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Author: T. A. Azlarov Publisher: Springer ISBN: Category : Mathematics Languages : en Pages : 152
Book Description
Problems of calculating the reliability of instruments and systems and the development of measures to increase efficiency and reduce operational costs confronted physicists and mathe maticians at the end of the '40's and the beginning of the '50's in connection with the unrelia bility of electro-vacuum instruments used in aviation. Since then steadily increasing demands for the accuracy, reliability and complexity required in electronic equipment have served as a stimulus in the development of the theory of reliability. From 1950 to 1955 Epstein and Sobel [67,68] and Davis [62], in an analysis of statistical data of the operating time of an instrument up to failure, showed that the distribution is exponential in many cases. Consequently, the ex ponential distribution became basic to research associated with experiments on life expectancy. Further research has shown that there are a whole series of problems in reliability theory for which the exponential distribution is inapplicable. However, it can practically always be used as a first approximation. The ease of computational work due to the nice properties of the exponential distribution (for example, the lack of memory property, see Section 1) is also a reason for its frequent use. AB a rule, data on the behavior of the failure rate function are used to test the hypothesis that a given distribution belongs to the class of exponential distributions, and order statistics are used to estimate the parameter of the exponential distribution.
Author: T. A. Azlarov Publisher: Springer ISBN: Category : Mathematics Languages : en Pages : 152
Book Description
Problems of calculating the reliability of instruments and systems and the development of measures to increase efficiency and reduce operational costs confronted physicists and mathe maticians at the end of the '40's and the beginning of the '50's in connection with the unrelia bility of electro-vacuum instruments used in aviation. Since then steadily increasing demands for the accuracy, reliability and complexity required in electronic equipment have served as a stimulus in the development of the theory of reliability. From 1950 to 1955 Epstein and Sobel [67,68] and Davis [62], in an analysis of statistical data of the operating time of an instrument up to failure, showed that the distribution is exponential in many cases. Consequently, the ex ponential distribution became basic to research associated with experiments on life expectancy. Further research has shown that there are a whole series of problems in reliability theory for which the exponential distribution is inapplicable. However, it can practically always be used as a first approximation. The ease of computational work due to the nice properties of the exponential distribution (for example, the lack of memory property, see Section 1) is also a reason for its frequent use. AB a rule, data on the behavior of the failure rate function are used to test the hypothesis that a given distribution belongs to the class of exponential distributions, and order statistics are used to estimate the parameter of the exponential distribution.
Author: T. A. Azlarov Publisher: Springer ISBN: 9781461249566 Category : Mathematics Languages : en Pages : 0
Book Description
Problems of calculating the reliability of instruments and systems and the development of measures to increase efficiency and reduce operational costs confronted physicists and mathe maticians at the end of the '40's and the beginning of the '50's in connection with the unrelia bility of electro-vacuum instruments used in aviation. Since then steadily increasing demands for the accuracy, reliability and complexity required in electronic equipment have served as a stimulus in the development of the theory of reliability. From 1950 to 1955 Epstein and Sobel [67,68] and Davis [62], in an analysis of statistical data of the operating time of an instrument up to failure, showed that the distribution is exponential in many cases. Consequently, the ex ponential distribution became basic to research associated with experiments on life expectancy. Further research has shown that there are a whole series of problems in reliability theory for which the exponential distribution is inapplicable. However, it can practically always be used as a first approximation. The ease of computational work due to the nice properties of the exponential distribution (for example, the lack of memory property, see Section 1) is also a reason for its frequent use. AB a rule, data on the behavior of the failure rate function are used to test the hypothesis that a given distribution belongs to the class of exponential distributions, and order statistics are used to estimate the parameter of the exponential distribution.
Author: Janos Galambos Publisher: Lecture Notes in Mathematics ISBN: Category : Mathematics Languages : en Pages : 186
Book Description
Preliminaries and basic results; Characterizations based on truncated distributions; Characterizations by properties of order statistics; Characterization of the poisson process; Characterizations of multivariate exponential distributions.
Author: K. Balakrishnan Publisher: Routledge ISBN: 1351449125 Category : Mathematics Languages : en Pages : 664
Book Description
The exponential distribution is one of the most significant and widely used distribution in statistical practice. It possesses several important statistical properties, and yet exhibits great mathematical tractability. This volume provides a systematic and comprehensive synthesis of the diverse literature on the theory and applications of the expon
Author: K. Balakrishnan Publisher: Routledge ISBN: 1351449117 Category : Mathematics Languages : en Pages : 414
Book Description
The exponential distribution is one of the most significant and widely used distribution in statistical practice. It possesses several important statistical properties, and yet exhibits great mathematical tractability. This volume provides a systematic and comprehensive synthesis of the diverse literature on the theory and applications of the expon
Author: Bozzano G Luisa Publisher: Academic Press ISBN: 0128015268 Category : Mathematics Languages : en Pages : 271
Book Description
The problem of identifiability is basic to all statistical methods and data analysis, occurring in such diverse areas as Reliability Theory, Survival Analysis, and Econometrics, where stochastic modeling is widely used. Mathematics dealing with identifiability per se is closely related to the so-called branch of "characterization problems" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.
Author: T. A. Azlarov
Author: T. A. Azlarov
Author: T. A. Azlarov
Author: Janos Galambos
Author: K. Balakrishnan
Author: K. Balakrishnan
Author: J. Leslie
Author: Thomas Shelburne Ferguson
Author: M. Ahsanullah
Author: M. Ahsanullah
Author: Bozzano G Luisa