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A successful program for missile reliability
588
World Abstracts on Microelectronics and Reliability
increases but so does the anticipated failure rate in the system. On the other hand, the hardware redundancy available in such systems is capable of providing, in addition to large amounts of computing power, improved reliability and graceful degradation. This paper analyzes the scalability of large degradable homogeneous multiprocessors. The objective is to assess the limitations, imposed by reliability considerations, on the number of processors. The analysis of the mean-time-to-failure and the mission-time shows that, for a given value of the coverage factor, there exists a value of the number of processors at which these measures are maximal. As the system size is increased beyond this value, the reliability of the system becomes a rapidly decreasing function of the number of processors. The measure of processor-hours is defined as the amount of potential computational work. This measure is upperbounded, and the upper-bound is independent of the initial number of processors. For computations with linear speedup, the amount of reliable computational work is constant for large system-sizes. When the speed-up is not linear, this amount is a decreasing function of the number of processors. Therefore, for large system-sizes and same technology, increasing the number of processors results in a decrease of the average amount of reliable computational work the system can deliver. Graceful degradation in large fault-tolerant systems is not scalable. In order to preserve the same performance and reliability level, an increase in the number of processors must be matched by a decrease of the same magnitude in the probability of failed recovery. Temperature-dependent standard deviation of log (failure time) distributions. C. K. Ca~,N. 1EEE Trans Reliab. 40(2), 157 (1991). Distributions of failure times at accelerated life-test temperatures are often analyzed assuming a constant-a model, where a is the standard deviation of log (failure times). Recent experimental and theoretical studies of laser degradation, time-dependent dielectric breakdown, and electromigration suggest that a is temperature-dependent. This paper derives a general relationship for temperature-dependent a from the Arrhenius relation. The relationship is used to analyze published electromigration data. The analysis suggests that the correlation coefficient between the activation energy and log (pre-exponential factor in the Arrhenius relation) is close to - 1. An example illustrates the use of the relationship to validate the electromigration design rule of a hypothetical microcircuit technology. Assuming a constant o could result in an invalid design rule. Factoring and reductions for networks with imperfect vertices. OLYMPIA R. THEOLOC,OU and JACQUES G. CARLIER, IEEE Trans. Reliab. 40(2), 210 (1991). Factoring and reductions are effective methods for computing the K-terminal reliability of undirected networks, but they have been applied mostly to networks with perfect vertices. However, in real problems, vertices may fail as well as edges. Imperfect vertices can be factored like edges, but the complexity then increases exponentially with their number. We have developed a new technique to account for the failure of vertices with small additional cost, using a modified method of factoring and reductions. This technique is very easy to integrate into a factoring algorithm and consists of factoring, not on a single element (e.g. a single edge) but on a set of elements (e.g. an edge and its endpoints). The problem is that random variables associated with the elements of the network are no longer independent. This can be handled by choosing factoring edges that have at least one perfect endpoint. Our technique leaves practically unchanged the factoring algorithm, The only difference is that some supplementary probability values are kept for the imperfect vertices of the original and the induced graphs. For algorithms using simple reductions, it has negligible compu-
tational cost. Polygon-to-chain reductions cannot be used when vertices are imperfect, and this restriction can increase the complexity of an algorithm that would otherwise use them; but this increase is smaller than the one for factoring on vertices. Examples illustrate the performance of a program using this method and compare it to others. The running times of this program for imperfect vertices are shorter than the ones given in the literature for the same networks with perfect vertices. Piecewise exponential estimator of the survivor function. J ~ Soo KIM and FRANK PROSCHAN. IEEE Trans. Reliab. 40(2), 134 (1991). A method for estimating the survivor function of a life distribution from a set of censored data is presented. We illustrate the method and explain how to calculate the survivor function from a censored data set. The estimator is compared with the well-known Kaplan-Meier estimator, using a set of data observed in a real engineering situation. The advantages and disadvantages of the method are discussed. Approximate MLEs for the location and scale parameters of the half-logistic distribution with type-H right-censoring. N, BALAKRISHNANand K. H. T. WON~. [EEE Trans. Reliab. 40(2), 140 (1991). For the half-logistic distribution, the maximum likelihood method does not provide an explicit estimator for the scale parameter based on either complete or right-censored samples. This paper provides a simple method of deriving an explicit estimator by approximating the likelihood function. We study the bias and variance of this estimator, and show that this estimator is as efficient as the best linear unbiased estimator. We present an example to illustrate this method. A successful program for missile reliability. GERALD P. IVIETTLERand PAUL D. TOWI'~R III. Proc. ,4. Reliab. Maintainab. Syrup., 481 (1991). With increasingly constrained federal budgets, weapon systems must adapt to expenditure and hardware resource limitations. This paper summarizes almost six years of FSD reliability engineering activity for the vertical launch ASROC (VLA) anti-submarine missile in such an environment. The program necessitated task tailoring and a search for cost effectiveness. This paper is a compilation of "lessons learned" for a low-cost, medium size reliability program. It shows that careful attention to technical and administrative details will lead to successful hardware functions as demonstrated through testing. Properly conducted reliability efforts can make substantial contributions to achieve desired results. Task tailoring for cost effectiveness was always a paramount consideration. Highlights from the conduct of each assigned task are presented in this paper, which are discussed under the headings and in the order of MIL-STD-785. This reflective view of those experiences may be of assistance for planning future reliability programs of any size in this cost conscious environment. A nonparametrlc aEproaeh to progreuive strem ueeelerated life testing. ZI-mSONINOLIs and HELIANGFEi. IEEE Trans. Reliab. 40(2), 173 (1991). We consider progressive-stress accelerated life testing wherein the stress on an unfailed item increases linearly with test time, when the time transformation function is a version of the inverse power law. Our approach here is nonparametric in that we do not make many assumptions about life distribution. We introduce a testing pattern and explain how to draw inferences from progressive stress tests. In some detail, we propose an estimator of life distribution at the usual stress level. Approximate MLFa for the iueation and scale paruseters of the extreme value dimilmflen with ¢t.amring. N. BALAKRISHNANand J. Vm,.~A~. [EEE Trans. Reliab. 40(2),
World Abstracts on Microelectronics and Reliability
increases but so does the anticipated failure rate in the system. On the other hand, the hardware redundancy available in such systems is capable of providing, in addition to large amounts of computing power, improved reliability and graceful degradation. This paper analyzes the scalability of large degradable homogeneous multiprocessors. The objective is to assess the limitations, imposed by reliability considerations, on the number of processors. The analysis of the mean-time-to-failure and the mission-time shows that, for a given value of the coverage factor, there exists a value of the number of processors at which these measures are maximal. As the system size is increased beyond this value, the reliability of the system becomes a rapidly decreasing function of the number of processors. The measure of processor-hours is defined as the amount of potential computational work. This measure is upperbounded, and the upper-bound is independent of the initial number of processors. For computations with linear speedup, the amount of reliable computational work is constant for large system-sizes. When the speed-up is not linear, this amount is a decreasing function of the number of processors. Therefore, for large system-sizes and same technology, increasing the number of processors results in a decrease of the average amount of reliable computational work the system can deliver. Graceful degradation in large fault-tolerant systems is not scalable. In order to preserve the same performance and reliability level, an increase in the number of processors must be matched by a decrease of the same magnitude in the probability of failed recovery. Temperature-dependent standard deviation of log (failure time) distributions. C. K. Ca~,N. 1EEE Trans Reliab. 40(2), 157 (1991). Distributions of failure times at accelerated life-test temperatures are often analyzed assuming a constant-a model, where a is the standard deviation of log (failure times). Recent experimental and theoretical studies of laser degradation, time-dependent dielectric breakdown, and electromigration suggest that a is temperature-dependent. This paper derives a general relationship for temperature-dependent a from the Arrhenius relation. The relationship is used to analyze published electromigration data. The analysis suggests that the correlation coefficient between the activation energy and log (pre-exponential factor in the Arrhenius relation) is close to - 1. An example illustrates the use of the relationship to validate the electromigration design rule of a hypothetical microcircuit technology. Assuming a constant o could result in an invalid design rule. Factoring and reductions for networks with imperfect vertices. OLYMPIA R. THEOLOC,OU and JACQUES G. CARLIER, IEEE Trans. Reliab. 40(2), 210 (1991). Factoring and reductions are effective methods for computing the K-terminal reliability of undirected networks, but they have been applied mostly to networks with perfect vertices. However, in real problems, vertices may fail as well as edges. Imperfect vertices can be factored like edges, but the complexity then increases exponentially with their number. We have developed a new technique to account for the failure of vertices with small additional cost, using a modified method of factoring and reductions. This technique is very easy to integrate into a factoring algorithm and consists of factoring, not on a single element (e.g. a single edge) but on a set of elements (e.g. an edge and its endpoints). The problem is that random variables associated with the elements of the network are no longer independent. This can be handled by choosing factoring edges that have at least one perfect endpoint. Our technique leaves practically unchanged the factoring algorithm, The only difference is that some supplementary probability values are kept for the imperfect vertices of the original and the induced graphs. For algorithms using simple reductions, it has negligible compu-
tational cost. Polygon-to-chain reductions cannot be used when vertices are imperfect, and this restriction can increase the complexity of an algorithm that would otherwise use them; but this increase is smaller than the one for factoring on vertices. Examples illustrate the performance of a program using this method and compare it to others. The running times of this program for imperfect vertices are shorter than the ones given in the literature for the same networks with perfect vertices. Piecewise exponential estimator of the survivor function. J ~ Soo KIM and FRANK PROSCHAN. IEEE Trans. Reliab. 40(2), 134 (1991). A method for estimating the survivor function of a life distribution from a set of censored data is presented. We illustrate the method and explain how to calculate the survivor function from a censored data set. The estimator is compared with the well-known Kaplan-Meier estimator, using a set of data observed in a real engineering situation. The advantages and disadvantages of the method are discussed. Approximate MLEs for the location and scale parameters of the half-logistic distribution with type-H right-censoring. N, BALAKRISHNANand K. H. T. WON~. [EEE Trans. Reliab. 40(2), 140 (1991). For the half-logistic distribution, the maximum likelihood method does not provide an explicit estimator for the scale parameter based on either complete or right-censored samples. This paper provides a simple method of deriving an explicit estimator by approximating the likelihood function. We study the bias and variance of this estimator, and show that this estimator is as efficient as the best linear unbiased estimator. We present an example to illustrate this method. A successful program for missile reliability. GERALD P. IVIETTLERand PAUL D. TOWI'~R III. Proc. ,4. Reliab. Maintainab. Syrup., 481 (1991). With increasingly constrained federal budgets, weapon systems must adapt to expenditure and hardware resource limitations. This paper summarizes almost six years of FSD reliability engineering activity for the vertical launch ASROC (VLA) anti-submarine missile in such an environment. The program necessitated task tailoring and a search for cost effectiveness. This paper is a compilation of "lessons learned" for a low-cost, medium size reliability program. It shows that careful attention to technical and administrative details will lead to successful hardware functions as demonstrated through testing. Properly conducted reliability efforts can make substantial contributions to achieve desired results. Task tailoring for cost effectiveness was always a paramount consideration. Highlights from the conduct of each assigned task are presented in this paper, which are discussed under the headings and in the order of MIL-STD-785. This reflective view of those experiences may be of assistance for planning future reliability programs of any size in this cost conscious environment. A nonparametrlc aEproaeh to progreuive strem ueeelerated life testing. ZI-mSONINOLIs and HELIANGFEi. IEEE Trans. Reliab. 40(2), 173 (1991). We consider progressive-stress accelerated life testing wherein the stress on an unfailed item increases linearly with test time, when the time transformation function is a version of the inverse power law. Our approach here is nonparametric in that we do not make many assumptions about life distribution. We introduce a testing pattern and explain how to draw inferences from progressive stress tests. In some detail, we propose an estimator of life distribution at the usual stress level. Approximate MLFa for the iueation and scale paruseters of the extreme value dimilmflen with ¢t.amring. N. BALAKRISHNANand J. Vm,.~A~. [EEE Trans. Reliab. 40(2),