reliability of a multi-phase mission system whose configuration changes during consecutive time periods, assuming failure and repair times of components are exponentially distributed and redundant components are repairable as long as the system is operational. The mission reliability is obtained for 3 cases, based on a Markov model. (1) Phase durations are deterministic; the computational compact set model is formulated and a programmable solution is developed using eigenvalues of reduced transition-rate matrices. (2) Phase durations are random variables of exponential distributions and the mission is required to be completed within a time limit; the solution is derived as a recursive formula, using the result of case 1 and mathematical treatment-a closed-form solution would be prohibitively complex and laborious to program. (3) Phase durations are random variables and there is no completion time requirement; the solution is derived similarly to case 1 using moment generating functions of phase durations. Generally, reliability problems of phased-mission systems are complex. The authors' method provides exact solutions which can be easily implemented on a computer     

相关竞争失效场合雷达功率放大系统可靠性评估

针对相关竞争失效场合难以获取高可靠部件的性能分布信息,无法对系统可靠性进行准确估计的问题.提出了相关竞争失效场合下考虑认知不确定性的多态系统可靠性评估方法.该方法首先通过假定部件突发失效阈值为递减型随机过程来表征累积退化与突发失效的相关性,同时为降低对部件认知不确定性的影响,假定冲击引起的部件性能损伤分布参数和突发失效参数均为区间变量,建立基于区间变量的部件性能分布模型;而后对传统的通用生成函数方法进行改进,给出了区间通用生成函数的定义及其运算法则;最后对某型雷达功率放大系统的可靠性进行分析.该方法不仅克服了部件的失效模式复杂、状态信息少的不足,且方法简单、思路清晰,具有很强的通用性和工程应用价值.     

On the reliability of a cold standby system attended by a single repairman

We present a reliability analysis of a multiple cold standby system satisfying the usual conditions (i.i.d. random variables, single repair facility, perfect repair, queueing). Each unit has a constant failure rate but an arbitrary repair time distribution. We introduce a basic set of measures related to a stochastic process defined on some filtered probability space. The set of measures constitutes a system of renewal integral equations. The solution is constructed by means of a Cauchy integral. A particular case (deterministic repair) provides some explicit results illustrated by a computer-plotted graph.     

Failure Probability of Strict Consecutive-k-out-of-n:F Systems

A system with n components in sequence is a strict consecutive-k-out-of-n:F system if and only if it fails when at least k consecutive components are failed, but isolated strings of component failures of length less than k do not occur. This paper gives the failure probability function of a strict linear consecutive-k-out-of-n:F system in a closed form. The calculation of the failure probability of a strict circular consecutive-k-out-of-n:F system is reduced to the linear case.     

A reliability physics model for parallel system

Reliability analysis of a nonrepairable 2-unit parallel system is carried out using the stress-strength model of failure physics. The analysis is carried out for correlated strengths and altered stress distribution depending upon the number of components surviving. The analysis includes both the cases of deterministic and random cycle times. In the case of random cycle times, Poisson distributed stress cycle occurrences have been considered. Various system characteristics, such as failure time distribution, reliability and moments of time to failure of the system, have been evaluated for both deterministic and random cycle times. Two particular cases, namely (i) bivariate exponential distribution for strength variables and univariate exponential distributions for stress variables and (ii) bivariate normal distribution for strength variables and univariate normal distributions for stress variables, have also been considered.     

Generalized moment matching for the linear combination of lognormal RVs: application to outage analysis in wireless systems

Moving from the need for a simple and versatile method for outage computation in various contexts of interest in wireless communications, in this paper we propose a lognormal approximation for the linear combination of a set of lognormal random variables (RV) with one-sided random weights. The approximation is based on a generalization of the well known moment matching approximation (MMA) for the sum of lognormal RVs, and it allows quite simple handling of the power sum of interfering signals even in rather complicated scenarios. Specifically, composite multiplicative channel models with unequal parameters can be handled, and generic (unequal) correlation patterns for some channel components can be handled with reference to any pair of signals. At this stage of the computation, only moments of the random weights are required. The probability density function of the random weight for the useful signal component may be required in computing outage probability, and numerical methods may be only required to solve a single integral at this second stage. The suitability of the approximation is examined by evaluating outage performance for various values of system parameters in some contexts of interest, namely spread spectrum systems and typical reuse-based systems with composite Rayleigh-lognormal and Nakagami-lognormal channels.     

A New Method to Determine the Failure Frequency of a Complex System

Two key indices in system reliability evaluation are the probability that the system is failed and the frequency of system failure. Other measures such as the mean cycle time and the mean down time can be easily derived from these quantities. This paper considers the reliability evaluation of a complex maintainable system using a cut set approach. The available literature on this subject generally deals with the failure probabilities. The technique proposed by Buzacott to determine the frequency of failure has the drawback that explicit formulae for system availability must be first derived. Numerical values are then obtained by further manipulation. This approach is, therefore, not suitable for computer application. The contribution of this paper is the development of a new formula for the frequency of system failure using a cut set approach, from which the numerical values can be obtained directly. This method overcomes the drawback of Buzacott's method and is suitable for computer application. Upper and lower bounds for frequency are also given and the method is illustrated by an example.     

Closed-form expressions for distribution of sum of exponentialrandom variables

In many systems which are composed of components with exponentially distributed lifetimes, the system failure time can be expressed as a sum of exponentially distributed random variables. A previous paper mentions that there seems to be no convenient closed-form expression for all cases of this problem. This is because in one case the expression involves high-order derivatives of products of multiple functions. The authors prove a simple intuitive multi-function generalization of the Leibnitz rule for high-order derivatives of products of two functions and use this to simplify this expression, thus giving a closed form solution for this problem. They similarly simplify the state-occupancy probabilities in general Markov models     

General Probability of System Failure

This paper presents a general method to determine probabilities of failure of any fixed subset of coherent system components under various conditions. The method uses a known reliability structure of the system and the known joint probability distribution of its component times-to-failure. This method is universal and can be applied in many cases. Nevertheless, for large systems it is troublesome. In practice a problem is solved using a numerical program.     

Fault-Tree Analysis by Fuzzy Probability

In conventional fault-tree analysis, the failure probabilities of components of a system are treated as exact values in estimating the failure probability of the top event. For many systems, it is often difficult to evaluate the failure probabilities of components from past occurrences because the environments of the systems change. Furthermore, it might be necessary to consider possible failure of components even if they have never failed before. We, therefore, propose to employ the possibility of failure, viz. a fuzzy set defined in probability space. The notion of the possibility of failure is more predictive than that of the probability of failure; the latter is a limiting case of the former. In the present approach based on a fuzzy fault-tree model, the maximum possibility of system failure is determined from the possibility of failure of each component within the system according to the extension principle. In calculating the possibility of system failure, some approximation is made for simplicity.     

Approximate Confidence Intervals for Reliability of a Series System

Two solutions are proposed for estimating s-confidence intervals for reliability of a repairable series system comprised of non-constant failure rate components: 1) the system is treated as a sum of renewal processes with the mean and variance of total number of system failures being computed from the moments of failure times of the components; and 2) a pseudo-Bayesian solution is derived for the mean and variance of the log-reliability of a system of Weibull components. In both solution approaches, the central limit theorem is invoked for a sum of component random variables determined from test data such as number of failures or log-reliabilities. s-Confidence limits are then approximated using Gaussian probability tables. The intervals derived yield close-to-exact frequency limits, depending on such variables as number of test failures, number of components, and component parameters.     

Failure Time for a Redundant Repairable System of Two Dissimilar Elements

The distribution of time to failure for a system consisting of two dissimilar elements or subsystems operating redundantly and susceptible to repair is discussed. It is assumed that the times to failure for the two system elements are independent random variables from possibly different exponential distributions, and that the repair times peculiar to each element are independently distributed in an arbitrary fashion. For this basic model a derivation is given of the Laplace-Stieltjes transform of the distribution function of time to system failure, i.e, the time until both elements are simultaneously down for repair, measured from an instant at which both are operating. An explicit formula is given for the mean or expected time to system failure, a natural approximation to the latter is exhibited, and numerical comparisons indicate the quality of this approximation for various repair time distributions. In a second model the possibility of system failures due to overloading the remaining element after a single element failure is explicitly recognized. The assumptions made for the basic model are augmented by a stochastic process describing the random occurrence of overloads. Numerical examples are given. Finally, it is shown how the above models may be easily modified to account for delays in initiating repairs resulting from only occasional system surveillance, and to account for random catastrophic failures.     

Physical Analysis of Stress Testing for Failure of Electronic Components

Starting with an assumption concerning the type of physical process causing failure and an assumption concerning the random distribution of components with respect to a failure threshold. cumulative distribution functions in time, temperature, and voltage are derived. These cumulative distribution functions are identical to each other if the random variables are certain functions of time, temperature, or voltage, thus showing the equivalence of time, temperature, and voltage as stresses. The cumulative distribution function in time is the familiar log-normal function. If it is known that the assumed physical process is the only one causing failure, then one can rigorously replace time by temperature or voltage. However, it is demonstrated that in an accelerated test, i.e., one in which time is replaced by another stress such as temperature, one can never be sure that another process will not be predominant at longer times; thus, one can never make a certain extrapolation to longer times. One might be able to circumvent this difficulty by having a thorough knowledge of the physics, chemistry, and metallurgy of the possible failure processes in the component.     

A simple procedure of computing variance sensitivity coefficients of top events in a fault tree

If there is uncertainty in the reliability (unreliability) of a system, it is necessary to know the components whose probability of uncertainty contribute significantly to the uncertainty of probability of the whole system. This helps in deciding the components for which more data should be collected so that the uncertainty of system failure probability can be reduced. To this end, Nakashima et al. [K. Nakashima et. al., Trans. IECE Jpn E65, 194–201 (1982)] introduced the concept of variance sensitivity coefficients and importance measures, and derived expressions using the Taylor series expansion. These expressions are lengthy even for simple series and parallel systems. In this paper a new method of computing the same measures is derived and an algorithm is described which computes the sensitivity coefficients and importance measures simultaneously. The method is also extended to a system with correlated variables.     

Alternative proofs for “On unique localization ofconstrained-signal sources”

We provide simple proofs for the theorems in “On Unique Localization of Constrained-Signal Sources” by M. Wax (see ibid. vol.40, p.1542-1547, June 1992). The approach is based on the topological dimension of a set. All the possible observation matrices form the legitimate set. The observation matrices that can have nonunique solutions form the ambiguity set. The components of the legitimate and ambiguity set are random matrices. We find the conditions under which the dimensionality of the ambiguity set is smaller than the dimensionality of the legitimate set. In such a case, the probability of the ambiguity set is zero and with probability one, a unique solution can be found for the localization problem     

First failure time of dependent parallel systems with safety periods

In this paper we consider the time to first failure of a parallel system in which the failure and repair rates of components depend on the state of the other components as well. A back-up unit with a random lifetime is employed whenever all the components of the system are down. The system fails when all the components of the system and the back-up unit are down. The first moment, the Laplace transform and the probability distribution of the time to first failure of this system are obtained. Sufficient conditions under which this distribution has the new better than used (NBU) and an exponential limit property are given. Special cases with phase type and deterministic back-up unit lifetimes are also considered. These results extend the results of Ross and Schechtman (1979).     

金属膜电阻失效前后概率分布及可靠性分析

产品在加工时总会有不可控的因素影响产品质量的稳定性,为解决这一问题,本文从可靠性分布函数的角度提出了提高电阻质量的方法。本文通过对金属膜电阻进行步进应力加速寿命试验以及电阻失效前后概率分布试验,得到了失效前后的阻值概率分布函数及正常应力下的概率分布函数与可靠性指标。实验结果表明,电阻阻值失效前后分布都属于威布尔分布。同时,给出了电阻损伤7.2%~15.6%,且失效模型为持续施加电压下不可逆的积累损伤模型时的分布函数,并获得了合格电阻与冒烟损坏电阻概率分布曲线的明显区别,从而,有可能从概率分布角度定义电阻的质量特性。     

Copper wire interconnect reliability evaluation using in-situ High Temperature Storage Life (HTSL) tests

This paper describes the use of in-situ High Temperature Storage Life (HTSL) tests based on a four point resistance method to evaluate Cu wire interconnect reliability. Although the same set up was used in the past to monitor Au–Al ball bond degradation, a different approach was needed for this system. Using conventional statistical methods of failure probability distributions and a fixed failure criterion were found to be unsuitable in this case. Besides this, tests usually take very long until a sufficient percentage of the population have failed according to that criterion. A simple physical model was used to electrically quantify ball bond degradation due to the prevailing failure mechanism in a substantially smaller amount of test time. The method enabled the determination of activation energies for a number of moulding compounds and is extremely useful for a fast screening of such materials regarding their suitability for Cu wire.     

A Probability Method for Determining the Reliability of Electric Power Systems

Reliability measures how well a system can be expected to perform its intended purpose; it is expressed as a probability function with time and environment as variables. This paper discusses the mechanics of component failure and repair and shows that power system behavior follows a Markov process. The reliability of simple system configurations is evaluated analytically by solving the Markov equations. The reliability of complex systems is more easily evaluated by the use of digital computer simulation. The simulation method is described.     

ESCAF for MTBF, Time Evolution, Sensitivity Coefficients, Cut-Set Importance, and Non-Coherence of Large Systems

ESCAF - an "Electronic Simulator to Compute and Analyze Failures" ? is a commercially available desktop apparatus, now in wide use, which employs special electronic circuit boards to simulate and analyze a system by methods and procedures that are easy to learn and apply by engineers with only very limited knowledge of electronics or computing. The apparatus has been used mainly to determine the cut sets and failure probabilities of very large systems, with up to 416 components, offering possibilities well beyond those of conventional methods of analysis. This article defines new parameters that can be calculated by ESCAF, including novel parameters (degree of non-coherence). It also explains how ESCAF determines, for systems of any complexity, measures that were previously inaccessible for other than very simple systems: ? Mean time between failures, mean time to failure, mean time to repair, failure and repair intensities, and equivalent failure or repair rates as a function of time, ? Time-derivative of the unavailability and/or failure probability, ? Sensitivity coefficients indicating the importance of each component in probability calculation, ? Importance of each minimal cut set (for coherent systems), ? Whether a system is coherent or not. The first three results can be obtained regardless of system coherency. All results are obtained very simply and very rapidly.