Reliability Importance Measures Research Articles

Error exponents for multi-keyhole MIMO channels

Along with the channel capacity, the error exponent is one of the most important information-theoretic measures of reliability, because it sets ultimate bounds on the performance of communication systems employing codes of finite complexity. In this paper, we derive closed-form expressions for the Gallager random coding and expurgated error exponents for multi-keyhole multiple-input multiple-output (MIMO) channels, which provide insights into a fundamental tradeoff between the communication reliability and information rate. We investigate the effect of keyholes on the error exponents and cutoff rate. Moreover, without an extensive Monte-Carlo simulation we can easily compute the codeword length necessary to achieve a predefined error probability at a given rate, which quantifies the effects of the number of antennas, channel coherence time, and the number of keyholes. In addition, we derive exact closed-form expressions for the ergodic capacity and cutoff rate based on the easily computable Meijer G-function. Finally, we extend our study to Rayleigh-product MIMO channels and keyhole MIMO channels.

Reliability measures of a computer system with priority to PM over the H/W repair activities subject to MOT and MRT

Article history: Received September 18, 2014 Accepted 15 December 2014 Available online December 16 2014 This paper concentrates on the evaluation of reliability measures of a computer system of twoidentical units having independent failure of h/w and s/w components. Initially one unit is operative and the other is kept as spare in cold standby. There is a single server visiting the system immediately whenever needed. The server conducts preventive maintenance of the unit after a maximum operation time. If server is unable to repair the h/w components in maximum repair time, then components in the unit are replaced immediately by new one. However, only replacement of the s/w components has been made at their failure. The priority is given to the preventive maintenance over repair activities of the h/w. The time to failure of the components follows negative exponential distribution whereas the distribution of preventive maintenance, repair and replacement time are taken as arbitrary. The expressions for some important reliability measures of system effectiveness have been derived using semi-Markov process and regenerative point technique. The graphical behavior of the results has also been shown for a particular case. Growing Science Ltd. All rights reserved. 5 © 201

Reliability Measures of a Two-Unit Cold Standby Repairable System with Priority to Operation over Preventive Maintenance

main objective of present work is to carry out various important reliability measures of a twounit cold s tandby repairable system with priority to operation over preventive maintenance by using regenerative points technique and semiMarkov process. A single repair facility is pr ovided to conduct repair and maintenance of the system as and when required. All times distributions are exponential except the repair and preventive maintenance time distributions which are considered as general.

Behavioural analysis of a hydroelectric production power plant under reworking scheme

By high calibre of the fundamental nature of electric power, both of our economic and personal interests, a system is expected to supply as electrical energy as possible with the highest degree of quality and reliability. This research work aimed to evaluate the reliability measures of a hydroelectric power station. The results of this study are deliberate to provide the improved criteria for upcoming proposals, and serves as a basis for generation expansion planning of hydroelectric power stations. This paper presents a Markov-process based mathematical model for a hydroelectric power plant. The important reliability measures have been derived and discussed with the help of failure and repair rates through the analysis. This research gives a clear view of how the hydropower plants are modelled by defining the states under the failure and repair rates.

Reliability analysis of a k-out-of-n:G repairable system with single vacation

This paper analyzes a k-out-of-n:G repairable system with one repairman who takes a single vacation, the duration of which follows a general distribution. The working time of each component is an exponentially distributed random variable and the repair time of each failed component is governed by an arbitrary distribution. Moreover, we assume that every component is “as good as new” after being repaired. Under these assumptions, several important reliability measures such as the availability, the rate of occurrence of failures, and the mean time to first failure of the system are derived by employing the supplementary variable technique and the Laplace transform. Meanwhile, their recursive expressions are obtained. Furthermore, through numerical examples, we study the influence of various parameters on the system reliability measures. Finally, the Monte Carlo simulation and two special cases of the system which are (n-1)-out-of-n:G repairable system and 1-out-of-n:G repairable system are presented to illustrate the correctness of the analytical results.

Error exponents for Nakagami-m fading channels

Along with the channel capacity, the error exponent is one of the most important information-theoretic measures of reliability, as it sets ultimate bounds on the performance of communication systems employing codes of finite complexity. In this paper, we derive an exact analytical expression for the random coding error exponent, which provides significant insight regarding the ultimate limits to communications through Nakagami-m fading channels. An important fact about this error exponent is that it determines the behavior of error probability in terms of the transmission rate and the code length that reflects the coding complexity required to achieve a certain level of reliability. Moreover, from the derived analytical expression, we can easily compute the necessary codeword length without extensive Monte-Carlo simulation to achieve a predefined upper bound for error probability at a rate below the channel capacity. We also improve the random coding bound by expurgating bad codewords from the code ensemble, since random coding error exponent is determined by selecting codewords independently according to the input distribution where good and bad codewords contribute equally to the overall average error probability. Finally, we derive exact analytical expressions for the cutoff rate, critical rate, and expurgation rate and verify the analytical expressions via Monte-Carlo simulation.

Redundancy Allocation using Component-Importance Measures for Maximizing System Reliability

SYNOPTIC ABSTRACTRedundancy allocation, being an important and effective way to improve system reliability, has been discussed by many authors. The main idea, which has been advocated in this article, lies in the fact that some components have more significance in the functioning of the system than the others; because of this, it is expected that if allocation of the redundant component is made according to some component-importance measure, optimality can be achieved easily. The novelty of this study is that the problem of redundancy allocation has been solved by allocating redundant components according to some component-importance measures that are not very difficult to obtain and comprehend for an engineered system, even when there is no information about the reliability of the components. The component structural-importance measure and reliability-importance measure have been used in this work for the purpose of allocating redundancy. The results derived can be used to maximize system reliability using redundancy allocation for a general n-component coherent system. Applications of the results have been illustrated with examples of coherent systems.

Based on Reliability Importance Measures Method of Comprehensive Evaluation of Electric Power Communication Equipment

Currently, the evaluation methods of importance measures such as structure importance measure, criticality reliability importance and B-reliability importance, have some shortcomings that the evaluation results are not comprehensive enough and the scope of usage. In order to accurately evaluate the importance measures of equipment, and to reflect the impact of the equipment on the communication network, a comprehensive evaluation method of importance measure is put forward. According to the influence of inherent structure of system and service reliability, the importance measure of equipment is calculated. By the coefficient modification, it can accurately evaluate comprehensive evaluation of electric power communication equipment based on reliability importance measures. Example result verifies the feasibility and validity of the comprehensive evaluation method.

The Number of Spanning Trees of the Cartesian Product of Regular Graphs

The number of spanning trees in graphs or in networks is an important issue. The evaluation of this number not only is interesting from a mathematical (computational) perspective but also is an important measure of reliability of a network or designing electrical circuits. In this paper, a simple formula for the number of spanning trees of the Cartesian product of two regular graphs is investigated. Using this formula, the number of spanning trees of the four well-known regular networks can be simply taken into evaluation.

EVALUATION OF OPERATIONAL EFFICIENCY OF URBAN ROAD NETWORK USING TRAVEL TIME RELIABILITY MEASURES

Abstract Efficiency of the road network system is analyzed by travel time reliability measures. The study overlooks on an important measure of travel time reliability and prioritizing Tiruchirappalli road network. Traffic volume and travel time were collected using license plate matching method. Travel time measures were estimated from average travel time and 95th travel time. Effect of non-motorized vehicle on efficiency of road system was evaluated. Relation between buffer time index and traffic volume was created. Travel time model has been developed and travel time measure was validated. Then service quality of road sections in network were graded based on travel time reliability measures.

Complexity of stacked book graph and cone graphs

The number of spanning trees in graphs (networks) is an important invariant, and it is also an important measure of reliability of a network. In this paper we derive simple formulas of the complexity, number of spanning trees, of some stacked book graphs and cone graph, using linear algebra, Chebyshev polynomials and matrix analysis techniques.

Reliability modeling of a single-unit system with arbitrary distributions subject to different weather conditions

The main concentration of the present study is on the evaluation of some important reliability measures of a single-unit system considering arbitrary distributions for the random variables associated with failure and repair times, time to change of weather conditions, inspection time and arrival time of the server. The system operates under two weather conditions-normal and abnormal. The unit fails completely via partial failure. There is a single server who takes some time to arrive at the system. Server inspects the unit at its complete failure to see the feasibility of its repair while repair of the unit at partial failure is done without inspection. The unit works as new after repair at partial failure whereas unit is assumed as degraded after repair at complete failure. Inspection of the degraded unit is also conducted at its failure to examine the feasibility of repair. The degraded unit is replaced by new one if inspection reveals that its repair is not feasible to the system. Some measures of system effectiveness are obtained using semi-Markov and regenerative point technique. Giving particular values to various parameters and costs, the numerical results for mean time to system failure, availability and profit function are obtained considering exponential and Rayleigh distributions for all random variables.

An approach for lifetime reliability analysis using theorem proving

Recently proposed formal reliability analysis techniques have overcome the inaccuracies of traditional simulation based techniques but can only handle problems involving discrete random variables. In this paper, we extend the capabilities of existing theorem proving based reliability analysis by formalizing several important statistical properties of continuous random variables like the second moment and the variance. We also formalize commonly used concepts about the reliability theory such as survival, hazard, cumulative hazard and fractile functions. With these extensions, it is now possible to formally reason about important measures of reliability (the probabilities of failure, the failure risks and the mean-time-to failure) associated with the life of a system that operates in an uncertain and harsh environment and is usually continuous in nature. We illustrate the modeling and verification process with the help of examples involving the reliability analysis of essential electronic and electrical system components.

Profit Analysis of Non-Identical Parallel System with Two Types of Failure Using Discrete Distribution

This paper has analyzed the two non-identical operative parallel system considering two units (automatic and manual one) by using regenerative point technique. For the automatic unit the concept of inspection policy has been introduced to detect the kind of failures (major or minor) before being repaired by some repair mechanism. But the manual unit is free from such inspection policy. Various important measures of reliability i.e MTSF, steady state availability, busy period of repairman and inspector, profit function has been evaluated by designing model for the system and using discrete distribution & regenerative point techniques. Profit function and MTSF are also analyzed graphically.

Complexity of Products of Some Complete and Complete Bipartite Graphs

The number of spanning trees in graphs (networks) is an important invariant; it is also an important measure of reliability of a network. In this paper, we derive simple formulas of the complexity, number of spanning trees, of products of some complete and complete bipartite graphs such as cartesian product, normal product, composition product, tensor product, and symmetric product, using linear algebra and matrix analysis techniques.

Evaluation of Components Reliability Importance Measures of Electric Transmission Systems Using the Bayesian Network

In this article, a novel approach is presented for the determination of reliability importance measures in electric transmission systems implementing the Bayesian network. By this method, the Bayesian network associated with a given power system is first constructed where the generation units are assumed fully reliable and the required training data is provided by using the state sampling method of Monte Carlo simulation. When the Bayesian network is constructed, it is readily used to determine the various reliability importance measures and to investigate their physical interpretations for the proposed transmission system.

Some Applications of Spanning Trees in Complete and Complete Bipartite Graphs

Problem statement: The number of spanning trees τ(G) in graphs (networks) is an important invariant, it is also an important measure of reliability of a network. Approach: Using linear algebra and matrix analysis techniques to evaluate the associated determinants. Results: In this study we derive simple formulas for the number of spanning trees of complete graph Kn and complete bipartite graph Kn,m and some of their applications. A large number of theorems of number of the spanning trees of known operations on complete graph Kn and complete bipartite graph Kn,m are obtained. Conclusion: The evaluation of number of spanning trees is not only interesting from a mathematical (computational) perspective, but also, it is an important measure of reliability of a network and designing electrical circuits. Some computationally hard problems such as the travelling salesman problem can be solved approximately by using spanning trees. Due to the high dependence of the network design and reliability on the graph theory we introduced the following important theorems and lemmas and their proofs.

최소절단집합과 최소경로집합을 이용한 구조 및 신뢰성 중요도 척도의 개발 및 적용

The research discusses interrelationship of structural and reliability importance measures which used in the probabilistic safety assessment. The most frequently used component importance measures, such as Birnbaum`s Importance (BI), Risk Reduction (RR), Risk Reduction Worth (RRW), RA (Risk Achievement), Risk Achievement Worth (RAW), Fussel Vesely (FV) and Critically Importance (CI) can be derived from two structure importance measures that are developed based on the size and the number of Minimal Path Set (MPS) and Minimal Cut Set (MCS). In order to show an effectiveness of importance measures which is developed in this paper, the three representative functional structures, such as series-parallel, k out of n and bridge are used to compare with Birnbaum`s Importance measure. In addition, the study presents the implementation examples of Total Productive Maintenance (TPM) metrics and alternating renewal process models with exponential distribution to calculate the availability and unavailability of component facility for improving system performances. System state structure functions in terms of component states can be converted into the system availability (unavailability) functions by substituting the component reliabilities (unavailabilities) for the component states. The applicable examples are presented in order to help the understanding of practitioners.

Complexity of Cocktail Party Graph and Crown Graph

Problem statement: The number of spanning trees τ(G) in graphs (networks) was an important invariant. Approach: Using the properties of the Chebyshev polynomials of the second kind and the linear algebra techniques to evaluate the associated determinants. Results: The complexity, number of spanning trees, of the cocktail party graph on 2n vertices, given in detail in the text was proved. Also the complexity of the crown graph on 2n vertices was shown to had the value nn-2 (n-1) (n-2)n-1. Conclusion: The number of spanning trees τ(G) in graphs (networks) is an important invariant. The evaluation of this number and analyzing its behavior is not only interesting from a mathematical (computational) perspective, but also, it is an important measure of reliability of a network and designing electrical circuits. Some computationally hard problems such as the travelling salesman problem can be solved approximately by using spanning trees. Due to the high dependence of the network design and reliability on the graph theory we introduced the above important theorems and lemmas and their proofs.

Number of Spanning Trees of Circulant Graphs C<sub>6n</sub> and their Applications

Problem statement: The number of spanning trees of a graph G is usually denoted by τ(G). A circulant graph with n vertices and k jumps is Cn (a1,…..,ak). Approach: In this study the number τ(G) of spanning trees of the circulant graphs C6n with some non-fixed jumps such as C6n (1, n), C6n (1, n, 2n), C6n (1, n, 3n), C6n (1, 2n 3n), C6n (1, n, 2n, 3n), are evaluated using Chebyshev polynomials. A large number of theorems of number of the spanning trees of circulate graphs C12n are obtained. Results: The number t(G) of spanning trees of the circulant graphs C6n(1, n), C6n(1, n, 2n), C6n(1, n, 3n), C6n(1, 2n, 3n), C6n(1, n, 2n, 3n), C12n(1, 2n, 3n), C12n(1, 3n, 6n), C12n(1, 3n, 4n), C12n(1, 2n, 3n, 4n), C12n(1, 2n, 3n, 6n), C12n(1, 3n, 4n, 6n) and C12n(1, 2n, 3n, 4n, 6n) are evaluated. Conclusion: The number of spanning trees τ(G) in graphs (networks) is an important invariant. The evaluation of this number and analyzing its behavior is not only interesting from a mathematical (computational) perspective, but also, it is an important measure of reliability of a network and designing electrical circuits. Some computationally hard problems such as the travelling salesman problem can be solved approximately by using spanning trees. Due to the high dependence of the network design and reliability on the graph theory we introduced the following important theorems and their proofs.