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Estimation of Suitable Methodology for Determining Weibull Parameters for the Vortex Shedding Analysis of Synovial Fluid
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 Title & Authors
Estimation of Suitable Methodology for Determining Weibull Parameters for the Vortex Shedding Analysis of Synovial Fluid
Singh, Nishant Kumar; Sarkar, A.; Deo, Anandita; Gautam, Kirti; Rai, S.K.;
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Weibull distribution with two parameters, shape (k) and scale (s) parameters are used to model the fatigue failure analysis due to periodic vortex shedding of the synovial fluid in knee joints. In order to determine the later parameter, a suitable statistical model is required for velocity distribution of synovial fluid flow. Hence, wide applicability of Weibull distribution in life testing and reliability analysis can be applied to describe the probability distribution of synovial fluid flow velocity. In this work, comparisons of three most widely used methods for estimating Weibull parameters are carried out; i.e. the least square estimation method (LSEM), maximum likelihood estimator (MLE) and the method of moment (MOM), to study fatigue failure of bone joint due to periodic vortex shedding of synovial fluid. The performances of these methods are compared through the analysis of computer generated synovial fluidflow velocity distribution in the physiological range. Significant values for the (k) and (s) parameters are obtained by comparing these methods. The criterions such as root mean square error (RMSE), coefficient of determination (), maximum error between the cumulative distribution functions (CDFs) or Kolmogorov-Smirnov (K-S) and the chi square tests are used for the comparison of the suitability of these methods. The results show that maximum likelihood method performs well for most of the cases studied and hence recommended.
Weibull distribution;vortex shedding;synovial fluid;least square estimation method;maximum likelihood estimator;method of moment;
 Cited by
M.A. Al-Fawzan, Methods for estimating the parameters of the Weibull distribution, King Abdulaziz City for Science and Technology, Riyadh, Saudi Arabia, 2000. [Unpublished]

E.A. Balazs, "Viscoelastic properties of hyaluronic acid and biological lubrication", Univ Mich Med Cent J [Special Issue], pp. 255-259, 1968.

E.A. Balazs, Some aspects of the aging and radiation sensitivity of the intercellular matrix with special regard to hyaluronic acid in synovial fluid and vitreous, Thule International Symposium: Aging of connective and skeletal tissue, Engel A and Larsson T (eds.), Stockholm: Nordiska Bokhandelns Forlag, 1969.

E.A. Balazs and D.A. Gibbs, Chemistry and molecular biology of the intercellular matrix III, New York: Academic Press, 1970.

E.A. Balazs and D. Watson, "Hyaluronic acid in synovial fluid. I. Molecular parameters of hyaluronic acid in normal and arthritic human fluids", Arthritis Rheum, vol. 10, pp. 357-376, 1967. crossref(new window)

N.W. Rydell, "Decreased granulation tissue formation after installment of hyaluronic acid", Acta Orthop Scand, vol. 41, pp. 307-311, 1970. crossref(new window)

D.A. Gibbs, E.W. Merrill, K.A. Smith and E.A. Balazs, "Rheology of hyaluronic acid", Biopolymers, vol. 6, pp. 777-791, 1968. crossref(new window)

K. Pekkan, R. Nalim and H. Yokota, "Computed synovial fluid flow in a simple knee joint model", 4th Joint Fluids Summer Engineering Conference (FEDSM), pp. 2085-2091, 2003.

W. Weibull, "A statistical distribution function of wide applicability", J Appl Mech-T ASME, pp. 293-297, 1951.

W. Weibull, "A statistical distribution function of wide applicability", J Appl Mech-T ASME, pp. 233-234, 1952.

Y.C. Fung, Biomechanics, mechanical properties of living tissues. 2nd ed., New York: Springer-Verlag, 1993.

R.G. King, "A rheological measurement of three synovial fluids", Acta Rheol, vol. 5, pp. 41-44, 1966. crossref(new window)

J.V. Seguro and T.W. Lambert, "Modern estimation of the parameters of the weibull wind speed distribution for wind energy analysis", J Wind Eng Ind Aero, vol. 85, pp. 75-84, 2000. crossref(new window)

T.P. Chang, "Performance comparison of six numerical methods in estimating weibull parameters for wind energy application", Appl Energ, vol. 88, pp. 272-282, 2011. crossref(new window)

D.C. Montgomery and G.C. Runger, Applied statistics and probability for engineers. 3rd ed., New York: John Wiley and Sons, 2003.

X. Gao, J.A. Joyce and C. Roe, "An investigation of the loading rate dependence of the weibull stress parameters", Eng Frac Mech, vol. 75, pp. 1451-1467, 2008. crossref(new window)

A. Ghosh, "A fortran program for fitting Weibull distribution and generating samples", Comput Geosci, vol. 25, pp. 729-738, 1999. crossref(new window)

A.H.-SAng and W.H. Tang, Probability concepts in engineering planning and design vol I: basic principles, New York: John Wiley and Sons, 1975.

A.M. Razali, A.A. Salih and A.A. Mahdi, "Estimation accuracy of weibull distribution parameters", vol. 5, pp. 790-795, 2009.

P. Pustejovska, "Mathematical modeling of synovial fluids flow", in Proc.17th Annual conference of doctoral students, Week of doctoral students, Part III, pp. 32-37.

M.R. Spiegel, Schaum's outline of theory and problems of statistics 2nd ed, Singapore: McGraw-Hill, 1992.

A.H.-SAng and W.H. Tang, Probability Concepts in Engineering and Design Vol II: risk and reliability, New York: John Wiley and Sons, 1984.

G.J. Hahn and Shapiro, Statistical Models in Engineering, New York: John Wiley and Sons, 1967.

S.S. Wilks, "Order statistics", Bulletin of the American Mathematical Society, ch.5, pp. 6-50, 1948.