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Systems with exponential life using components with HNBUE lives
World Abstracts on Microelectronics and Reliability queueing model of a bi-level stochastic service system using a Markov process. The existence of two modes of operation in some real situations such as reliability, inventory, and production problems is outlined. A recursive solution technique is developed for computing steady-state probabilities and the relevant performance measures for such a system. A bi-level system is completely analyzed. The effect of the two modes of operation on the system performance measures is also discussed. The recursive solution technique is consistently superior to other c o m m o n solution techniques with respect to computation time and memory requirement. A procedure is outlined for extension to a multi-level service system.
Systems with exponential life using components with H N B U E lives. A. N. AHMEDand A. A. ALZAID. I E E E Trans. Reliab. R37, 424 (1988). We show, a m o n g other results, that if the convolution of n H N B U E distributions is exponential, then n - 1 of the distributions are degenerate at zero and the other distribution is exponential. This result is also shown to hold for the wider H N B U E (31 class. Our result extends similar results previously published for the IFRA and N B U cases. We conjecture that if a monotonic system formed with independent components has exponential life, it must be essentially a series system with exponential components. Shrinkage estimation of scale parameter of the extreme-value distribution. PAUL C m o u . I E E E Trans. Reliab. R-37, 370 (1988). This paper studies the usual preliminary test estimator of the scale parameter of the extreme-value distribution in censored samples. The optimum levels of significance and their corresponding critical values for the preliminary test are obtained based on the minimax regret criterion. A preliminary lest shrinkage estimator that is smoother than the usual preliminary test estimator is proposed as well. The optimum values of shrinkage coefficients for the preliminary test shrinkage estimator are obtained, and are also based on the minimax regret criterion. Comparison of these two estimators shows that if the mean square error is a criterion of goodness of estimation then the preliminary test shrinkage estimator is better than the usual preliminary test estimator. Assessing throughput and reliability in communication and computer networks. PETER KUBAT. I E E E Trans. Reliab. R-37, 308 (1988). System performance and reliability are jointly assessed for highly reliable communication/computer networks. The model assumes that at most a small number of components can be down at a time and that the average repair/replacement time of a failed component is small when compared with the average failure times of network components. The system performance is measured in terms of network throughput at steady-state operation. Sequential imperfect preventive maintenance policies. TOSHIO NAKAGAWA. I E E E Trans. Reliab. R-37, 295 (1988). This paper introduces improvement factors in hazard rate and age for a sequential preventive maintenance (pm) policy and analyzes two imperfect pm models: (1) pm reduces the hazard rate while it increases with the n u m b e r of pro's, and (2) p m reduces the age. The pm is done at intervals x k ( k - 1, 2 ..... N) and is imperfect. The optimal policies to minimize the mean cost-rates are discussed. The optimal pm sequences {Xk} are computed for a Weibull distribution. Reliability-constrained dimensioning of transmission resources in packet-switched networks. ACHILLE PATTAVINA. I E E E Trans. Reliab. R-37, 434 (1988). This paper investigates the problem of dimensioning the transmission resources of a packet-switched communication network satisfying suitable reliability targets. The goal is a communication network providing a minimal transport capability in the presence of failures in network components. This goal is expressed in
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terms of availability functions to be satisfied by the reliability of communication links. The design procedure is based on the routing of each communication link on more than one transmission path, so that the availability of small shares of the communication link capacity can be increased. An analytic evaluation of the availability figures considered during the design phase is provided and the tools developed are used to compute an end-to-end reliability figure, which also takes into account the a m o u n t of user traffic.
Variance importance of system components by Monte Carlo. ZHI-J1E PAN and YA-CHUAN TAI. I E E E Trans. Reliab. R-37, 421 (1988). The paper presents an algorithm to compute variance importance, a measure of uncertainty importance for system components. A simple equation has been derived for the measure, and Monte Carlo simulation is used to obtain numerical estimates. The algorithm overcomes NPdifficulty (non-polynomial difficulty) which exists in earlier methods for computing uncertainty importance, and is simpler, more accurate, and more practical. Moreover, it shows the direct relationship between probabilistic importance and uncertainty importance. An example illustrates the evaluation of Monte Carlo variance importance for sample system. Reliability of an m-out of-n system when component failure induces higher failure rates in survivors. ERNEST M. SCHEUER. I E E E Trans. Reliab. R-37, 73 (1988). An m-out-of-n:G system is composed of statistically independent and identically distributed components with exponential lifetimes. The reliability of such a system is obtained under the assumption that the fitilure of a component changes the failure rate of the surviving components. Minimizing the total sample size when multiple 1-shot systems are compared against a common baseline. ARTHUR FRIES. I E E E Trans. Reliab. R-37, 108 (1988). A test design is to be determined for simultaneously comparing the individual reliabilities of each of multiple alternative 1-shot systems against the reliability of a single baseline, with a c o m m o n specification for the size and power of each alternative-vsbaseline comparison. Using the procedure of Lee, the total sample size (baseline plus alternatives) can be minimized by setting the ratio of the number of baseline system replicates to the number of replicates for each alternative system equal to the square root of the number of alternative systems. Optimal"series parallel" networks of 3-state devices. LAVON B. PAGE and Jo ELLEN PERRY. I E E E Trans. Reliab. R-37, 388 (1988). A 3-state component is one which can fail in two different modes: an open mode and a shorted mode. Systems built from such components can also experience either of these two failure modes. For a given number of s-identical sindependent components, a pure "series" or pure "parallel" configuration would be most reliable if only one of the two failure modes were possible. This paper treats the problem of designing the most reliable configuration of a given number of s-identical components that can experience both failure modes. Two simple algorithms for designing an optimal configuration are presented, and by analysis of 6, 8, and 20component systems they illustrate the extent to which other configurations can be more reliable than "series-parallel" or "parallel series" arrays. For configurations of 3 or 4 3-state components, arrays are optimal for a wide range of probability inputs. With larger configurations we have described an appropriate programmable methodology for constructing all possible configurations and selecting the optimal one for a given pair of probability inputs s and q. The number of possible configurations grows so rapidly as the number of available components increases that a complete enumeration method is not feasible for analyzing configurations of more than about 10 components. An alternative algorithm called Keep3
Systems with exponential life using components with H N B U E lives. A. N. AHMEDand A. A. ALZAID. I E E E Trans. Reliab. R37, 424 (1988). We show, a m o n g other results, that if the convolution of n H N B U E distributions is exponential, then n - 1 of the distributions are degenerate at zero and the other distribution is exponential. This result is also shown to hold for the wider H N B U E (31 class. Our result extends similar results previously published for the IFRA and N B U cases. We conjecture that if a monotonic system formed with independent components has exponential life, it must be essentially a series system with exponential components. Shrinkage estimation of scale parameter of the extreme-value distribution. PAUL C m o u . I E E E Trans. Reliab. R-37, 370 (1988). This paper studies the usual preliminary test estimator of the scale parameter of the extreme-value distribution in censored samples. The optimum levels of significance and their corresponding critical values for the preliminary test are obtained based on the minimax regret criterion. A preliminary lest shrinkage estimator that is smoother than the usual preliminary test estimator is proposed as well. The optimum values of shrinkage coefficients for the preliminary test shrinkage estimator are obtained, and are also based on the minimax regret criterion. Comparison of these two estimators shows that if the mean square error is a criterion of goodness of estimation then the preliminary test shrinkage estimator is better than the usual preliminary test estimator. Assessing throughput and reliability in communication and computer networks. PETER KUBAT. I E E E Trans. Reliab. R-37, 308 (1988). System performance and reliability are jointly assessed for highly reliable communication/computer networks. The model assumes that at most a small number of components can be down at a time and that the average repair/replacement time of a failed component is small when compared with the average failure times of network components. The system performance is measured in terms of network throughput at steady-state operation. Sequential imperfect preventive maintenance policies. TOSHIO NAKAGAWA. I E E E Trans. Reliab. R-37, 295 (1988). This paper introduces improvement factors in hazard rate and age for a sequential preventive maintenance (pm) policy and analyzes two imperfect pm models: (1) pm reduces the hazard rate while it increases with the n u m b e r of pro's, and (2) p m reduces the age. The pm is done at intervals x k ( k - 1, 2 ..... N) and is imperfect. The optimal policies to minimize the mean cost-rates are discussed. The optimal pm sequences {Xk} are computed for a Weibull distribution. Reliability-constrained dimensioning of transmission resources in packet-switched networks. ACHILLE PATTAVINA. I E E E Trans. Reliab. R-37, 434 (1988). This paper investigates the problem of dimensioning the transmission resources of a packet-switched communication network satisfying suitable reliability targets. The goal is a communication network providing a minimal transport capability in the presence of failures in network components. This goal is expressed in
1097
terms of availability functions to be satisfied by the reliability of communication links. The design procedure is based on the routing of each communication link on more than one transmission path, so that the availability of small shares of the communication link capacity can be increased. An analytic evaluation of the availability figures considered during the design phase is provided and the tools developed are used to compute an end-to-end reliability figure, which also takes into account the a m o u n t of user traffic.
Variance importance of system components by Monte Carlo. ZHI-J1E PAN and YA-CHUAN TAI. I E E E Trans. Reliab. R-37, 421 (1988). The paper presents an algorithm to compute variance importance, a measure of uncertainty importance for system components. A simple equation has been derived for the measure, and Monte Carlo simulation is used to obtain numerical estimates. The algorithm overcomes NPdifficulty (non-polynomial difficulty) which exists in earlier methods for computing uncertainty importance, and is simpler, more accurate, and more practical. Moreover, it shows the direct relationship between probabilistic importance and uncertainty importance. An example illustrates the evaluation of Monte Carlo variance importance for sample system. Reliability of an m-out of-n system when component failure induces higher failure rates in survivors. ERNEST M. SCHEUER. I E E E Trans. Reliab. R-37, 73 (1988). An m-out-of-n:G system is composed of statistically independent and identically distributed components with exponential lifetimes. The reliability of such a system is obtained under the assumption that the fitilure of a component changes the failure rate of the surviving components. Minimizing the total sample size when multiple 1-shot systems are compared against a common baseline. ARTHUR FRIES. I E E E Trans. Reliab. R-37, 108 (1988). A test design is to be determined for simultaneously comparing the individual reliabilities of each of multiple alternative 1-shot systems against the reliability of a single baseline, with a c o m m o n specification for the size and power of each alternative-vsbaseline comparison. Using the procedure of Lee, the total sample size (baseline plus alternatives) can be minimized by setting the ratio of the number of baseline system replicates to the number of replicates for each alternative system equal to the square root of the number of alternative systems. Optimal"series parallel" networks of 3-state devices. LAVON B. PAGE and Jo ELLEN PERRY. I E E E Trans. Reliab. R-37, 388 (1988). A 3-state component is one which can fail in two different modes: an open mode and a shorted mode. Systems built from such components can also experience either of these two failure modes. For a given number of s-identical sindependent components, a pure "series" or pure "parallel" configuration would be most reliable if only one of the two failure modes were possible. This paper treats the problem of designing the most reliable configuration of a given number of s-identical components that can experience both failure modes. Two simple algorithms for designing an optimal configuration are presented, and by analysis of 6, 8, and 20component systems they illustrate the extent to which other configurations can be more reliable than "series-parallel" or "parallel series" arrays. For configurations of 3 or 4 3-state components, arrays are optimal for a wide range of probability inputs. With larger configurations we have described an appropriate programmable methodology for constructing all possible configurations and selecting the optimal one for a given pair of probability inputs s and q. The number of possible configurations grows so rapidly as the number of available components increases that a complete enumeration method is not feasible for analyzing configurations of more than about 10 components. An alternative algorithm called Keep3