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Fitting a multivariate failure time distribution
World Abstracts on Microelectronics and Reliability
1202
metal. Shorts are caused by theta phase (A12Cu) hillocks which nucleate and grow during high-temperature vacuum heat treatment and processing. Hillock growth occurs at high-energy sites such as silicon precipitates and grain boundary nodal points. The growth of AI2Cu hillocks depends on heat treatment/processing temperature and aluminum film purity. The growth kinetics indicate that grain boundary diffusion is the dominant mass transport mechanism. Methods used to limit theta phase hillock formation and growth concentrate on the diffusion and nucleation mechanisms involved. Decreasing heat treatment/processing temperature slows the atomic diffusion required for hillock growth, and delays, but does not prevent, theta phase hillock formation. A l-h heat treatment (213Pa, N 2
3. C I R C U I T
AND
SYSTEMS
RELIABILITY,
A Bayes approach to simultaneous evaluation of similar assemblies. Louts HART. IEEE Trans. Reliab. 38(4), 483 (1989). Simultaneous qualification testing of similar electronic-assembly designs that have the same reliability objectives lends itself to a Bayes approach. I present a method for obtaining the number of units to be put on test (test units) and the number of survivors required for this problem. The Bayes approach can reduce the total number of test units. The similarity of any two assemblies can be qualified using projected failure rates of components common to each design and components that differ between them. Under binomial sampling, survival probabilities follow the conjugate beta distribution. Two systems of linear equations are developed. Their solutions are vectors that describe, for each design: 1) the number of test units, and 2) minimum number of survivors to demonstrate the reliability objective. Treatment of catastrophic events in availability assessment. TERJE AVEN and HANS JORGEN GRUNDT. IEEE Trans. Reliab. 38(4), 506 (1989). This paper is concerned with how catastrophic events, viz. rare failure events which violently affect the system if they occur, should be treated when assessing availability. Shrinkage estimation of threshold parameter of the exponential distribution. PAUL CHIOU and C. P. HAN. IEEE Trans. Reliab. 38(4), 449 (1989). This paper studies the usual preliminary test estimator of the threshold parameter of the exponential distribution in censored samples. The optimal levels of significance and their corresponding critical values for the preliminary test are obtained. The optimal values of shrinkage coefficients for a preliminary test shrinkage estimator are also obtained based on the minimax regret criterion. A model for system reliability with common-eanse failures. LAVON B. PAGE and Jo ELLEN PERRY. IEEE Trans. Reliab. 38(4), 406 (1989). A model is proposed for the analysis of systems subject to common-cause failures. The system consists of a finite number of components that are subject to: 1) statistically independent failures, and 2) external failurecauses (they need not be mutually statistically independent) for groups of components. Applications to fault-tree analysis and network reliability problems are discussed. Availability evaluation of flow networks with varying throughput-demand and deferred repair. TERJE AVEN. IEEE Trans. Reliab. 38(4), 499 (1989). This paper presents some simple formulae for availability of flow networks with several levels of performance and variable throughput-demands. The system comprises highly available independent components. Two main types of component failures are considered: 1) the
ambient) at 350°C produces a high density of large hillocks. Hillock density and height are greatly reduced at 300°C. Altering the layered structure of a metallization alters A12Cu hillock growth. Deposition of a hard coating as a cap on the layered structure of an aluminum-based metallization mechanically suppresses hillock formation. A layer of pure aluminum deposited beneath the aluminum-copper layer acts as a sink for copper and delays hillock formation. Increasing film copper content reduces hillock formation: theta phase hillocks, up to 13 #m in height, are observed in films with 1 wt% copper, whereas negligible (<0.2/~m in height) hillock formation is observed in 11 wt% Cu films. Addition of chromium or oxygen to A1Cu also reduces hillock, height and density, apparently by slowing grain boundary diffusion.
MAINTENANCE
AND
REDUNDANCY
corresponding repair can be deferred to a more convenient time, 2) all other failures. This more convenient time is set to a fixed data in the present model. This model is relevant to gas/oil production and transportation systems. Availability concepts like throughput, demand, and onstream, are discussed; the throughput availability is usually the most important. The computation of these measures can be time consuming, therefore efficient algorithms and formulae are vital. The calculations are fast so that sensitivity of various factors can be studied easily. The calculations show which components are contributing the most to unavailability. Fitting a multivariate failure time distribution. PHILIP HOUGAARD. IEEE Trans. Reliab. 38(4), 444 (1989). A class of continuous multivariate distributions is reviewed. It is derived in a survival/reliability context, where the dependence is modeled as random effects, viz. by an unobserved covariate common to the components in a system and assumed to follow a positive stable distribution. Accounting for censored data is straightforward. The class is well fitted to proportional hazard models and distributions of minimums are simple. An important subfamily is the multivariate Weibull distributions. The theory is illustrated with an example. Muitistate consecutively-connected systems. F. K. HWANG and Y. C. YAO. IEEE Trans. Reliab. 38(4), 472 (1989). Shanthikumar has proposed a new system called consecutively-connected system which is a generalization of the well studied consecutive-k-out-of-n :F system. He gave an O(n 2) algorithm for computing the reliability of the consecutively-connected system. This paper further generalizes it by assuming that the components are multistate. We give an O(Kn) algorithm for computing the reliability of the multistate system where K(K < n) is the maximum number of states for a component. We discuss the difficulties of obtaining corresponding algorithms for circular systems and 2-way communication, although for 2-state components we are able to extend the Shanthikumar algorithm to circular systems. A new estimation approach based on periodic inspection. RONALD DATTERO and EDNA M. WHITE. IEEE Trans. Reliab. 38(4), 436 (1989). The paper presents a good new approach for estimating the failure time distribution based on count data, the number of failures per interval, from periodic inspection of a standby redundant system. The procedure is based on a result for stationary renewal processes that relates the forward recurrence time to the inter-event time distribution. The procedure performed well in a simulation study for 5 Weibull distributions, and is general enough to work for any failure-time distribution.
1202
metal. Shorts are caused by theta phase (A12Cu) hillocks which nucleate and grow during high-temperature vacuum heat treatment and processing. Hillock growth occurs at high-energy sites such as silicon precipitates and grain boundary nodal points. The growth of AI2Cu hillocks depends on heat treatment/processing temperature and aluminum film purity. The growth kinetics indicate that grain boundary diffusion is the dominant mass transport mechanism. Methods used to limit theta phase hillock formation and growth concentrate on the diffusion and nucleation mechanisms involved. Decreasing heat treatment/processing temperature slows the atomic diffusion required for hillock growth, and delays, but does not prevent, theta phase hillock formation. A l-h heat treatment (213Pa, N 2
3. C I R C U I T
AND
SYSTEMS
RELIABILITY,
A Bayes approach to simultaneous evaluation of similar assemblies. Louts HART. IEEE Trans. Reliab. 38(4), 483 (1989). Simultaneous qualification testing of similar electronic-assembly designs that have the same reliability objectives lends itself to a Bayes approach. I present a method for obtaining the number of units to be put on test (test units) and the number of survivors required for this problem. The Bayes approach can reduce the total number of test units. The similarity of any two assemblies can be qualified using projected failure rates of components common to each design and components that differ between them. Under binomial sampling, survival probabilities follow the conjugate beta distribution. Two systems of linear equations are developed. Their solutions are vectors that describe, for each design: 1) the number of test units, and 2) minimum number of survivors to demonstrate the reliability objective. Treatment of catastrophic events in availability assessment. TERJE AVEN and HANS JORGEN GRUNDT. IEEE Trans. Reliab. 38(4), 506 (1989). This paper is concerned with how catastrophic events, viz. rare failure events which violently affect the system if they occur, should be treated when assessing availability. Shrinkage estimation of threshold parameter of the exponential distribution. PAUL CHIOU and C. P. HAN. IEEE Trans. Reliab. 38(4), 449 (1989). This paper studies the usual preliminary test estimator of the threshold parameter of the exponential distribution in censored samples. The optimal levels of significance and their corresponding critical values for the preliminary test are obtained. The optimal values of shrinkage coefficients for a preliminary test shrinkage estimator are also obtained based on the minimax regret criterion. A model for system reliability with common-eanse failures. LAVON B. PAGE and Jo ELLEN PERRY. IEEE Trans. Reliab. 38(4), 406 (1989). A model is proposed for the analysis of systems subject to common-cause failures. The system consists of a finite number of components that are subject to: 1) statistically independent failures, and 2) external failurecauses (they need not be mutually statistically independent) for groups of components. Applications to fault-tree analysis and network reliability problems are discussed. Availability evaluation of flow networks with varying throughput-demand and deferred repair. TERJE AVEN. IEEE Trans. Reliab. 38(4), 499 (1989). This paper presents some simple formulae for availability of flow networks with several levels of performance and variable throughput-demands. The system comprises highly available independent components. Two main types of component failures are considered: 1) the
ambient) at 350°C produces a high density of large hillocks. Hillock density and height are greatly reduced at 300°C. Altering the layered structure of a metallization alters A12Cu hillock growth. Deposition of a hard coating as a cap on the layered structure of an aluminum-based metallization mechanically suppresses hillock formation. A layer of pure aluminum deposited beneath the aluminum-copper layer acts as a sink for copper and delays hillock formation. Increasing film copper content reduces hillock formation: theta phase hillocks, up to 13 #m in height, are observed in films with 1 wt% copper, whereas negligible (<0.2/~m in height) hillock formation is observed in 11 wt% Cu films. Addition of chromium or oxygen to A1Cu also reduces hillock, height and density, apparently by slowing grain boundary diffusion.
MAINTENANCE
AND
REDUNDANCY
corresponding repair can be deferred to a more convenient time, 2) all other failures. This more convenient time is set to a fixed data in the present model. This model is relevant to gas/oil production and transportation systems. Availability concepts like throughput, demand, and onstream, are discussed; the throughput availability is usually the most important. The computation of these measures can be time consuming, therefore efficient algorithms and formulae are vital. The calculations are fast so that sensitivity of various factors can be studied easily. The calculations show which components are contributing the most to unavailability. Fitting a multivariate failure time distribution. PHILIP HOUGAARD. IEEE Trans. Reliab. 38(4), 444 (1989). A class of continuous multivariate distributions is reviewed. It is derived in a survival/reliability context, where the dependence is modeled as random effects, viz. by an unobserved covariate common to the components in a system and assumed to follow a positive stable distribution. Accounting for censored data is straightforward. The class is well fitted to proportional hazard models and distributions of minimums are simple. An important subfamily is the multivariate Weibull distributions. The theory is illustrated with an example. Muitistate consecutively-connected systems. F. K. HWANG and Y. C. YAO. IEEE Trans. Reliab. 38(4), 472 (1989). Shanthikumar has proposed a new system called consecutively-connected system which is a generalization of the well studied consecutive-k-out-of-n :F system. He gave an O(n 2) algorithm for computing the reliability of the consecutively-connected system. This paper further generalizes it by assuming that the components are multistate. We give an O(Kn) algorithm for computing the reliability of the multistate system where K(K < n) is the maximum number of states for a component. We discuss the difficulties of obtaining corresponding algorithms for circular systems and 2-way communication, although for 2-state components we are able to extend the Shanthikumar algorithm to circular systems. A new estimation approach based on periodic inspection. RONALD DATTERO and EDNA M. WHITE. IEEE Trans. Reliab. 38(4), 436 (1989). The paper presents a good new approach for estimating the failure time distribution based on count data, the number of failures per interval, from periodic inspection of a standby redundant system. The procedure is based on a result for stationary renewal processes that relates the forward recurrence time to the inter-event time distribution. The procedure performed well in a simulation study for 5 Weibull distributions, and is general enough to work for any failure-time distribution.