Data processing: artificial intelligence – Neural network – Learning task
Reexamination Certificate
1999-12-01
2003-05-06
Davis, George B. (Department: 2121)
Data processing: artificial intelligence
Neural network
Learning task
C702S181000, C702S185000
Reexamination Certificate
active
06560584
ABSTRACT:
REFERENCE OF COMPUTER PROGRAM LISTING APPENDIX
This application contains a computer program listing, attached as Appendix A. This appendix has been submitted on a single compact disc (in duplicate which contains Appendix A in a file named “09452825. APPENDIX A.txt” of size 33 KB created on May 17, 2002. The material contained in this file is hereby incorporated by reference.
FIELD OF THE INVENTION
The present invention relates to a method and apparatus for prediction of system reliability, and in particular, to a method and apparatus that can be used to predict reliability of complex systems composed of many components.
BACKGROUND OF THE INVENTION
A system is by definition a combination of interrelated elements (or components) designed to work as a coherent entity. During use, one or more of these elements may fail, thus causing the entire system or part of a system, to fail. The times at which such failures will occur are unknown, but it is often possible to determine the probability of failure for the individual elements and from these to determine the reliability of the system of the whole.
Reliability studies are extremely important in engineering design. The ability to compute the reliability of a system or subsystem enables designers to identify and address those systems more likely to fail. For example, as is well known in the art, the ability to compute a subsystem's or component's reliability is critical to numerous aspects of production quality control and manufacturing efficiency. Furthermore, as is also well known in the art, system reliability can directly impact system design when safety is a primary concern.
For example, a television manufacturer desires to make certain that its product will likely remain operational for an extended period of time, such as ten years. A fire detection system should remain operational for even longer, such as thirty years. If a product developer has developed two competing designs for a product, it wishes to know the reliability of each design to make its decision as to the preferred design.
Reliability predictions rely heavily on principles of probability. As systems become more complex and contain larger numbers of elements, the problems of reliability become more difficult and take on added significance. In turn, as the number of elements grows larger, the difficulty in computing system reliability grows exponentially.
Various approaches have been taken to deal with system reliability. Approaches range from actual testing of the product to computation of the exact system reliability. Some of these approaches are patented. For example, one methodology used to actually test the product is disclosed in U.S. Pat. No. 5,548,718 in which a mapping mechanism and automated testing system are used for testing software functionality. U.S. Pat. No. 5,014,220 discloses a reliability model generator which aggregates low level reliability models into a single reliability model based on the desired system architecture.
In the past, numerous approaches to estimate system reliability of complex systems have been proposed since computation of the actual reliability is monumental or impractical for systems composed of many components. However, these prior art approaches have distinct limitations. One such approach well known in the art was proposed by Aven. (Aven, T., “Reliability/Availability Evaluation of Coherent System based on Minimal Cut Sets”,
Reliability Engineering
, 13, 93-104 (1986)). Aven attempted to compute exact system reliability using a method based on minimal cut sets. A cut set is a set of components, which by failing causes the whole system to fail. A cut set is minimal if it cannot be reduced without losing its status as a cut set. The prominent shortcoming of this approach is that the method depends on the initial choices of two parameters. Any error introduced in the initial choice of these parameters would propagate through the computation. As a result, as the system being studied grew larger, the accuracy of the approach declined. Further, the method of Aven is unable to deal with the case when the component survival functions belong to the Increasing Failure Rate Average (IFRA) class of life distributions. The IFRA class is defined as follows: a life distribution function F is said to belong to an IFRA class if −(1/t) log (1−F(t) is non-decreasing in t≧0. It is known to be the most important class of life distributions. The well-known distributions like Exponential, Weibull, and Lognormal are included in this class.
Another approach used often in industry is the Barlow & Proschan bound (“B-P bound”) in which bounds are placed on system reliability. (Barlow, R. E. and F. Proschan,
Statistical Theory of Reliability and Life Testing
, Holt, Rinehart and Winston Inc, New York (1975).) The B-P bound approach is limited because it is, after all, a bound, and thus cannot predict the exact system reliability. Also, the bound is not valid on the entire real line. The bound is point-wise. Further, the B-P bound approach cannot deal with the IFRA case. Yet another approach has been to resort to minimum or maximum bounds of a system's reliability. The min-max bounds approach is limited because they are bounds, and thus cannot predict exact system reliability. Also, the min-max bounds cannot deal with the IFRA case. Further, the min-max bounds require the knowledge of both path and cut sets. However, these approaches are inherently inaccurate as they seek only to give upper and lower values rather than to predict exact reliability of the system. Accordingly, in many applications where cost or accuracy are critical, such results are inadequate.
In an effort to minimize the increasing inaccuracy of these approaches as the complexity of a system increases, it is well known in the art to divide a complex system into subsystems each having fewer components, and to compute the reliability of each subsystem. The aforementioned U.S. Pat. No. 5,014,220, takes such an approach by dividing a complex system into simpler subsystems based on the use of a knowledge database. Although the general approach of computing “sub-reliability” addresses the inherent difficulty of computing reliability of complex systems, this approach introduces additional error into the computation, as each sub-reliability must be joined with the others to yield the reliability of the entire system. Since this joinder is usually inaccurate, it introduces error into the calculation of reliability.
Thus, for complex systems determination of the exact reliability of the system is extremely difficult and sometimes thought to be impossible to determine. It is therefore desired to develop an approach to determine exact system reliability which accurately calculates the reliability of even very complex systems without being computationally burdensome. The desired approach should be easy to implement and to use, should not require that the system be dissected into subsystems for determination of reliability, and should not be dependent on selection of parameters whose inaccurate selection is detrimental to the determination of reliability. Further, the method should predict exact reliability rather than bounds on the reliability.
REFERENCES:
patent: 5548715 (1996-08-01), Maloney et al.
patent: 5991707 (1999-11-01), Searles et al.
Nair et al, “Real—Number Codes for Fault-Tolerant Martix Operations on processor Arrays” IEEE Transactions on Computers. Apr. 1990.
Afshar Nader
Chaudhuri Gopal
Hu Kuolung
Advanced Research & Technology Institute
Davis George B.
Gridley Doreen J.
Ice Miller
Walsh Thomas A.
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