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2022 | 23 | nr 4 | 59--76
Tytuł artykułu

The Weibull Lifetime Model with Randomised Failure-Free Time

Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper shows that treating failure-free time in the three-parameter Weibull distribution not a constant, but as a random variable makes the resulting distribution much more flexible at the expense of only one additional parameter. (original abstract)
Rocznik
Tom
23
Numer
Strony
59--76
Opis fizyczny
Twórcy
  • Pomeranian University in Słupsk
  • Poznań University of Technology, Poznań, Poland
Bibliografia
  • Ahrens, J. H., Dieter, U. (1982). Generating gamma variates by a modified rejection technique. Communications of the ACM, 25, pp. 47-54.
  • Ahrens, J. H., Dieter, U. (1974). Computer methods for sampling from gamma, beta, poisson and binomial distributions. Computing, 12, pp. 223-246.
  • Alamlki, S. J.,Nadarajah, S., (2014). ,Modifications of the Weibull distribution: a review. Reliability Engineering and System Safety, 124, pp. 32-55.
  • Balakrishnan, N., Ristic, M. M., (2016). Multivariate families of gamma-generated distributions with finite or infinite support above or below the diagonal, Journal of Multivariate Analysis, 143, pp. 194-207.
  • Drapella, A., (1993). Complementary Weibull distribution: Unknown or just forgotten. Quality and Reliability Engineering International, 9, pp. 383-385.
  • Drapella, A., (1999). An improved failure-free time estimation method. Quality and Reliability Engineering International, 15, pp. 235-238.
  • Dubey, S. D. (1968). A compound Weibull distribution. Naval Research Logistics Quarterly, 15, pp. 179-188.
  • Gertsbakh, I. B., Kordonskiy, K. H. B., (1969). Models of failure, Verlag: Springer.
  • Kao, J. H. K. (1966). Lifetime models with applications, In: Reliability Handbook. W.G. Ireson Editor-in-chief. McGraw-Hill Company.
  • Kao, J. H. K. (1960). A summary of some new techniques on failure analysis, Proc. Sixth Natl. Symp. on Reliability and Quality Control.
  • Kececioglu, D. (1991). Reliability Engineering Handbook, New York: Prentice Hall, Eaglewood Cliffs.
  • Kendall, M. G., Stuart, A. (1961). The advanced theory of statistics, Vol. 2, Charles Griffin and Company.
  • Lai, C. D. (2014). Generalized Weibull Distributions, New York: Springer.
  • Lai, C. D., Xie, M. (2006). Stochastic ageing and dependence for reliability, Springer Science and Business Media.
  • Lam, S. W., Halim, T., Muthusamy, K. (2010). Models with failure-free life-Applied review and extensions, IEEE Transactions on Device and Materials Reliability, 10(2), pp. 263-270.
  • Mahmood, S. W., Algamal, Z. Y. (2021). Reliability Estimation of Three Parameters Gamma Distribution via Particle Swarm Optimization, Thailand Statisticia, 19(2), pp. 308-316.
  • Mudholkar, G. S., Srivastava, D. K., (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data IEEE Transactions on Reliability, 42, pp. 299-302.
  • Murthy, D. N. P., Xie, M., Jiang, R., (2004). Weibull models, Hoboken: Wiley.
  • O'Connor, P. D. T. (1985). Practical reliability engineering, New York: Wiley.
  • Park, C. (2018). A Note on the Existence of the Location Parameter Estimate of the Three- Parameter Weibull Model Using the Weibull Plot, Mathematical Problems in Engineering, 10(2), pp. 1-6.
  • Qutb, N., Rajhi, E., (2016). Estimation of the Parameters of Compound Weibull Distribution, IOSR Journal of Mathematics, 12, pp. 11-18.
  • Ramakrishnan, M., Viswanathan, N., (2017). Comparing the methods of estimation of three-parameterWeibull distribution, IOSR Journal of Mathematics, 13(1), pp. 42-45.
  • Rossberg, H. J., Jesiak, B., Siegel, G., (1985). Analytic Methods of Probability Theory, Berlin: Academie Verlag.
  • Saffawy, S. Y., Algmal, Z. Y (2006). The Use of Maximum Likelihood and Kaplan-Meir method to Estimate the Reliability Function An Application on Babylon Tires Factory, Tanmiyat Al-Rafidain, 82(28), pp. 9-20.
  • Seidel, W. (2010). Mixture model, In Lovric, M., International Encyclopedia of Statistical Science, Heidelberg: Springer.
  • Stacy, E.W., (1962). A generalization of the gamma distribution, The Annals of Mathematical Statistics, pp. 1187-1192.
  • Szymkowiak, M. (2018a). Characterizations of distributions through aging intensity, IEEE Transactions on Reliability, 67(2), pp. 446-296.
  • Szymkowiak, M. (2018b). Generalized aging intensity functions, Reliability Engineering and System Safety, 178, pp. 198-208.
  • Szymkowiak, M., (2020). Lifetime analysis by aging intensity functions, Cham: Springer.
  • Weber, M. D., Leemis, L. M., Kincaid, R. (2006). Minimum Kolmogorov-Smirnov test statistic parameter estimates, Journal of Statistical Computation and Simulation, 76(3), pp. 195-206.
  • Weibull, W. (1951). A statistical distribution function of wide applicability, Journal of Applied Mechanics, 18, pp. 29-296.
  • Wichura, M. J., (1988). Algorithm AS 241: The percentage points of the normal distribution, Applied Statistics, 37, pp. 477-484.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
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