A Decomposition Method for Computing System Reliability by a Boolean Expression

A substitutionary decomposition method for computing the reliability of a redundant system S given by a Boolean expression is proposed, System S is decomposed into two subsystems S(x) and S(x?) according to up-and down-states of its keystone variable x. This is repeated until all terms become s-independent in each decomposed subsystem. A criterion for choosing the keystone variable and a property which saves computation time are obtained.     

Reliability analysis of an automotive transmission system

The complexity of vehicles and equipment in present day defence services is growing considerably, and the importance of equipment availability as a prime battle-winning factor for the defence services cannot be overemphasized. In defence services the reliability in totality of an automotive system such as a battle tank, troop carrier, etc. is essential to meet the inescapable warlike requirements. It is not in the interest of any fighting force to go into operation with the slightest doubt about the performance of the equipment. To keep the warlike equipment/vehicles rolling, all subsystems need to be in serviceable condition in all types of terrain. One of the most essential subsystems whose reliability cannot be compromised at any stage is the transmission system. In the present paper a reliability analysis of an automotive transmission system of the general service type of vehicle being used by the Indian Army is reported. The complete transmission system has been subdivided into 12 subsystems and maintenance policies for these 12 subsystems have also been suggested.     

Bayesian Decomposition Method for Computing the Reliability of an Oriented Network

For a nonoriented network, Bayesian decomposition is straightforward and well known. A keystone element is assumed perfect (shorted), then failed (open) and the reliabilities of the two subnetworks are calculated. But for an oriented network, when the keystone element is assumed perfect, it cannot always be shorted (the 2 nodes brought together), because even a perfect element still retains its orientation. A technique for choosing keystone elements is proposed.     

Symbolic reliability analysis via Shannon's expansion and statistical independence

A simple procedure for evaluating the symbolic reliability of a complex system in presented. The switching (Boolean) functions of system success and system failure are expressed as the intersections of complements to the prime implicants of these functions. Shannon's expansion about suitable keystone variables is repeatedly applied to either or both functions until subexpressions with statistically independent terms are obtained. The procedure applies to a variety of reliability problems. In addition, it is relatively fast and yields simple symbolic expressions.     

Survey of reliability and availability evaluation of complex networks using Monte Carlo techniques

Generally there are four main difficulties in evaluating complex large-scale system reliability, availability and MTBF: the system structure may be very complex; subsystems may follow various failure distributions; subsystems may conform to arbitrary failure and repair distributions for maintained systems; the failure data of subsystems are sometimes not sufficient, reliability test sample sizes tend to be small. It is difficult and often impossible to obtain s-confidence limits of them by classical statistics. Monte Carlo technique combined with Bayes method is a powerful tool to solve this kind of problems. In this survey, the typical existing Monte Carlo reliability, availability and MTBF simulation procedures, variance reduction methods, and random variate generation algorithms are analyzed and summarized. The advantages, drawbacks, accuracy and computer time of Monte Carlo simulation in evaluating reliability, availability and MTBF of a complex network are discussed. Finally, some conclusions are drawn and a general Monte Carlo reliability and MTTF assessment procedure is recommended.     

Optimal design of k-out-of-n:G subsystems subjected to imperfect fault-coverage

Systems subjected to imperfect fault-coverage may fail even prior to the exhaustion of spares due to uncovered component failures. This paper presents optimal cost-effective design policies for k-out-of-n:G subsystems subjected to imperfect fault-coverage. It is assumed that there exists a k-out-of-n:G subsystem in a nonseries-parallel system and, except for this subsystem, the redundancy configurations of all other subsystems are fixed. This paper also presents optimal design polices which maximize overall system reliability. As a special case, results are presented for k-out-of-n:G systems subjected to imperfect fault-coverage. Examples then demonstrate how to apply the main results of this paper to find the optimal configurations of all subsystems simultaneously. In this paper, we show that the optimal n which maximizes system reliability is always less than or equal to the n which maximizes the reliability of the subsystem itself. Similarly, if the failure cost is the same, then the optimal n which minimizes the average system cost is always less than or equal to the n which minimizes the average cost of the subsystem. It is also shown that if the subsystem being analyzed is in series with the rest of the system, then the optimal n which maximizes subsystem reliability can also maximize the system reliability. The computational procedure of the proposed algorithms is illustrated through the examples.     

Reliability and ageing of repairable systems

This paper discusses some of the complexities of ageing repairable systems, especially those relating to computation of their reliability. In order to cope with them in a realistic manner, a discrete event simulation model using the time between successive failures of the subsystems has been proposed. The model has been used for the evaluation of improvement or deterioration of system reliability with increasing age. The effects of the design modification of one or more subsystems on the system reliability are studied by conducting simulation experiments. Live data from the operation of a fleet of trainer aircraft is used for illustration purposes; the results are presented and discussed.     

Symbolic Reliability Analysis with the Aid of Variable-Entered Karnaugh Maps

A method for finding the symbolic reliability of a moderately complex system is presented. The method uses Bayesian decomposition to reduce the system into simpler series-parallel subsystems. The successes or failures of these subsystems are found by inspection and then recast into disjoint sum-of-product forms with the aid of the Karnaugh map. Subsequently, an almost minimal disjoint expression for the system success or failure is obtained with the aid of a variable-entered Karnaugh map (VEKM). This VEKM method is illustrated by applying it to some examples recently solved in the literature. The main advantage of the method is the pictorial insight it provides to the reliability analyst.     

Approximation Formulas for Reliability with Repair

A system consists of n-identical parallel subsystems, each having an exponential distribution of times to failure and an exponential distribution of times to repair. The system reliability with repair is the probability of no more than q out of n subsystems being simultaneously in a failed state during time t. Under conditions frequently met in practice, system reliability with repair R(t) can be approximated by: R(t) ? exp [?t/Tm] where Tm is the mean time for the system to pass for the first time from zero to (q + 1) simultaneous subsystem failures. Exact and approximate methods of calculating Tm are developed. A detailed error analysis is presented showing the limitations of using Tm to calculate system reliability with repair.     

A scenario-based reliability analysis approach for component-based software

This paper introduces a reliability model, and a reliability analysis technique for component-based software. The technique is named Scenario-Based Reliability Analysis (SBRA). Using scenarios of component interactions, we construct a probabilistic model named Component-Dependency Graph (CDG). Based on CDG, a reliability analysis algorithm is developed to analyze the reliability of the system as a function of reliabilities of its architectural constituents. An extension of the proposed model and algorithm is also developed for distributed software systems. The proposed approach has the following benefits: 1) It is used to analyze the impact of variations and uncertainties in the reliability of individual components, subsystems, and links between components on the overall reliability estimate of the software system. This is particularly useful when the system is built partially or fully from existing off-the-shelf components; 2) It is suitable for analyzing the reliability of distributed software systems because it incorporates link and delivery channel reliabilities; 3) The technique is used to identify critical components, interfaces, and subsystems; and to investigate the sensitivity of the application reliability to these elements; 4) The approach is applicable early in the development lifecycle, at the architecture level. Early detection of critical architecture elements, those that affect the overall reliability of the system the most, is useful in delegating resources in later development phases.     

Optimal Design of a Series-Parallel System with Time-Dependent Reliability

The paper formulates an optimal reliability design problem for a series system made of parallel redundant subsystems. The variables for optimization are the number of redundant units in each subsystem and the reliability of each unit. There is a cost-constraint. The time for which the system reliability exceeds a specified value is to be maximized. Similarly the cost could be minimized for a constraint on the mission time and reliability. A solution method for the formulated problems is presented along with an example.     

Reliability Growth Apportionment

A method is presented for apportioning reliability growth to the subsystems that make up a system in order to achieve the required reliability at least cost. Reliability growth apportionment is handled as an s-expected cost minimization problem subject to the constraint of meeting a system reliability requirement. The problem is formulated in terms of Duane's reliability growth model, and is solved using geometric programming. The method can be useful in the early stages of system design to determine subsystem reliability growth that will allow a system reliability requirement to be met, and in the latter stages of system design when reliability has fallen short of the required goal and improvements are necessary.     

Steady-State Reliability of Systems of Mutually Independent Subsystems

Predicting the reliability of a redundant system with repair is considerably simplified when the system can be subdivided into mutually independent subsystems. Results can be obtained without knowing the failure of repair time distributions of the subsystems. In this paper formulae are developed for the ``steady-state' availability and MTBF of a complex system in terms of the availabilities and MTBF's of its constituent subsystems. The basic concepts required are introduced and discussed in a review of a simplex system. These concepts are then applied to a complex system to obtain the main results of the paper. Finally, two examples are given to illustrate the application of these results.     

Bayesian Confidence Limits for the Reliability of Mixed Exponential and Distribution-Free Cascade Subsystems

The problem treated here is the theoretical one of deriving exact Bayesian confidence intervals for the reliability of a system consisting of some independent cascade subsystems with exponential failure probability density functions (pdf) mixed with other independent cascade subsystems whose failure pdf's are unknown. The Mellin integral transform is used to derive the posterior pdf of the system reliability. The posterior cumulative distribution function (cdf) is then obtained in the usual manner by integrating the pdf, which serves the dual purpose of yielding system reliability confidence limits while at the same time providing a check on the derived pdf. A computer program written in Fortran IV is operational. It utilizes multiprecision to obtain the posterior pdf to any desired degree of accuracy in both functional and tabular form. The posterior cdf is tabulated at any desired increments to any required degree of accuracy.     

Bayesian Confidence Limits for the Reliability of Cascade Exponential Subsystems

The problem treated here is that of deriving exact Bayesian confidence intervals for the reliability of a cascade system consisting of N independent subsystems each having an exponential distribution of life with a failure rate which is estimated from life test data. The posterior probability density function of the system reliability is derived in closed form, using the method of the Mellin integral transform. The posterior distribution function is obtained, yielding Bayesian confidence limits on the total system reliability. These results, which are believed to be new for N > 3, have an immediate application to problems of reliability evaluation and test planning.     

神光Ⅲ片状放大器系统可靠性仿真研究

片状放大器系统是神光Ⅲ装置主放系统的基本组成单元,也是最重要的组成单元,其可靠性水平直接影响到整个装置的可靠运行情况。首先对片状放大器系统的结构进行简要介绍,然后建立可靠性模型,给出了片状放大器系统可靠性仿真的算法和程序流程,最后给出了仿真结果,并对结果进行了简要分析。     

Steady-state availability of a system with two subsystems working alternately

The authors have considered the reliability aspect of a system with two subsystems working alternately in the previous paper in this issue. As the system was modelled on an electric power system with two subsystems of hydroelectric power supply and thermal electric supply, the steady state availability of the system assumes importance. We have a system consisting of two subsystems working alternately. In model I, no subsystem works in the period of working of the other. In model II, subsystem 2 is switched on when subsystem 1 fails in its working period. When a unit of subsystem 1 is repaired, it continues to work in its period and subsystem 2 is off line. On the other hand if subsystem 2 fails in its working period, subsystem 1 is not switched on. The availability expressions for both models are derived.     

Reliability Prediction for Continuously Operating Systems

The paper considers the prediction of reliability for a complex system designed for continuous operation. The state of the system is defined by identifying the subsystems which are functioning, the remainder undergoing repair (no inactive standby). The system is described as up whenever it is in one of an arbitrarily selected set of the system states. It is assumed that maintenance facilities are always adequate, and that the system conforms to a few other very mild restrictions. An exponential failure law is not assumed. Formulas are developed giving the mean durations of system up-times and down-times in terms of the corresponding quantities for the subsystems. The sensitivities of the formulas to errors in the input data are considered.     

基于改进模糊层次分析法的复杂装备可靠性分配研究

根据风力发电机传动链系统的可靠性分配指标具有多层次、多因素且定量与定性指标并存的特点,提出一种改进的模糊层次分析法,从影响可靠性分配的众多不确定因素出发建立可靠性分配的层次分析结构,定量分析计算出组成传动链系统的齿轮箱等各组件的权重。根据权重完成对传动链系统可靠性的合理分配。所得结果与传动链实际运行情况基本吻合,证明该方法具有较好的实用性,较传统层次分析法更科学、合理且更简单易行,能够为传动链的设计提供一定的依据。