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Reliability evaluation and optimization of redundant dynamic systems
World Abstracts on Microelectronics and Reliability node or a network composed of only nonoriented lines has such a reliability-equivalent-separable node, then the network can be separated into two or more s-independent subnetworks by separating the node into two or more nodes. The network reliability can be obtained as a product of the subnetwork reliabilities. If a network has such a separate node, then computation of the network reliability can be appreciably reduced by separating the nodes. Examples are provided.
Reliability evaluation and optimization of redundant dynamic systems. MIRKO VUJOSEVICand DANIEL MEADE.IEEE Trans. Reliab. R-34 (2) 171 (1985). This paper analyzes the reliability of a simple dynamic system with redundant element and demonstrates an optimization technique for system reliability. A computer program was implemented to calculate the true reliability and the near optimal redundancy allocation for a dynamic subsystem. The solutions for the examples were always truly optimum which is illustrated by an example.
Hazard model for repaired system. SATISH J. KAMAT and SUNIL S. DESAL IEEE Trans. Reliab. R-34 (2) 177 (1985). A scalar modification model is suggested for the hazard-rate function of a repaired system. This model retains the shape of the hazard-rate function of the original system and shows the effects of aging before failure and repair. It seems reasonable and lends itself to estimation. As an example, a constant hazard-rate is used for the original system; a numerical example is worked out. Further research is needed to study the properties of and variations to this model.
Recursive algorithm for reliability evaluation of k-out-ofn:. G system. S. P. JAIN and KRISHNA GOPAL. IEEE Trans. Reliab. R-34 (2) 144 (1985). An algorithm for computing recursively the exact system reliability of k-out-of-n systems is proposed. It is simple, easy to implement, fast, and memory efficient. It gives a reliability expression with minimal number of terms, C(k, n) and involves only a few multiplications. The reduction in number of terms and multiplications is over 50 percent compared to some methods. The recursive nature of the algorithm enables one to design easily the number of units in the system to meet a reliability target. An alternative representation of the algorithm which is easy to remember and good for manual computation is given. However, it involves a few more multiplications compared to the original one but fewer than those required with existing methods.
Optimal selection methods for failure and repair rates using homographs. MASAFUMI SASAKI and YASUO KUWAHARA. IEEE Trans. Reliab. R-34 (2) 154 (1985). This paper explains the optimal selection methods using nomographs to solve two essentially different problems. The one is the problem of unit level, and the other is the one of system level. The unit level assumes that the cost information as a function of failure rate 2 and repair rate # are empirically known. The paper presents a method, by which a nomograph is used to select easily the optimum pair from the infinitely many pairs (2, #) of feasible solutions, to gain the required unit availability at minimum cost of this assumption. At the system level, the system is composed on n serial /-units which are selectable from a group provided for each/-unit (i = 1, 2,..., n), several different repair plans are available for the unit. Each unit has a specific failure rate and associated cost, and each repair plan has a specific repair rate and associated cost. There are service personnel for each unit. The failure and repair rates are constant. The paper presents: (1) A method using nomographs to select the optimum pairs from the many pairs (2~,#i) (i = 1, 2. . . . . n) of feasible solutions, to gain the required system availability at the minimum system cost, (2) A method to select the optimum pairs, from the many pairs (2i, #1) (i = 1, 2. . . . . n) of feasible solutions, to gain maximum system availability within a system cost constraint, (3) ProceMR 26:4-M
789
dures to draw a unit level nomograph and a hot-standby system level nomograph. This paper shows how to use nomographs with several numerical examples.
Cut-set intersections and node partitions. J. A. BUZACOTTand JACK S. K. CHANG. IEEE Trans. Reliab. R-33 (5) 385 (1984). With any cut set of a graph can be associated a partition of the nodes into two cells. We show that each cut-set intersection term in the cut-set inclusion and exclusion formula can be associated with a k-cell partition of the nodes. Thus, the number of distinct terms in the cut-set inclusion and exclusion formula cannot exceed the number of partitions of the set of nodes. This leads to a simplified formula for graph reliability: the node partition formula. When finding the overall reliability in complete graphs no terms cancel, thus the number of terms is equal to the number of partitions. In other graphs we show that the number of non-cancelling terms in the cut-set inclusion and exclusion formula is equal to the number of minimal partition sets of the graph. It follows that cut-set inclusion and exclusion is inherently an inefficient method for the exact calculation of network reliability measures. A Bayes explanation of an apparent failure rate paradox. RICHARD E. BARLOW. IEEE Trans. Reliab. R-34 (2) 107 (1985). For the exponential life distribution model and any prior distribution for the failure rate parameter, the predictive distribution has a decreasing failure rate. A Bayes explanation is given of why this is logically reasonable.
A new technique in minimal path and cut-set evaluation. G. B. JASMON and O. S. KAI. IEEE Trans. Reliab. R-34 (2) 136 (1985). This paper presents a new technique for deducing the minimal paths and cutsets of a general network. A powerful concept of reducing the total number of minimal paths to its basic minimal paths is introduced. This concept reduces the computational time and required storage in deducing the minimal cutsets. A new technique for evaluating minimal cutsets has been adopted. Examples demonstrate the power of the technique in reducing the computational requirements as compared to the conventional method, and show that the task for analysing large systems now becomes trivial.
Exact reliability formulas for linear and circular consecutivek-out-of-n:F systems. MENELAOS LAMBIRIS and STAVROS PAPASTAVRIDIS. 1EEE Trans. Reliab. R-34 (2) 124 (1985). A consecutive-k-out-of-n:F system, with n linearly or circularly arranged i.i.d, components is examined. The system reliability has an exact formula which is straightforward and more effective than those given elsewhere; the two formulas are given.
The application of statistical regression to yield modeling. STUART L. WEISBROD. Semiconductor Int. 261 (May 1985). The formulation of a defect density model using critical dimensions and other global predictors provides a consistent yield estimate to determine product viability and cost.
Optimal repair of a 2-component series-system with partially repairable components. MICHAEL N. KATEHAKISand PRAVIN K. JOrIRL IEEE Trans. Reliab. R-33 (5) 427 (1984). A 2component series system is maintained by one repairman. The up-times of the components are s-independent r.v.'s with exponential distributions. The time required to repair a failed component is the sum of a number of s-independent, exponential r.v.'s. Components can be partially repaired, and a working component can fail even while the system as a whole is not functioning. The analysis finds repairman allocation policies which maximize the system availability. Under the assumption that it is permissible to reassign the repairman instantaneously among failed components, the explicit form of optimal policies is obtained. And, the optimal policies are
Reliability evaluation and optimization of redundant dynamic systems. MIRKO VUJOSEVICand DANIEL MEADE.IEEE Trans. Reliab. R-34 (2) 171 (1985). This paper analyzes the reliability of a simple dynamic system with redundant element and demonstrates an optimization technique for system reliability. A computer program was implemented to calculate the true reliability and the near optimal redundancy allocation for a dynamic subsystem. The solutions for the examples were always truly optimum which is illustrated by an example.
Hazard model for repaired system. SATISH J. KAMAT and SUNIL S. DESAL IEEE Trans. Reliab. R-34 (2) 177 (1985). A scalar modification model is suggested for the hazard-rate function of a repaired system. This model retains the shape of the hazard-rate function of the original system and shows the effects of aging before failure and repair. It seems reasonable and lends itself to estimation. As an example, a constant hazard-rate is used for the original system; a numerical example is worked out. Further research is needed to study the properties of and variations to this model.
Recursive algorithm for reliability evaluation of k-out-ofn:. G system. S. P. JAIN and KRISHNA GOPAL. IEEE Trans. Reliab. R-34 (2) 144 (1985). An algorithm for computing recursively the exact system reliability of k-out-of-n systems is proposed. It is simple, easy to implement, fast, and memory efficient. It gives a reliability expression with minimal number of terms, C(k, n) and involves only a few multiplications. The reduction in number of terms and multiplications is over 50 percent compared to some methods. The recursive nature of the algorithm enables one to design easily the number of units in the system to meet a reliability target. An alternative representation of the algorithm which is easy to remember and good for manual computation is given. However, it involves a few more multiplications compared to the original one but fewer than those required with existing methods.
Optimal selection methods for failure and repair rates using homographs. MASAFUMI SASAKI and YASUO KUWAHARA. IEEE Trans. Reliab. R-34 (2) 154 (1985). This paper explains the optimal selection methods using nomographs to solve two essentially different problems. The one is the problem of unit level, and the other is the one of system level. The unit level assumes that the cost information as a function of failure rate 2 and repair rate # are empirically known. The paper presents a method, by which a nomograph is used to select easily the optimum pair from the infinitely many pairs (2, #) of feasible solutions, to gain the required unit availability at minimum cost of this assumption. At the system level, the system is composed on n serial /-units which are selectable from a group provided for each/-unit (i = 1, 2,..., n), several different repair plans are available for the unit. Each unit has a specific failure rate and associated cost, and each repair plan has a specific repair rate and associated cost. There are service personnel for each unit. The failure and repair rates are constant. The paper presents: (1) A method using nomographs to select the optimum pairs from the many pairs (2~,#i) (i = 1, 2. . . . . n) of feasible solutions, to gain the required system availability at the minimum system cost, (2) A method to select the optimum pairs, from the many pairs (2i, #1) (i = 1, 2. . . . . n) of feasible solutions, to gain maximum system availability within a system cost constraint, (3) ProceMR 26:4-M
789
dures to draw a unit level nomograph and a hot-standby system level nomograph. This paper shows how to use nomographs with several numerical examples.
Cut-set intersections and node partitions. J. A. BUZACOTTand JACK S. K. CHANG. IEEE Trans. Reliab. R-33 (5) 385 (1984). With any cut set of a graph can be associated a partition of the nodes into two cells. We show that each cut-set intersection term in the cut-set inclusion and exclusion formula can be associated with a k-cell partition of the nodes. Thus, the number of distinct terms in the cut-set inclusion and exclusion formula cannot exceed the number of partitions of the set of nodes. This leads to a simplified formula for graph reliability: the node partition formula. When finding the overall reliability in complete graphs no terms cancel, thus the number of terms is equal to the number of partitions. In other graphs we show that the number of non-cancelling terms in the cut-set inclusion and exclusion formula is equal to the number of minimal partition sets of the graph. It follows that cut-set inclusion and exclusion is inherently an inefficient method for the exact calculation of network reliability measures. A Bayes explanation of an apparent failure rate paradox. RICHARD E. BARLOW. IEEE Trans. Reliab. R-34 (2) 107 (1985). For the exponential life distribution model and any prior distribution for the failure rate parameter, the predictive distribution has a decreasing failure rate. A Bayes explanation is given of why this is logically reasonable.
A new technique in minimal path and cut-set evaluation. G. B. JASMON and O. S. KAI. IEEE Trans. Reliab. R-34 (2) 136 (1985). This paper presents a new technique for deducing the minimal paths and cutsets of a general network. A powerful concept of reducing the total number of minimal paths to its basic minimal paths is introduced. This concept reduces the computational time and required storage in deducing the minimal cutsets. A new technique for evaluating minimal cutsets has been adopted. Examples demonstrate the power of the technique in reducing the computational requirements as compared to the conventional method, and show that the task for analysing large systems now becomes trivial.
Exact reliability formulas for linear and circular consecutivek-out-of-n:F systems. MENELAOS LAMBIRIS and STAVROS PAPASTAVRIDIS. 1EEE Trans. Reliab. R-34 (2) 124 (1985). A consecutive-k-out-of-n:F system, with n linearly or circularly arranged i.i.d, components is examined. The system reliability has an exact formula which is straightforward and more effective than those given elsewhere; the two formulas are given.
The application of statistical regression to yield modeling. STUART L. WEISBROD. Semiconductor Int. 261 (May 1985). The formulation of a defect density model using critical dimensions and other global predictors provides a consistent yield estimate to determine product viability and cost.
Optimal repair of a 2-component series-system with partially repairable components. MICHAEL N. KATEHAKISand PRAVIN K. JOrIRL IEEE Trans. Reliab. R-33 (5) 427 (1984). A 2component series system is maintained by one repairman. The up-times of the components are s-independent r.v.'s with exponential distributions. The time required to repair a failed component is the sum of a number of s-independent, exponential r.v.'s. Components can be partially repaired, and a working component can fail even while the system as a whole is not functioning. The analysis finds repairman allocation policies which maximize the system availability. Under the assumption that it is permissible to reassign the repairman instantaneously among failed components, the explicit form of optimal policies is obtained. And, the optimal policies are