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Synthesis of reliable networks; a survey
936
World Abstracts on Microelectronics and Reliability
Dagger sampling and sequential construction offer limited benefits when compared to the bounds and failure-sets methods. The failure-sets method performs best on the example for small failure probabilities. However, in general it offers no guarantee of a smaller variance than crude Monte Carlo and requires substantially more memory than the other methods. Moreover, this memory requirement can grow rapidly as the size of the network increases. By contrast, the bounds method guarantees a smaller variance than for crude Monte Carlo sampling and has modest memory requirements.
Conditional availability of intermittently-used systems in nonMarkov environment. KYUNG S. PARK. IEEE Trans. Reliab. R-35 (2), 175 (1986). This paper discusses the steady-state conditional availability of intermittently-used systems during the periods of demand. All the distributions governing system and demand status are arbitrary. The history dependence of the system and demand behavior is tackled by introducing history and cumulative-history functions. The system is assumed to fail only in use. Two processing disciplines regarding an interrupted demand (due to a system failure) are treated: fail-resume and fail-repeat. The steadystate conditional availability under the fail-resume discipline is M T B F / ( M T B F + M T T R ) , but not under the fail-repeat discipline. Therefore, care must be exercised not to misuse the formula. Evaluating MTBF approximations for simple maintained systems. ATUL K. BHATT and TIM O. HAIFLEY. IEEE Trans. Reliab. R-35 (2), 137 (1986). This paper compares two approximations for evaluating the reliability of redundant systems subject to periodic maintenance (PM) wherein failed portions are periodically replaced. Such approximations are useful because exact analytic methods become burdensome even for seemingly simple redundant schemes. Factoring algorithms for computing K-terminal network reliability. R. KEVIN WOOD. IEEE Trans. Reliab. R-35 (3), 269 (1986). Let GK denote a graph G whose edges can fail and with a set K _~ V specified. Edge failures are independent and have known probabilities. The K-terminal reliability of GK, R(GK), is the probability that all vertices in K are connected by working edges. A factoring algorithm for computing network reliability recursively applies the formula R(G~c) = piR(GK *e~)+q~R(GK-ei), where G~- *e~ is GK, with edge e~ contracted, GK--e~ is Gg with e~ deleted and p~ = l - q , is the reliability of edge e~. Various reliabilitypreserving reductions can be performed after each factoring operation in order to reduce computation. A unified framework is provided for complexity analysis and for determining optimal factoring strategies. Recent results are received and extended within this framework. A semi-parametric approach to testing for reliability growth, with application to software systems. RON KENETT and MOSHE POLLAK. IEEE Trans. Reliab. R-35 (3), 304 (1986). We consider the following general model for reliability growth: the distribution of times between failures belongs to a known parametric family (not necessarily exponential), and the parameter corresponding to the distribution of a particular time between failures is either an u n k n o w n constant or an unobservable random variable with a (possibly unknown) distribution which can depend on past observations. We propose that acceptable reliability can sometimes be formulized as a state in which the value of the parameters is lower than a level set before testing begins. We apply sequential detection methodology to the problem of ascertaining that an acceptable state of reliability has been attained and illustrate our approach by applying it to testing for reliability growth of a software system, using actual data.
Best linear unbiased estimators for normal distribution quantiles for sample sizes up to to 20. KHATAB M. HASSANEIN, A. K. MD. EHSANES SALEH and EDWARD F. BROWN. IEEE Trans. Reliab. R-35 (3), 327 (1986). This paper provides tables for estimating the quantities of the normal distribution by using order statistics in small samples. Linear unbiased estimators with m i n i m u m variance and based on ordered observations are constructed for sample sizes from 2 through 20. Synthesis of reliable networks; a survey. F. T. BOESCH. IEEE Trans. Reliab. R-35 (3), 240 (1986). In contrast to the usual probabilistic model for network reliability, one can use a deterministic model which is called network vulnerability. Many different vulnerability criteria and the related synthesis results are reviewed. These synthesis problems are all graph external questions. Certain reliability synthesis problems can be converted to a vulnerability question. Several open problems and conjectures are presented. Reliability and availability of duplex systems: some simple models. SPENCER W. NG. IEEE Trans. Reliab. R-35 (3), 295 (1986). 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. Evaluation of an opportunistic replacement policy for a 2-unit system. KAREN W. PULLEN and MARLIN U. THOMAS. IEEE Trans. Reliab. R-35 (3), 320 (1986). A probabilistic model represents a robust maintenance circumstance: a scheduled activity and a randomly-occurring activity with cost savings if they are combined. The activities are combined if the elapsed time for either activity exceeds a control limit, called a screen. The long-run of single and joint replacements are evaluated when the randomly-occurring activity is uniformly distributed. Bounds for reliability of large consecutive-k-out-of-n:F systems with unequal component reliability. JAMES C. Fu. IEEE Trans. Reliab. R-35 (3), 316 (1986). This paper examines upper and lower bounds for the reliability of a large consecutive-k-out-of-n:F system with unequal failure probabilities of components. The reliability of a large consecutivek-out-of-n: F system can be derived under certain conditions, from the upper and lower bounds. Examples are given. Distribution of failures in an array of cells. MICHAEL S. BRIDGMAN. IEEE Trans. Reliab. R-35 (3), 293 (1986). Consider a system which is an array of cells in which the system function is performed by the rows. The level of performance of the system depends on the failure rate of the cells and on the distribution of the failed cells in the array. For example, a system may operate at only 50 per cent efficiency if 3 or more cells in a row are failed. This paper presents a procedure for computing the probabilities of various failure distributions in the array rows for a given number of failed cells. Combined with a failure model for the individual cells, the results can be used to compute probabilities about performance of the array. Cell failures are assumed to be statistically independent and identically distributed. Bounds on the reliability of networks. J. SCOTT PROVAN. IEEE Trans. Reliab. R-35 (3), 260 (1986). This paper presents criteria for acceptable schemes to approximate system reliability and investigates such schemes for a special class of network reliability problems. In this framework, we are able to use powerful combinatorial theory to obtain strong bounds for network reliability which can be computed by efficient algorithms. We demonstrate these bounds on a small example, and give some computational experience.
World Abstracts on Microelectronics and Reliability
Dagger sampling and sequential construction offer limited benefits when compared to the bounds and failure-sets methods. The failure-sets method performs best on the example for small failure probabilities. However, in general it offers no guarantee of a smaller variance than crude Monte Carlo and requires substantially more memory than the other methods. Moreover, this memory requirement can grow rapidly as the size of the network increases. By contrast, the bounds method guarantees a smaller variance than for crude Monte Carlo sampling and has modest memory requirements.
Conditional availability of intermittently-used systems in nonMarkov environment. KYUNG S. PARK. IEEE Trans. Reliab. R-35 (2), 175 (1986). This paper discusses the steady-state conditional availability of intermittently-used systems during the periods of demand. All the distributions governing system and demand status are arbitrary. The history dependence of the system and demand behavior is tackled by introducing history and cumulative-history functions. The system is assumed to fail only in use. Two processing disciplines regarding an interrupted demand (due to a system failure) are treated: fail-resume and fail-repeat. The steadystate conditional availability under the fail-resume discipline is M T B F / ( M T B F + M T T R ) , but not under the fail-repeat discipline. Therefore, care must be exercised not to misuse the formula. Evaluating MTBF approximations for simple maintained systems. ATUL K. BHATT and TIM O. HAIFLEY. IEEE Trans. Reliab. R-35 (2), 137 (1986). This paper compares two approximations for evaluating the reliability of redundant systems subject to periodic maintenance (PM) wherein failed portions are periodically replaced. Such approximations are useful because exact analytic methods become burdensome even for seemingly simple redundant schemes. Factoring algorithms for computing K-terminal network reliability. R. KEVIN WOOD. IEEE Trans. Reliab. R-35 (3), 269 (1986). Let GK denote a graph G whose edges can fail and with a set K _~ V specified. Edge failures are independent and have known probabilities. The K-terminal reliability of GK, R(GK), is the probability that all vertices in K are connected by working edges. A factoring algorithm for computing network reliability recursively applies the formula R(G~c) = piR(GK *e~)+q~R(GK-ei), where G~- *e~ is GK, with edge e~ contracted, GK--e~ is Gg with e~ deleted and p~ = l - q , is the reliability of edge e~. Various reliabilitypreserving reductions can be performed after each factoring operation in order to reduce computation. A unified framework is provided for complexity analysis and for determining optimal factoring strategies. Recent results are received and extended within this framework. A semi-parametric approach to testing for reliability growth, with application to software systems. RON KENETT and MOSHE POLLAK. IEEE Trans. Reliab. R-35 (3), 304 (1986). We consider the following general model for reliability growth: the distribution of times between failures belongs to a known parametric family (not necessarily exponential), and the parameter corresponding to the distribution of a particular time between failures is either an u n k n o w n constant or an unobservable random variable with a (possibly unknown) distribution which can depend on past observations. We propose that acceptable reliability can sometimes be formulized as a state in which the value of the parameters is lower than a level set before testing begins. We apply sequential detection methodology to the problem of ascertaining that an acceptable state of reliability has been attained and illustrate our approach by applying it to testing for reliability growth of a software system, using actual data.
Best linear unbiased estimators for normal distribution quantiles for sample sizes up to to 20. KHATAB M. HASSANEIN, A. K. MD. EHSANES SALEH and EDWARD F. BROWN. IEEE Trans. Reliab. R-35 (3), 327 (1986). This paper provides tables for estimating the quantities of the normal distribution by using order statistics in small samples. Linear unbiased estimators with m i n i m u m variance and based on ordered observations are constructed for sample sizes from 2 through 20. Synthesis of reliable networks; a survey. F. T. BOESCH. IEEE Trans. Reliab. R-35 (3), 240 (1986). In contrast to the usual probabilistic model for network reliability, one can use a deterministic model which is called network vulnerability. Many different vulnerability criteria and the related synthesis results are reviewed. These synthesis problems are all graph external questions. Certain reliability synthesis problems can be converted to a vulnerability question. Several open problems and conjectures are presented. Reliability and availability of duplex systems: some simple models. SPENCER W. NG. IEEE Trans. Reliab. R-35 (3), 295 (1986). 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. Evaluation of an opportunistic replacement policy for a 2-unit system. KAREN W. PULLEN and MARLIN U. THOMAS. IEEE Trans. Reliab. R-35 (3), 320 (1986). A probabilistic model represents a robust maintenance circumstance: a scheduled activity and a randomly-occurring activity with cost savings if they are combined. The activities are combined if the elapsed time for either activity exceeds a control limit, called a screen. The long-run of single and joint replacements are evaluated when the randomly-occurring activity is uniformly distributed. Bounds for reliability of large consecutive-k-out-of-n:F systems with unequal component reliability. JAMES C. Fu. IEEE Trans. Reliab. R-35 (3), 316 (1986). This paper examines upper and lower bounds for the reliability of a large consecutive-k-out-of-n:F system with unequal failure probabilities of components. The reliability of a large consecutivek-out-of-n: F system can be derived under certain conditions, from the upper and lower bounds. Examples are given. Distribution of failures in an array of cells. MICHAEL S. BRIDGMAN. IEEE Trans. Reliab. R-35 (3), 293 (1986). Consider a system which is an array of cells in which the system function is performed by the rows. The level of performance of the system depends on the failure rate of the cells and on the distribution of the failed cells in the array. For example, a system may operate at only 50 per cent efficiency if 3 or more cells in a row are failed. This paper presents a procedure for computing the probabilities of various failure distributions in the array rows for a given number of failed cells. Combined with a failure model for the individual cells, the results can be used to compute probabilities about performance of the array. Cell failures are assumed to be statistically independent and identically distributed. Bounds on the reliability of networks. J. SCOTT PROVAN. IEEE Trans. Reliab. R-35 (3), 260 (1986). This paper presents criteria for acceptable schemes to approximate system reliability and investigates such schemes for a special class of network reliability problems. In this framework, we are able to use powerful combinatorial theory to obtain strong bounds for network reliability which can be computed by efficient algorithms. We demonstrate these bounds on a small example, and give some computational experience.