Some Reliability Applications of the Hazard Transform

Previous article Next article Some Reliability Applications of the Hazard TransformJ. D. Esary, A. W. Marshall, and F. ProschanJ. D. Esary, A. W. Marshall, and F. Proschanhttps://doi.org/10.1137/0118077PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Richard E. Barlow, , Albert W. Marshall and , Frank Proschan, Properties of probability distributions with monotone hazard rate, Ann. Math. Statist., 34 (1963), 375–389 MR0171328 0249.60006 CrossrefISIGoogle Scholar[2] Richard E. Barlow and , Frank Proschan, Mathematical theory of reliability, With contributions by Larry C. Hunter. The SIAM Series in Applied Mathematics, John Wiley & Sons Inc., New York, 1965xiii+256 pp. (1 insert) MR0195566 0132.39302 Google Scholar[3] Z. W. Birnbaum, , J. D. Esary and , A. W. Marshall, A stochastic characterization of wear-out for components and systems, Ann. Math. Statist, 37 (1966), 816–825 MR0193727 0144.41904 CrossrefISIGoogle Scholar[4] Z. W. Birnbaum, , J. D. Esary and , S. C. Saunders, Multicomponent systems and structures and their reliability, Technometrics, 3 (1961), 55–77 MR0122658 CrossrefISIGoogle Scholar[5] A. M. Bruckner and , E. Ostrow, Some function classes related to the class of convex functions, Pacific J. Math., 12 (1962), 1203–1215 MR0148822 0121.29501 CrossrefISIGoogle Scholar[6] J. D. Esary, , A. W. Marshall and , F. Proschan, Reliability applications of the hazard transform, Document, D1-82-0805, Boeing Scientific Research Labs., Seattle, Washington, 1968 Google Scholar[7] J. D. Esary, , A. W. Marshall and , F. Proschan, Determining an approximate constant failure rate for a system whose components have constant failure rates, Presented at NATO Reliability Conference, Torino, 1969, Document D1-82-0899, Boeing Scientific Research Labs., Seattle, Washington, 1969 0281.90037 Google Scholar[8] J. D. Esary and , F. Proschan, Coherent structures of non-identical components, Technometrics, 5 (1963), 191–209 MR0187912 0128.38805 CrossrefISIGoogle Scholar[9] James D. Esary and , Frank Proschan, Relationship between system failure rate and component failure rates, Technometrics, 5 (1963), 183–189 MR0187911 CrossrefISIGoogle Scholar[10] G. H. Hardy, , J. E. Littlewood and , G. Pólya, Inequalities, Cambridge, at the University Press, 1952xii+324, 2nd ed. MR0046395 0047.05302 Google Scholar[11] H. Mine, Reliability of physical system, Trans. 1959 International Symposium on Circuit and Information Theory, Los Angeles, Calif., 1959 Google Scholar[12] R. A. Rosenbaum, Sub-additive functions, Duke Math. J., 17 (1950), 227–247 10.1215/S0012-7094-50-01721-2 MR0036796 0038.06603 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Statistical Modeling of Some Cancerous Diseases Using the Laplace Transform Approach of Basic Life Testing IssuesComputational and Mathematical Methods in Medicine, Vol. 2022 Cross Ref Non-parametric hypothesis testing to model some cancers based on goodness of fitAIMS Mathematics, Vol. 7, No. 8 Cross Ref The alpha-mixture of survival functions11 December 2019 | Journal of Applied Probability, Vol. 56, No. 4 Cross Ref Mathematics of Systems' Reliability: Systems' Structure and Stochastic PerformanceIEICE ESS Fundamentals Review, Vol. 12, No. 4 Cross Ref THE FAILURE RATE SHAPE FOR A MIXTURE OF TWO GAMMAS26 January 2015 | Probability in the Engineering and Informational Sciences, Vol. 29, No. 2 Cross Ref On Allocation of Active Redundancies to Systems: A Brief Review14 May 2013 Cross Ref A Glaser Twist: Focus on the Mixture Parameters1 March 2016 | Journal of Applied Probability, Vol. 49, No. 04 Cross Ref A Glaser Twist: Focus on the Mixture Parameters30 January 2018 | Journal of Applied Probability, Vol. 49, No. 4 Cross Ref Reversed Preservation Properties for Series and Parallel Systems14 July 2016 | Journal of Applied Probability, Vol. 44, No. 04 Cross Ref Reversed Preservation Properties for Series and Parallel Systems14 July 2016 | Journal of Applied Probability, Vol. 44, No. 4 Cross Ref A note on closure of the ILR and DLR classes under formation of coherent systemsStatistical Papers, Vol. 44, No. 2 Cross Ref On the closure of the IFR(2) and NBU(2) classes14 July 2016 | Journal of Applied Probability, Vol. 38, No. 01 Cross Ref On the closure of the IFR(2) and NBU(2) classes14 July 2016 | Journal of Applied Probability, Vol. 38, No. 1 Cross Ref Structural duration analysis of management dataJournal of Econometrics, Vol. 57, No. 1-3 Cross Ref A unified theory for coherent systems in reliability I. 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Cross Ref Volume 18, Issue 4| 1970SIAM Journal on Applied Mathematics History Submitted:03 June 1969Published online:31 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0118077Article page range:pp. 849-860ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics