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Redundant systems with appreciable exchange time
World Abstracts on Microelectronics and Reliability
The highest and lowest reliability achievable with redundancy. PETERW. BECKER.IEEE Trans. Reliab. R-26, (3) 209 (August 1977). Often system reliability can be enhanced through the use of redundancy. Redundancy may, however, have a detrimental effect on the statistical relationship of redundant elements. When the components in a redundant system have more than one failure-mode and when failures are sdependent, it is difficult to assess the reliability of the system. The paper describes the 0-transformation by which the highest and lowest reliability achievable can be determined for a configuration using components with specified reliabilities. As a by-product we become able to pinpoint the statistical relationships that give rise to highest and lowest system reliabilities.
Cost-optimised burn-in duration for repairable electronic systems. KENNETHT. PLESSERand THOMASO. FIELD. IEEE Trans. Reliab. R-26, (3) 195 (August 1977). A mathematical model permits determining the duration of cost-optimized burn-in and evaluating the resultant saving for repairable electronics systems. Infant mortality failures occur according to a nonhomogeneous Poisson Process; repair actions restore the system to a bad-as-old condition. The s-expected costs associated with factory and field failures are traded-off with the costs of implementing a burn-in program. Under the constraints of the model, the optimum burn-in duration and consequent cost saving are independent of the eventual life of the system in the field. A numerical example illustrates these concepts.
Techniques for servicing LSl-based gear evolve. STEPHEN E. SCRUPSKI.Electronics p. 120 (27 October 1977). The impact of microprocessors on instruments is proving to be more indirect than direct--but revolutionary all the same. Users of microprocessor-based equipment are urgently demanding test systems capable of servicing it, and already a few of the larger instrument companies have made significant moves toward filling this vacuum. Next year many others will also contribute to a bumper crop of service-oriented instruments, espousing many different approaches to fault diagnosis.
Optimum preventive maintenance policies for repairable systems. TOSHIO NAKAGAWA.IEEE Trans. Reliab. R-26, (3) 168 (August 1977). This paper summarizes my recent work in analyzing preventive maintenance of the following kinds of repairable systems: 1-unit systems, 2-unit standby systems, and a system with unrepairable spare units. Some appropriate reliability measures of such systems are given, and optimum preventive maintenance policies which maximize or minimize these measures are derived under suitable conditions.
Minimum cost systems with specified reliability. K. K. AGGARWAL. IEEE Trans. Reliab. R-26, (3) 166 (August 1977). A method is presented for allocating reliability to each unit of a system with a view to minimizing the system cost. The practical utility of this method, as well as other methods, depends heavily on the availability of costreliability data for the constituent units. Unfortunately, for most components such data are not readily available. There is a need for manufacturers and users to make these data available to reliability theoreticians so that the derived results are usefully applied to practical systems. So far, very little seems to have been done in this direction.
Determining component reliability and redundancy for optimum system reliability. FRANK A. TILLMAN, CHING-LA1 HWANG and WAY Kuo. IEEE Trans. Reliab. R-26, (3) 162 (August 1977). The usual constrained reliability optimization problem is extended to include determining the optimal level of component reliability and the number of redundancies in each stage. With cost, weight, and volume constraints, the problem is one in which the component reliability is a
353
variable, and the optimal trade-off between adding components and improving individual component reliability is determined. This is a mixed integer nonlinear programming problem in which the system reliability is to be maximized as a function of component reliability level and the number of components used at each stage. The model is illustrated with three general non linear constraints imposed on the system. The Hooke and Jeeves pattern search technique in combination with the heuristic approach by Aggarwal et al. is used to solve the problem. The Hooke and Jeeves pattern search technique is a sequential search routine for maximizing the system reliability, Rs(R, X). The argument in the Hooke and Jeeves pattern search is the component reliability,/~, which is varied according to exploratory moves and pattern moves until the maximum of Rs(R, X) is obtained. The heuristic approach is applied to each value of the component reliability, R, to obtain the optimal number of redundancies, X, which maximizes Rs(R, X) for the stated
Optimization techniques for system reliability with redundancy--a review. FRANK A. TILLMAN, CHING-LAI HWANG and WAY Kuo. IEEE Trans. Reliab. R-26, (3) 148 (August 1977). This paper is a state-of-art review of the literature related to optimal system reliability with redundancy. The literature is classified as follows.
A heuristic method for determining optimal reliability allocation. YuJi NAKAGAWA and KYOlCHI NAKASHIMA.IEEE Trans. Reliab. R-26, (3) 156 (August 1977). The paper presents a method for obtaining an optimal reliability allocation of an n-stage series system. In each stage, redundant components can be added (in parallel, stand-by, or k-out-ofn:G, etc.), or a more reliable component can be used in order to improve the system reliability. The solution is obtained by repeatedly using a more reliable candidate at each stage that has the greatest value of a "weighted sensitivity function". The balance between the objective function and the constraints is controlled by a "balancing coefficient". The overall computational procedure is given and an example is presented. The computations are given for a set of randomly generated test problems in which the optimal parallel redundancy under linear constraints is determined. The proposed method is then compared with other methods. System 250--a fault-tolerant, modular processing system for control applications. K. J. HAMER-HODGES and G. B. K. STAGG. Systems Technol. 27, 26 (November 1977). This article concentrates on the philosophies embodied in the design of System 250 which ensure its role as a highavailability, modular, real-time processing system. Particular reference is made to the advantages of the distributed arrangement of both processors and high-speed store modules (as compared with conventional, dual-processor configurations), to the powerful error control and diagnostic features, and to the fault recovery strategy. The discussion of error containment makes detailed reference to the use of "capability" techniques, by which the hardware and software are structured into discrete protected domains leading to unusually powerful fault tolerance, data privacy and security.
Redundant systems with appreciable exchange time. JENDE HSU. IEEE Trans. Reliab. R-26, (2) 125 (June 1977). In dealing with redundant systems, the time required to exchange the failed unit for a spare one is often assumed to be negligible and only the time required for repair is considered. If exchange time is indeed appreciable, numerical methods are applied to analyze the system because it is usually thought to be too complicated to be solved analytically. This paper proposes an analytic solution, in which states of the system are grouped into rows; states having the same number of up-units are in the same row. Steady state probability of each state is expressed in terms of the
354
World Abstracts on Mieroelectronics and Reliability
probabilities of the states in the same row and in the row immediately above. Through these recursive relationships and simple substitutions, the steady state probabilities are solved.
Efficient construction of minimal cut sets from fault trees. S. GARRIBA, P. MUSSIO, F. NALD1, G. REINA and G. VOLTA. IEEE Trans. Reliab. R-26, (2) 88 (June 1977). A formal method and an algorithm are presented to determine minimal cut sets (MCSs) from fault trees. The method is based upon segmenting the tree, constructing MCSs of subtrees and subsequent expanding into the MCS of the original tree. The major advantage of the method is the direct determination of MCSs up to any order required. More particularly, the algorithm DICOM1CS allows straightforward analyses for all those cases (large trees, high order cut sets, repeated elements) where present combinatorial and Monte Carlo techniques are not effective. Compared with other structural algorithms now in use, DICOMICS provides a near optimal effective construction of MCSs. Thus, even when there are many redundant cut sets, computer implementations yield a substantial reduction of computing steps and effort. Hand calculation and interactive programming are also possible. A new method for recognition of defects in electronic devices. V o s HoRsx RODER. Frequenz 31, (8) 253 (1977). (In German.) The presently available tests rule out any prediction and detection of a possible defect which may occur during the operation of the electronic device. The new method described here enables such a prediction already during preliminary testing through short time measurements of phase noise. A detailed description of the device and its applicability is given. Optimal design of a series-parallel system with time-dependent reliability. KYOICHI NAKASHIMA and KAZUHARU YAMATO. IEEE Trans. Reliab. R-26, (2) 119 (June 1977). The paper formulates on 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 problerns is presented along with an example. Interval reliability and optimum preventive maintenance policy. HISASHI MINE and TOSHIO NAKAGAWA.IEEE Trans. Reliab. R-26, (2) (June 1977). This paper discusses an interval reliability R(x, T) of a 1-unit system with repair. The R(x, TI is derived explicitly for the case in which T and x are distributed exponentially. This paper also discusses the optimum preventive maintenance policies maximizing the limiting interval reliability when T is constant and maximizing the interval reliability when T has an exponential distribution. The confidence in reliability predictions. ASHOK K. BABAR. QR Journal (India) p. 33 (January 1977). Reliability prediction is inherently not so accurate since it utilises data obtained from previous experience. Nevertheless, it is possible to improve upon the predictions and also the basic data if these are compared with the observed data. If a distribution based on some parameter depending upon the observed and predicted failures is obtained, it will help in attaching confidence levels to the predictions. A case study is described in which predicted/observed MTBF data was tested and a lognormal distribution fit was observed. The method of stages for non-Markov models. C. SINGH, R. BILUNTON and S. Y. LEE. IEEE Trans. Reliab. R-26, (2) 135 (June 1977). Several techniques are available for
solving reliability models containing non-exponential state residence times. All of these techniques, other than the method of stages, involve derivation of closed-form expressions in time domain or Laplace form. Though the closedform solutions are useful, they are often impossible to derive due to complexity of the interstate transition rates Stage combinations can be used either to fit the available data or approximate a known probability distribution. The main advantage with this method is that though an explicit mathematical expression does not emerge, the numerical solution can be generally obtained. This paper briefly describes some fundamental stage combinations that can be used to simulate a wide range of distributions, and refers to more-extensive explanations.
An application of optimal control theory to repairman problem with machine interference. IEEE Trans. Reliab. R-26, (2) 121 (June 1977). Optimal preventive maintenance policy for a system of machines subject to random breakdowns and repairs is derived using optimal control theory. The optimal policy is shown to be "bang-bang'. The model accounts for the waiting line at the repair facility and establishes a link between machine maintenance and classical repairman problem involving machine interference. An example illustrates the procedure to obtain the optimal preventive maintenance policy. An important feature of this work is that the usual assumption of the steady-state behaviour of the queue is relaxed (by-directly considering the Kolmogorov differential equations as state equations of the system) and its transient behaviour is explicitly taken into account. Pragmatic software reliability prediction. JOHN K. WALL and PAUL A. FERGUSON. Proc. IEEE Reliab. Mai,tainab. Syrup. Philadelphia, 18--20 Jan. 1977. p. 485. It is shown that expressions of the form C = Co(M/M0) ~ and R := Ro(M/Mo) ~, where C is the cumulative number of errors detected, R is the rate of failure detection, M is a measure of the software maturity, and Co, Ro, Mo and ~ are constants, correlate well with software failure data flom six widely different sources. It is shown that ~ generally lies in the range of 0.3 to 0.7, but that Co and Ro must be determined from observational data for the particular program under study. An investigation of software reliability models. Capt. ALAN N. SUKERT. Proc. IEEE Reliab. Maintainab. Syrup. Philadelphia, 18~20 Jan. 1977. p. 478. This paper reports on the initial phase of a software reliability modeling study, in which nine software reliability models were applied against software error data detailing the complete error history from the start of formal testing through delivery of a large command and control software development project with over 100,000 lines of Jovial code. The paper describes the models considered and the procedures used to prepare the data for model input. Model predictions are then compared and analyzed against the actual post-delivery error data for this project. From this analysis, conclusions concerning model applicability and some possible extensions of this study are discussed. Some theoretical bases of error analysis in analogue circuits. H. K. RAMBEER.Nachrichtentechnik Elektronik 27, 117 (1977). (In German.) The multiple-gate theory and network analysis as applied to the determination of element parameters by measurement are described to derive methods of fault location in analogue linear circuits. Terminals accessible to measurements of multiple-gate characteristics of the circuit are classified by suitable actions to be made in these measurements. From them a discrimination of various types of network is derived. Some conditions necessary for determining element parameters from multiple-gate ones are given.
The highest and lowest reliability achievable with redundancy. PETERW. BECKER.IEEE Trans. Reliab. R-26, (3) 209 (August 1977). Often system reliability can be enhanced through the use of redundancy. Redundancy may, however, have a detrimental effect on the statistical relationship of redundant elements. When the components in a redundant system have more than one failure-mode and when failures are sdependent, it is difficult to assess the reliability of the system. The paper describes the 0-transformation by which the highest and lowest reliability achievable can be determined for a configuration using components with specified reliabilities. As a by-product we become able to pinpoint the statistical relationships that give rise to highest and lowest system reliabilities.
Cost-optimised burn-in duration for repairable electronic systems. KENNETHT. PLESSERand THOMASO. FIELD. IEEE Trans. Reliab. R-26, (3) 195 (August 1977). A mathematical model permits determining the duration of cost-optimized burn-in and evaluating the resultant saving for repairable electronics systems. Infant mortality failures occur according to a nonhomogeneous Poisson Process; repair actions restore the system to a bad-as-old condition. The s-expected costs associated with factory and field failures are traded-off with the costs of implementing a burn-in program. Under the constraints of the model, the optimum burn-in duration and consequent cost saving are independent of the eventual life of the system in the field. A numerical example illustrates these concepts.
Techniques for servicing LSl-based gear evolve. STEPHEN E. SCRUPSKI.Electronics p. 120 (27 October 1977). The impact of microprocessors on instruments is proving to be more indirect than direct--but revolutionary all the same. Users of microprocessor-based equipment are urgently demanding test systems capable of servicing it, and already a few of the larger instrument companies have made significant moves toward filling this vacuum. Next year many others will also contribute to a bumper crop of service-oriented instruments, espousing many different approaches to fault diagnosis.
Optimum preventive maintenance policies for repairable systems. TOSHIO NAKAGAWA.IEEE Trans. Reliab. R-26, (3) 168 (August 1977). This paper summarizes my recent work in analyzing preventive maintenance of the following kinds of repairable systems: 1-unit systems, 2-unit standby systems, and a system with unrepairable spare units. Some appropriate reliability measures of such systems are given, and optimum preventive maintenance policies which maximize or minimize these measures are derived under suitable conditions.
Minimum cost systems with specified reliability. K. K. AGGARWAL. IEEE Trans. Reliab. R-26, (3) 166 (August 1977). A method is presented for allocating reliability to each unit of a system with a view to minimizing the system cost. The practical utility of this method, as well as other methods, depends heavily on the availability of costreliability data for the constituent units. Unfortunately, for most components such data are not readily available. There is a need for manufacturers and users to make these data available to reliability theoreticians so that the derived results are usefully applied to practical systems. So far, very little seems to have been done in this direction.
Determining component reliability and redundancy for optimum system reliability. FRANK A. TILLMAN, CHING-LA1 HWANG and WAY Kuo. IEEE Trans. Reliab. R-26, (3) 162 (August 1977). The usual constrained reliability optimization problem is extended to include determining the optimal level of component reliability and the number of redundancies in each stage. With cost, weight, and volume constraints, the problem is one in which the component reliability is a
353
variable, and the optimal trade-off between adding components and improving individual component reliability is determined. This is a mixed integer nonlinear programming problem in which the system reliability is to be maximized as a function of component reliability level and the number of components used at each stage. The model is illustrated with three general non linear constraints imposed on the system. The Hooke and Jeeves pattern search technique in combination with the heuristic approach by Aggarwal et al. is used to solve the problem. The Hooke and Jeeves pattern search technique is a sequential search routine for maximizing the system reliability, Rs(R, X). The argument in the Hooke and Jeeves pattern search is the component reliability,/~, which is varied according to exploratory moves and pattern moves until the maximum of Rs(R, X) is obtained. The heuristic approach is applied to each value of the component reliability, R, to obtain the optimal number of redundancies, X, which maximizes Rs(R, X) for the stated
Optimization techniques for system reliability with redundancy--a review. FRANK A. TILLMAN, CHING-LAI HWANG and WAY Kuo. IEEE Trans. Reliab. R-26, (3) 148 (August 1977). This paper is a state-of-art review of the literature related to optimal system reliability with redundancy. The literature is classified as follows.
A heuristic method for determining optimal reliability allocation. YuJi NAKAGAWA and KYOlCHI NAKASHIMA.IEEE Trans. Reliab. R-26, (3) 156 (August 1977). The paper presents a method for obtaining an optimal reliability allocation of an n-stage series system. In each stage, redundant components can be added (in parallel, stand-by, or k-out-ofn:G, etc.), or a more reliable component can be used in order to improve the system reliability. The solution is obtained by repeatedly using a more reliable candidate at each stage that has the greatest value of a "weighted sensitivity function". The balance between the objective function and the constraints is controlled by a "balancing coefficient". The overall computational procedure is given and an example is presented. The computations are given for a set of randomly generated test problems in which the optimal parallel redundancy under linear constraints is determined. The proposed method is then compared with other methods. System 250--a fault-tolerant, modular processing system for control applications. K. J. HAMER-HODGES and G. B. K. STAGG. Systems Technol. 27, 26 (November 1977). This article concentrates on the philosophies embodied in the design of System 250 which ensure its role as a highavailability, modular, real-time processing system. Particular reference is made to the advantages of the distributed arrangement of both processors and high-speed store modules (as compared with conventional, dual-processor configurations), to the powerful error control and diagnostic features, and to the fault recovery strategy. The discussion of error containment makes detailed reference to the use of "capability" techniques, by which the hardware and software are structured into discrete protected domains leading to unusually powerful fault tolerance, data privacy and security.
Redundant systems with appreciable exchange time. JENDE HSU. IEEE Trans. Reliab. R-26, (2) 125 (June 1977). In dealing with redundant systems, the time required to exchange the failed unit for a spare one is often assumed to be negligible and only the time required for repair is considered. If exchange time is indeed appreciable, numerical methods are applied to analyze the system because it is usually thought to be too complicated to be solved analytically. This paper proposes an analytic solution, in which states of the system are grouped into rows; states having the same number of up-units are in the same row. Steady state probability of each state is expressed in terms of the
354
World Abstracts on Mieroelectronics and Reliability
probabilities of the states in the same row and in the row immediately above. Through these recursive relationships and simple substitutions, the steady state probabilities are solved.
Efficient construction of minimal cut sets from fault trees. S. GARRIBA, P. MUSSIO, F. NALD1, G. REINA and G. VOLTA. IEEE Trans. Reliab. R-26, (2) 88 (June 1977). A formal method and an algorithm are presented to determine minimal cut sets (MCSs) from fault trees. The method is based upon segmenting the tree, constructing MCSs of subtrees and subsequent expanding into the MCS of the original tree. The major advantage of the method is the direct determination of MCSs up to any order required. More particularly, the algorithm DICOM1CS allows straightforward analyses for all those cases (large trees, high order cut sets, repeated elements) where present combinatorial and Monte Carlo techniques are not effective. Compared with other structural algorithms now in use, DICOMICS provides a near optimal effective construction of MCSs. Thus, even when there are many redundant cut sets, computer implementations yield a substantial reduction of computing steps and effort. Hand calculation and interactive programming are also possible. A new method for recognition of defects in electronic devices. V o s HoRsx RODER. Frequenz 31, (8) 253 (1977). (In German.) The presently available tests rule out any prediction and detection of a possible defect which may occur during the operation of the electronic device. The new method described here enables such a prediction already during preliminary testing through short time measurements of phase noise. A detailed description of the device and its applicability is given. Optimal design of a series-parallel system with time-dependent reliability. KYOICHI NAKASHIMA and KAZUHARU YAMATO. IEEE Trans. Reliab. R-26, (2) 119 (June 1977). The paper formulates on 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 problerns is presented along with an example. Interval reliability and optimum preventive maintenance policy. HISASHI MINE and TOSHIO NAKAGAWA.IEEE Trans. Reliab. R-26, (2) (June 1977). This paper discusses an interval reliability R(x, T) of a 1-unit system with repair. The R(x, TI is derived explicitly for the case in which T and x are distributed exponentially. This paper also discusses the optimum preventive maintenance policies maximizing the limiting interval reliability when T is constant and maximizing the interval reliability when T has an exponential distribution. The confidence in reliability predictions. ASHOK K. BABAR. QR Journal (India) p. 33 (January 1977). Reliability prediction is inherently not so accurate since it utilises data obtained from previous experience. Nevertheless, it is possible to improve upon the predictions and also the basic data if these are compared with the observed data. If a distribution based on some parameter depending upon the observed and predicted failures is obtained, it will help in attaching confidence levels to the predictions. A case study is described in which predicted/observed MTBF data was tested and a lognormal distribution fit was observed. The method of stages for non-Markov models. C. SINGH, R. BILUNTON and S. Y. LEE. IEEE Trans. Reliab. R-26, (2) 135 (June 1977). Several techniques are available for
solving reliability models containing non-exponential state residence times. All of these techniques, other than the method of stages, involve derivation of closed-form expressions in time domain or Laplace form. Though the closedform solutions are useful, they are often impossible to derive due to complexity of the interstate transition rates Stage combinations can be used either to fit the available data or approximate a known probability distribution. The main advantage with this method is that though an explicit mathematical expression does not emerge, the numerical solution can be generally obtained. This paper briefly describes some fundamental stage combinations that can be used to simulate a wide range of distributions, and refers to more-extensive explanations.
An application of optimal control theory to repairman problem with machine interference. IEEE Trans. Reliab. R-26, (2) 121 (June 1977). Optimal preventive maintenance policy for a system of machines subject to random breakdowns and repairs is derived using optimal control theory. The optimal policy is shown to be "bang-bang'. The model accounts for the waiting line at the repair facility and establishes a link between machine maintenance and classical repairman problem involving machine interference. An example illustrates the procedure to obtain the optimal preventive maintenance policy. An important feature of this work is that the usual assumption of the steady-state behaviour of the queue is relaxed (by-directly considering the Kolmogorov differential equations as state equations of the system) and its transient behaviour is explicitly taken into account. Pragmatic software reliability prediction. JOHN K. WALL and PAUL A. FERGUSON. Proc. IEEE Reliab. Mai,tainab. Syrup. Philadelphia, 18--20 Jan. 1977. p. 485. It is shown that expressions of the form C = Co(M/M0) ~ and R := Ro(M/Mo) ~, where C is the cumulative number of errors detected, R is the rate of failure detection, M is a measure of the software maturity, and Co, Ro, Mo and ~ are constants, correlate well with software failure data flom six widely different sources. It is shown that ~ generally lies in the range of 0.3 to 0.7, but that Co and Ro must be determined from observational data for the particular program under study. An investigation of software reliability models. Capt. ALAN N. SUKERT. Proc. IEEE Reliab. Maintainab. Syrup. Philadelphia, 18~20 Jan. 1977. p. 478. This paper reports on the initial phase of a software reliability modeling study, in which nine software reliability models were applied against software error data detailing the complete error history from the start of formal testing through delivery of a large command and control software development project with over 100,000 lines of Jovial code. The paper describes the models considered and the procedures used to prepare the data for model input. Model predictions are then compared and analyzed against the actual post-delivery error data for this project. From this analysis, conclusions concerning model applicability and some possible extensions of this study are discussed. Some theoretical bases of error analysis in analogue circuits. H. K. RAMBEER.Nachrichtentechnik Elektronik 27, 117 (1977). (In German.) The multiple-gate theory and network analysis as applied to the determination of element parameters by measurement are described to derive methods of fault location in analogue linear circuits. Terminals accessible to measurements of multiple-gate characteristics of the circuit are classified by suitable actions to be made in these measurements. From them a discrimination of various types of network is derived. Some conditions necessary for determining element parameters from multiple-gate ones are given.