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Reliability improvement by redundancy voting in analogue electronic systems
World Abstracts on Microelectronics and Reliability operational availability of a certain operating item as a function of the occurrence of failures with all other items and the repair strategy. Formulas are derived for the following cases: Repairs are made continuously; No repairs are made; Repairs are only made in urgent cases. In the second part of this paper, these considerations will be illustrated by the example of a radio relay system.
Optimum number of checks in checking policy. S. YAMADA and S. OSAKI. Microelectron. Reliab. 16, 589 (1977). We consider the checking problem under the case that if system failure is detected by checking, then the problem ends. By the methods of calculus of variations, we find the optimum number of checks which minimizes the expected loss up to detection of the first failure subject to the condition that the expected cost of checking is restricted. Applying the obtained results of the Gamma distribution with a shape parameter 2, we show the curve of the optimum number of checks graphically. Optimal placement of spare modules in a cascaded chain. B. PARHAMI. IEEE Trans. Reliab. R-26, (4) 280 (October 1977). A class of redundant cascaded chains with i.i.d, modules is considered in which recovery from a failure takes place by replacing the faulty module by a spare module. The complexity of the reconfiguration process depends upon the location of spare modules in the cascade. This paper deals with the question of optimally placing the spare modules in order to minimize the s-expected recovery time (down time) of the system. Exact analysis is carried out for cascades with one and two spare modules and an approximate analysis is given for three or more spares. Even though exact analysis does not seem to be practical in the general case, the symmetry of spare module positions in the special cases discussed here and linearity of the system suggest that one might expect the optimal positions to be symmetric in general. Because of this symmetry, one can reduce the number of variables to be considered in the general case, however, some inaccuracies might be introduced. Reliability improvement by redundancy voting in analogue electronic systems. K. B. KLAASSEN and J. C. L. VAN PEPPEN. Microelectron. Reliab. 16, 593 (1977). In this paper the reliability improvement obtained with redundancy voting applied to a number of analogue electronic subsystems is evaluated. Two different voting strategies that can easily be realized are considered in more detail; median voting and reduced-mean voting. For these voters the combined effect of partial and total failures in the redundant subsystems is analysed. In addition, simple expressions are derived that approximate well to the reliability improvement. It is further shown that a reduced-mean voter gives a considerably higher improvement than a median voter. The circuitry for the implementation of a reduced-mean voter is, however, more complex than that for a median voter. Therefore, a reduced-mean voter will form a reliability limiting factor in the system design more quickly than a median voter. Sensitivity of Bayes estimates of reciprocal MTBF and reliability to an incorrect failure model. J. J. HZGGrNS and
419
C. P. TSOKOS. IEEE Trans. Reliab. R-26, (4) 286 (October 1977). A unit is placed on test for a fixed time, and the number of failures is observed. The stochastic process generating the failures is assumed to have s-independent, Erlang distributed times between failures. Bayes estimates of reciprocal MTBF (RMTBF) and reliability are given where the loss function is squared.error and the prior distribution for RMTBF is gamma. We investigate what happens to the Bayes estimates when the shape parameter in the failure model is incorrectly specified (e.g., the failure model is assumed to be Poisson when it is not). This question is answered for parameters which are typical of a wide range of actual military equipment failure data. As the shape parameter in the failure model changes (1) there is only a small to moderate change in the estimates of RMTBF; (2) there is a small to moderate change in the estimate of reliability for small numbers of failures but a larger change for an unusually large number of failures; (3) there is little change in the s-efficiencies of the estimates as measured by s-expected squared error loss. For the range of parameters in this study, not much is lost in s-efficiency by restricting attention to the mathematically tractable Erlang failure model instead of using a more generaI gamma failure model. A rough approximation of the value of the shape parameter in the failure model is nearly as good as the exact value in terms of estimating RMTBF and reliability since these estimates are relatively insensitive to changes in the shape parameter.
Failure-rate as a function of time due to Iognormal life distribution(s) of weak parts. O. HALLBERG. Microelectron. Reliab. 16, 155 (1977). The presence of weak parts (i.e. damaged; with shorter life length expectancy) within a batch of components will give rise to a high initial failurerate which will then decrease by time. Life tests have shown that weak parts have a more or less lognormal life distribution. This distribution has been assumed when calculating the failure-rate as a function of time as well as the influence of burn-in on the failure rate during actual use. A calculator program has been developed that makes it easy to predict the failure-rate during normal use from data retained from life tests. Availability prediction by using a method of simulation. B. A. BASKER and P. MARTIN. Microelectron. Reliab. 16, 135 (1977). The work described in the literature on the subject of Availability is based mainly on the assumption of exponential distribution of failure and repair times. If this assumption is not valid, evaluation of Availability itself is a complex problem and has rarely been attempted. This paper describes a method based on simulation to evaluate Availability of units in a system, be it an electrical or a production system. The failure and repair rates of units in the system need not necessarily follow the exponential distribution. A test approach for commercial communication satellites. F. BEISEL. Microelectron. Reliab. 16, 91 (1977). A description is given of the test philosophy presently being used for the commercial communication satellites to assure good confidence in the design and flight hardware before launch. A summary overview of a typical test program is presented.
4. M I C R O E L E C T R O N I C S - - G E N E R A L
Plastic encapsulated semiconductor devices--A bibliography. C. H. TAYLOR. Microelectron. Reliab. 16, 701 (1977). Bibliography, compiled by C. H. Taylor, RSRE, Malvern, Worcs., U.K., covering 1973 to 1976 inclusive. Calculating the cost of testing LSI chips. C. CHRO~S. Elec-
tronics p. 171 (January 5, 1978). Before making the leap into large-scale integration, a product designer should look realistically at the cost of LSI testing. It can easily skyrocket to as much as $10 a chip, since LSI test systems are expensive to buy and even more expensive to run. To make an intelligent design decision, therefore, the engineer
Optimum number of checks in checking policy. S. YAMADA and S. OSAKI. Microelectron. Reliab. 16, 589 (1977). We consider the checking problem under the case that if system failure is detected by checking, then the problem ends. By the methods of calculus of variations, we find the optimum number of checks which minimizes the expected loss up to detection of the first failure subject to the condition that the expected cost of checking is restricted. Applying the obtained results of the Gamma distribution with a shape parameter 2, we show the curve of the optimum number of checks graphically. Optimal placement of spare modules in a cascaded chain. B. PARHAMI. IEEE Trans. Reliab. R-26, (4) 280 (October 1977). A class of redundant cascaded chains with i.i.d, modules is considered in which recovery from a failure takes place by replacing the faulty module by a spare module. The complexity of the reconfiguration process depends upon the location of spare modules in the cascade. This paper deals with the question of optimally placing the spare modules in order to minimize the s-expected recovery time (down time) of the system. Exact analysis is carried out for cascades with one and two spare modules and an approximate analysis is given for three or more spares. Even though exact analysis does not seem to be practical in the general case, the symmetry of spare module positions in the special cases discussed here and linearity of the system suggest that one might expect the optimal positions to be symmetric in general. Because of this symmetry, one can reduce the number of variables to be considered in the general case, however, some inaccuracies might be introduced. Reliability improvement by redundancy voting in analogue electronic systems. K. B. KLAASSEN and J. C. L. VAN PEPPEN. Microelectron. Reliab. 16, 593 (1977). In this paper the reliability improvement obtained with redundancy voting applied to a number of analogue electronic subsystems is evaluated. Two different voting strategies that can easily be realized are considered in more detail; median voting and reduced-mean voting. For these voters the combined effect of partial and total failures in the redundant subsystems is analysed. In addition, simple expressions are derived that approximate well to the reliability improvement. It is further shown that a reduced-mean voter gives a considerably higher improvement than a median voter. The circuitry for the implementation of a reduced-mean voter is, however, more complex than that for a median voter. Therefore, a reduced-mean voter will form a reliability limiting factor in the system design more quickly than a median voter. Sensitivity of Bayes estimates of reciprocal MTBF and reliability to an incorrect failure model. J. J. HZGGrNS and
419
C. P. TSOKOS. IEEE Trans. Reliab. R-26, (4) 286 (October 1977). A unit is placed on test for a fixed time, and the number of failures is observed. The stochastic process generating the failures is assumed to have s-independent, Erlang distributed times between failures. Bayes estimates of reciprocal MTBF (RMTBF) and reliability are given where the loss function is squared.error and the prior distribution for RMTBF is gamma. We investigate what happens to the Bayes estimates when the shape parameter in the failure model is incorrectly specified (e.g., the failure model is assumed to be Poisson when it is not). This question is answered for parameters which are typical of a wide range of actual military equipment failure data. As the shape parameter in the failure model changes (1) there is only a small to moderate change in the estimates of RMTBF; (2) there is a small to moderate change in the estimate of reliability for small numbers of failures but a larger change for an unusually large number of failures; (3) there is little change in the s-efficiencies of the estimates as measured by s-expected squared error loss. For the range of parameters in this study, not much is lost in s-efficiency by restricting attention to the mathematically tractable Erlang failure model instead of using a more generaI gamma failure model. A rough approximation of the value of the shape parameter in the failure model is nearly as good as the exact value in terms of estimating RMTBF and reliability since these estimates are relatively insensitive to changes in the shape parameter.
Failure-rate as a function of time due to Iognormal life distribution(s) of weak parts. O. HALLBERG. Microelectron. Reliab. 16, 155 (1977). The presence of weak parts (i.e. damaged; with shorter life length expectancy) within a batch of components will give rise to a high initial failurerate which will then decrease by time. Life tests have shown that weak parts have a more or less lognormal life distribution. This distribution has been assumed when calculating the failure-rate as a function of time as well as the influence of burn-in on the failure rate during actual use. A calculator program has been developed that makes it easy to predict the failure-rate during normal use from data retained from life tests. Availability prediction by using a method of simulation. B. A. BASKER and P. MARTIN. Microelectron. Reliab. 16, 135 (1977). The work described in the literature on the subject of Availability is based mainly on the assumption of exponential distribution of failure and repair times. If this assumption is not valid, evaluation of Availability itself is a complex problem and has rarely been attempted. This paper describes a method based on simulation to evaluate Availability of units in a system, be it an electrical or a production system. The failure and repair rates of units in the system need not necessarily follow the exponential distribution. A test approach for commercial communication satellites. F. BEISEL. Microelectron. Reliab. 16, 91 (1977). A description is given of the test philosophy presently being used for the commercial communication satellites to assure good confidence in the design and flight hardware before launch. A summary overview of a typical test program is presented.
4. M I C R O E L E C T R O N I C S - - G E N E R A L
Plastic encapsulated semiconductor devices--A bibliography. C. H. TAYLOR. Microelectron. Reliab. 16, 701 (1977). Bibliography, compiled by C. H. Taylor, RSRE, Malvern, Worcs., U.K., covering 1973 to 1976 inclusive. Calculating the cost of testing LSI chips. C. CHRO~S. Elec-
tronics p. 171 (January 5, 1978). Before making the leap into large-scale integration, a product designer should look realistically at the cost of LSI testing. It can easily skyrocket to as much as $10 a chip, since LSI test systems are expensive to buy and even more expensive to run. To make an intelligent design decision, therefore, the engineer