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Confidence bounds for the reliability of a system from subsystem data

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Języki publikacji
EN
Abstrakty
EN
The paper is concerned with the construction of lower bounds for the reliability of a system when statistical data comes from independent tests of its elements. The overview of results known from literature and obtained under the assumption that elements in a system are independent is given. It has been demonstrated using a Monte Carlo experiment that in the case when these elements are dependent and when their dependence is described by Clayton and Gumbel copulas these confidence bounds are not satisfactory. New simple bounds have been proposed which in some practical cases have better properties than the classical ones.
Rocznik
Tom
Strony
157--170
Opis fizyczny
Bibliogr. 25 poz., wykr.
Twórcy
  • Systems Research Institute, Warsaw, Poland
Bibliografia
  • [1] Barlow, R. E. & Proschan, F. (1965). Mathematical Theory of Reliability. John Wiley, New York.
  • [2] Barlow, R. E. & Proschan, F. (1975). Statistical Theory of Reliability and Life Testing. Probability Models. Holt Rinehart and Winston, Inc., New York.
  • [3] Belyaev, Y. K. (1966). Confidence intervals for the functions of many unknown parameters. Proc. of the Sov. Acad. Sci, 169, 755-758 (in Russian).
  • [4] Belyaev, Y. K. (1968). On simple methods of Confidence Limits Construction. Eng. Cybernetics, No. 5, 96-101 (in Russian, exists English translation of this journal).
  • [5] Bol’shev, L. N. & Loginov E. A. (1966). Interval estimates under noisy parameters. Theory of Prob. and its Appl. v. 11, No. 1, 94-107 (in Russian, exists English translation of this journal).
  • [6] Buehler R. J. (1957). Confidence Intervals for the Product of two Binomial Parameters. Journal of the American Statistical Association, 52, 482-493.
  • [7] Easterling, R. G. (1972). Approximate Confidence Limits for the System Reliability. Journal of the American Statistical Association, 67, 220-222.
  • [8] El Mawaziny, A. H. (1965), Chi-square distribution theory with applications to reliability problems. PhD Thesis, Iowa State Univ., Ames, Iowa.
  • [9] Gnedenko, B., Pavlov, I., Ushakov, I. & Chakravarty S. (1999). Statistical Reliability Engineering. John Wiley, New York.
  • [10] Lentner, M. M. & Buehler, R. J. (1963). Some inferences about gamma parameters with an application to a reliability problem. Journal of the Amer. Stat. Assoc. 58, 670-677.
  • [11] Lloyd, D. K. & Lipow, M. (1962). Reliability Management. Methods and Mathematics. Prentice-Hall, Englewood Cliffs, NJ.
  • [12] Madansky, A. (1965). Approximate Confidence Limits for the Reliability of Series and Parallel Systems. Technometrics, 7, 493-503.
  • [13] Mann, N. R. (1974). Approximate Optimum Confidence Bounds on Series and Series-Parallel System Reliability for Systems with Binomial Subsystem Data. IEEE Transactions on Reliability, R-23, 295-304.
  • [14] Mann, N. R. (1974). simplified expressions for obtaining approximately optimum systemreliability confidence bounds from exponential subsystem data. Journal of the Amer. Stat. Assoc., 69, 492-495.
  • [15] Mann, N. R. & Grubbs, F. E. (1972). Approximately Optimum Confidence Bounds on Series-System Reliability for Exponential Time to Fail Data. Biometrika, 50, 191-204.
  • [16] Mann, N. R. & Grubbs, F. E. (1974). Approximately Optimum Confidence Bounds for System Reliability Based on Component Test Plan. Technometrics, 16, 335-347.
  • [17] Mann, N. R., Schaefer, R. E. & Singpurwalla, N. D. (1974). Methods of Statistical Analysis of Reliability and Life Data. John Wiley, New York.
  • [18] Martz, H. F. & Duran, I. S. (1985). A Comparison of Three Methods for Calculating Lower Confidence Limits on System Reliability Using Binomial Component Data. IEEE Transactions on Reliability, R-34, 113-120.
  • [19] Mirnyi, R. A. & Solovyev, A. D. (1964). Estimation of system reliability on the basis on its units tests. In: Cybernetics in Service for Communism, vol. 2, Energiya, Moscow, 213-218.
  • [20] Myhre, J. & Saunders, S. C. (1968). Comparison of Two Methods of Obtaining Approximate Confidence Intervals for System Reliability. Technometrics, 10, 37-49.
  • [21] Nelsen, R. B. (2006). An Introduction to Copulas (2nd edition), Springer, New York.
  • [22] Neyman, J. (1935). On the Problem of Confidence Intervals. Annals of Mathematical Statistics, 6, 111-116.
  • [23] Pavlov, I.V. (1973). Confidence limits for system reliability on the basis on its components testing. Eng. Cybernetics, No. 1, 52-61 (in Russian, exists English translation of this journal).
  • [24] Pavlov, I. V. (1982). Statistical methods of reliability estimation by tests results. Radio i Svyaz, Moscow (in Russian).
  • [25] Sudakov, R. S. (1974). About interval estimation of reliability of series system. Eng. Cybernetics, No. 3, 86-94 (in Russian, exists English translation of this journal).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-478da260-7958-4deb-ac1e-566e236ffd5e
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