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Year 2021, Volume: 34 Issue: 1, 290 - 309, 01.03.2021
https://doi.org/10.35378/gujs.736084

Abstract

References

  • [1] Weibull, W., “A Statistical Theory of the Strength of Materials”. Ingvetenskaps Akad. Handl. 151, Stockholm (1939).
  • [2] Barbero, E., Fernández-Sáez, J. and Navarro, C., “Statistical analysis of the mechanical properties of composite materials”, Compos. Part B-Eng, 31(5): 375-381, (2000).
  • [3] McCool, J., “Flexural strength tests of brittle materials: selecting the number of specimens and determining confidence limits for Weibull parameters”, J. Test Eval., 45(2): 664-670 (2016).
  • [4] Barbero, E., Fernández-Sáez, J. and Navarro, C., “Statistical distribution of the estimator of Weibull modulus”, J. Mater. Sci. Lett., 20(9): 847-849, (2001).
  • [5] McCool, J.I., Using the Weibull distribution: Reliability, Modeling, and Inference, 1st ed. NJ: John Wiley & Sons Inc, (2012).
  • [6] Wua, D., Lia, Y., Zhanga, J., Changa, L., Wu, D. ,Fang, Z. and Shic, Y., “Effects of the number of testing specimens and the estimation methods on the Weibull parameters of solid catalysts”, Chem. Eng. Sci., 56(24): 7035-7044, (2001).
  • [7] Bao, Y.W. and Zhou, Y., “Investigation on Reliability of Nanolayer Grained Ti3SiC2 via Weibull Statistics”, J. Mater. Sci., 42(12): 4470-4475, (2007).
  • [8] Nohut, S., “Influence of sample size on strength distribution of advanced ceramics”, Ceram. Int., 40(3): 4285-4295, (2014).
  • [9] Khalili, A. and Kromp, K., “Statistical properties of Weibull estimators”, J. Mater. Sci., 26(24): 6741-6752, (1991).
  • [10] Durham, S., Lynch, J. and Padgett, W., “Inference for strength distributions of brittle fibers under increasing failure rate”, J. Composite Mater., 22(12): 1131–1140, (1988).
  • [11] Durham, S., Lynch, J. and Padgett, W., “A theoretical justification for an increasing average failure rate strength distribution in fibrous composites”, Naval Res. Logistics (NRL), 36(5): 655–661, (1989).
  • [12] Durham, S., Lynch, J. and Padgett, W., “TP 2-orderings and the IFR property with applications”, Probability Eng. Inf. Sci., 4(01): 73–88, (1990).
  • [13] Yalcinkaya, M. and Birgoren, B., “Confidence interval estimation of Weibull lower percentiles in small samples via Bayesian inference”, J. Eur. Ceram. Soc., 37: 2983-2990, (2017).
  • [14] Meyers, M.A. and Chawla, K.K., Mechanical Behavior of Materials, Cambridge: Cambridge University Press, (2009).
  • [15] Askeland, D.R., Fulay, P. and Wright, W., The Science and Engineering of Materials, 6th ed. Starnford: Thomson Learning Inc, (2010).
  • [16] Bousquet, N., “Eliciting vague but proper maximal entropy priors in Bayesian experiments”, Stat Pap., 51(3): 613–628, (2010).
  • [17] Abernethy, R.B., The New Weibull Handbook, 5th ed. North Palm Beach: Fla.R.B. Abernethy, (2006).
  • [18] Rinne, H., The Weibull Distribution: A Handbook, FL: CRC Press, (2009).
  • [19] Dodson, B., The Weibull Analysis Handbook, 2nd ed. Milwaukee: ASQ Quality Press, (2006).
  • [20] Ambrožič, M. and Gorjan, L., “Reliability of a Weibull analysis using the maximum-likelihood method”, J. Mater. Sci., 46(6): 1862-1869, (2011).
  • [21] Davies, I.J., “Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach”, J. Eur. Ceram. Soc., 37(1): 369-380, (2017).
  • [22] Bergman, B., “Estimation of Weibull parameters using a weight function”, J. Mater. Sci. Lett., 5(6): 611-614, (1986).
  • [23] Faucher, B. and Tyson, W., “On the determination of Weibull parameters”, J. Mater. Sci. Lett., 7(11): 1199-1203, (1988).
  • [24] Birgoren, B., Ceramics and Composite Materials: New Research, New York : Nova Science Publishers, 215-235, (2006).
  • [25] Nelson, W., Applied Life Data Analysis, New York: John Wiley & Sons, (2005).
  • [26] Johnson, N.L., Kotz, S. and Balakrishnan, N., Continuous Univariate Distributions, 2nd ed. New York: Wiley, (1995).
  • [27] Murthy, D.N.P, Xie, M. and Jiang, R., Weibull Models, New York: Wiley, (2004).
  • [28] Langlois, R., “Estimation of Weibull parameters”, J. Mater. Sci. Lett., 10(18): 1049-1051, (1991).
  • [29] Gurvich, M., Dibenedetto, A. and Pegoretti, A., “Evaluation of the statistical parameters of a Weibull distribution”, J. Mater. Sci., 32(14): 3711-3716, (1997).
  • [30] Gong, J., “Determining the confidence intervals for Weibull estimators”, J. Mater. Sci. Lett., 18(17): 1405-1407, (1999).
  • [31] Gong, J., “A new probability index for estimating Weibull modulus for ceramics with the least-square method”, J. Mater. Sci. Lett., 19(10): 827-829, (2000).
  • [32] Davies, I., “Empirical correction factor for the best estimate of Weibull modulus obtained using linear least squares analysis”, J. Mater. Sci. Lett., 20(11): 997-999, (2001).
  • [33] Davies, I., “Best estimate of Weibull modulus obtained using linear least squares analysis: an improved empirical correction factor”, J. Mater. Sci. Lett., 39(4): 1441-1444, (2004).
  • [34] Griggs, J. and Zhang, Y., “Determining the confidence intervals of Weibull parameters estimated using a more precise probability estimator”, J. Mater. Sci. Lett., 22(24): 1771-1773, (2003).
  • [35] Wu, D. and Jiang, H., “Comment on “A new probability index for estimating Weibull modulus for ceramics with the least-square method”, J. Mater. Sci. Lett., 22(24):1745-1746, (2003).
  • [36] Tiryakioğlu, M., “On estimating Weibull modulus by moments and maximum likelihood methods”, J. Mater. Sci., 43(2): 793-798, (2008).
  • [37] Tiryakioğlu, M., Hudak, D., “Guidelines for two-parameter Weibull analysis for flaw-containing materials”, Metall. Mater. Trans. B., 42(6): 1130-5, (2011).
  • [38] Phan, L. and McCool, J., “Exact confidence intervals for Weibull parameters and percentiles”, P. I. Mech. Eng. O-J Ris., 223(4): 387-394, (2009).
  • [39] Menon, M.V., “Estimation of the shape and scale parameters of the Weibull distribution”, Technometrics, 5: 175-182, (1963).
  • [40] McCool, J.I., “Software for Weibull inference”, Quality Engineering, 23: 253-264, (2011).
  • [41] Bütikofera, L., Stawarczykb, B. and Roosa, M., “Two regression methods for estimation of a two-parameter Weibull distribution for reliability of dental materials”, Dent. Mater., 31: 33-50, (2015).
  • [42] Ahmed, A.O.M., Ibrahim, N.A. and Al-Kutubi, H.S., “Comparison of the Bayesian and maximum likelihood estimation for Weibull distribution”, J. Math. Stat., 6(2): 100-104, (2010).
  • [43] Alkutubi, H.S., AlShemmary E.N.A., Yasseen S.A. and Alwan Y.H., “New bayes estimator of parameter Weibull distribution using simulation study”, IJBAS, 1(3): 237-243, (2012).
  • [44] Aslam, M., Kazmi, S.M.A. and Ahmad, I., “Bayesian estimation for parameters of the Weibull distribution”, Sci.Int.(Lahore), 27(1): 259-264, (2014).
  • [45] Guure, C.B., Ibrahim, N.A. and Ahmed, A.O.M., “Bayesian estimation of two-parameter Weibull distribution using extension of Jeffreys' prior information with three loss functions”, Math. Probl. Eng., 2012(13), (2012).
  • [46] Guure, C.B. and Ibrahim, N.A., “Approximate Bayesian estimates of Weibull parameters with Lindley's method”, Sains Malaysiana, 43(9): 1433-1437, (2014).
  • [47] Jia, J., Yan, Z. and Peng, X., “A New Discrete Extended Weibull Distribution”,  IEEE Access , 7: 175474- 175486, (2019).
  • [48] Aron, A., Guo, H., Mettas, A. and Ogden D., “Improving the 1-parameter weibull: A bayesian approach”, Annual Reliability and Maintainability Symposium, 432–435, (2009).
  • [49] http://reliawiki.com/index.php/The_Weibull_Distribution. Access date: 13.05.2020.
  • [50] Simoa, N.F., Wieler, M., Feltenb, F. and Reh S., “Bayesian analysis for determination and uncertainty assessment of strength and crack growth parameters of brittle materials”, J. Eur. Ceram. Soc., 37: 1769–1777, (2017).
  • [51] Nguyen, D.L. Thai, D.K., Ngo, T.T, Tran, T.K. and Nguyen, T.T., “Weibull modulus from size effect of high-performance fiber-reinforced concrete under compression and flexure”, Constr. Build. Mater., 226 (30): 743-758, (2019).
  • [52] Ono, K., “A Simple Estimation Method of Weibull Modulus and Verification with Strength Data”, Appl. Sci., 9(8): 1575, (2019)
  • [53] Zellner, A., New developments in the applications of Bayesian methods, Amsterdam:University of Chicago Press, 211-232, (1977).
  • [54] Zellner, A., Maximum entropy and Bayesian methods, Boston: Kluwer, 17–31, (1991).
  • [55] Zellner, A., “Models, prior information and Bayesian analysis”, J. Econom., 75: 51–68, (1996).
  • [56] Berger, J.O., Statistical decision theory and Bayesian analysis, 2nd ed. New York: Springer, (2013).
  • [57] Soofi, E.S., Bayesian Analysis in Statistics and Econometrics, D.A. Berry, K.M. Chaloner, J.K. Geweke (eds).New York: Wiley, (1992).
  • [58] Skilling, J., Maximum entropy and Bayesian methods, Dordrecht:Kluwer Academic Publisher, (1989).
  • [59] LeBesnerais, G., Bercher, J.F. and Demoment, G., “A new look at entropy for solving linear inverse problems”, IEEE Trans. Inform. Theory, 45: 1565–1578, (1999).
  • [60] Soofi, E.S., “Principal information theoretic approaches”, J. Am. Stat. Assoc., 95: 1349–1353, (2000).
  • [61] Miller, D.J. and Yan, L., “Approximate maximum entropy joint feature inference consistent with arbitrary lower order probability constraints: application to statistical classification”, Neural Comput., 12: 2175– 2208, (2000).
  • [62] Green, N.R. and Campbell J., Mater. Sci. Eng. A, A137: 261-266, (1993).
  • [63] Ćurković, L., Bakić, A., Kodvanj, J. and Haramina, T., “Flexural strength of alumina ceramics: Weibull analysis”, Transactions of FAMENA, 34(1): 13-19, (2010).
  • [64] Askeland, D.R. and Fulay, P.P., Essentials of Materials Science and Engineering, 3nd ed., Canada: Cengage Learning, (2013).
  • [65] Tobias, P.A. and Trindade, D., Applied Reliability. 3nd ed., Boca Raton: CRC Press, (2011).
  • [66] Birgoren, B. and Dirikolu, M.H., “A computer simulation for estimating lower bound fracture strength of composites using Weibull distribution”, Compos. Part B-Eng., 35(3): 263-266, (2004).
  • [67] Thoman, D.R., Bain L.J. and Antle C.E., “Inferences on the parameters of theWeibull distribution”, Technometrics, 11: 445–460, (1969).
  • [68] Suen, H.K., Principles of Test Theories, New York: Routledge, (2012).
  • [69] Glasgow, L.A., Applied Mathematics for Science and Engineering, John Wiley & Sons, (2014).
  • [70] Casella, G. and Berger, R.L., Statistical Inference, 2nd ed. USA: Thomson Learning, (2002).
  • [71] Riedel, R. and Chen, I.W., Ceramics Science and Technology, John Wiley & Sons, (2011).
  • [72] Juritz, J. M., Juritz, J. W. F. and Stephens, M. A., “On the accuracy of simulated percentage points”, J. Am. Stat. Assoc., 83: 441–444, (1983).
  • [73] Dirikolu, M.H., Aktas¸ A. and Birgören, B., “Statistical analysis of fracture strength of composite materials using Weibull distribution”, Turkish J Engng Environ Sci, 26(1): 45–8, (2002).

Bayesian Confidence Interval Estimation of Weibull Modulus Under Increasing Failure Rate

Year 2021, Volume: 34 Issue: 1, 290 - 309, 01.03.2021
https://doi.org/10.35378/gujs.736084

Abstract

Estimating the confidence interval of the Weibull modulus is an important problem in the fracture strength modeling of ceramic and composite materials. It is particularly important in cases where the sample size is small due to high experimental costs. For this purpose, several classical methods, including the popular maximum likelihood method, and Bayesian methods have been developed in the literature. However, studies on Bayesian inference have remained very limited in the materials science literature. Recently a Bayesian Weibull model has been proposed for estimating confidence lower bounds for Weibull percentiles using the prior knowledge that the failure rates are increasing. This prior argument requires the Weibull modulus to be more than 1 due to wear-out failure. In this study, under the same prior information, two Bayesian Weibull models, one using the same prior argument and the other a relaxed version of it, have been developed for confidence interval estimation of the Weibull modulus. Their estimation performances have been compared against the maximum likelihood method with Monte Carlo simulations. The results show that the Bayesian Weibull models significantly outperform the maximum likelihood method for almost all Weibull modulus and sample size values.

References

  • [1] Weibull, W., “A Statistical Theory of the Strength of Materials”. Ingvetenskaps Akad. Handl. 151, Stockholm (1939).
  • [2] Barbero, E., Fernández-Sáez, J. and Navarro, C., “Statistical analysis of the mechanical properties of composite materials”, Compos. Part B-Eng, 31(5): 375-381, (2000).
  • [3] McCool, J., “Flexural strength tests of brittle materials: selecting the number of specimens and determining confidence limits for Weibull parameters”, J. Test Eval., 45(2): 664-670 (2016).
  • [4] Barbero, E., Fernández-Sáez, J. and Navarro, C., “Statistical distribution of the estimator of Weibull modulus”, J. Mater. Sci. Lett., 20(9): 847-849, (2001).
  • [5] McCool, J.I., Using the Weibull distribution: Reliability, Modeling, and Inference, 1st ed. NJ: John Wiley & Sons Inc, (2012).
  • [6] Wua, D., Lia, Y., Zhanga, J., Changa, L., Wu, D. ,Fang, Z. and Shic, Y., “Effects of the number of testing specimens and the estimation methods on the Weibull parameters of solid catalysts”, Chem. Eng. Sci., 56(24): 7035-7044, (2001).
  • [7] Bao, Y.W. and Zhou, Y., “Investigation on Reliability of Nanolayer Grained Ti3SiC2 via Weibull Statistics”, J. Mater. Sci., 42(12): 4470-4475, (2007).
  • [8] Nohut, S., “Influence of sample size on strength distribution of advanced ceramics”, Ceram. Int., 40(3): 4285-4295, (2014).
  • [9] Khalili, A. and Kromp, K., “Statistical properties of Weibull estimators”, J. Mater. Sci., 26(24): 6741-6752, (1991).
  • [10] Durham, S., Lynch, J. and Padgett, W., “Inference for strength distributions of brittle fibers under increasing failure rate”, J. Composite Mater., 22(12): 1131–1140, (1988).
  • [11] Durham, S., Lynch, J. and Padgett, W., “A theoretical justification for an increasing average failure rate strength distribution in fibrous composites”, Naval Res. Logistics (NRL), 36(5): 655–661, (1989).
  • [12] Durham, S., Lynch, J. and Padgett, W., “TP 2-orderings and the IFR property with applications”, Probability Eng. Inf. Sci., 4(01): 73–88, (1990).
  • [13] Yalcinkaya, M. and Birgoren, B., “Confidence interval estimation of Weibull lower percentiles in small samples via Bayesian inference”, J. Eur. Ceram. Soc., 37: 2983-2990, (2017).
  • [14] Meyers, M.A. and Chawla, K.K., Mechanical Behavior of Materials, Cambridge: Cambridge University Press, (2009).
  • [15] Askeland, D.R., Fulay, P. and Wright, W., The Science and Engineering of Materials, 6th ed. Starnford: Thomson Learning Inc, (2010).
  • [16] Bousquet, N., “Eliciting vague but proper maximal entropy priors in Bayesian experiments”, Stat Pap., 51(3): 613–628, (2010).
  • [17] Abernethy, R.B., The New Weibull Handbook, 5th ed. North Palm Beach: Fla.R.B. Abernethy, (2006).
  • [18] Rinne, H., The Weibull Distribution: A Handbook, FL: CRC Press, (2009).
  • [19] Dodson, B., The Weibull Analysis Handbook, 2nd ed. Milwaukee: ASQ Quality Press, (2006).
  • [20] Ambrožič, M. and Gorjan, L., “Reliability of a Weibull analysis using the maximum-likelihood method”, J. Mater. Sci., 46(6): 1862-1869, (2011).
  • [21] Davies, I.J., “Unbiased estimation of Weibull modulus using linear least squares analysis—A systematic approach”, J. Eur. Ceram. Soc., 37(1): 369-380, (2017).
  • [22] Bergman, B., “Estimation of Weibull parameters using a weight function”, J. Mater. Sci. Lett., 5(6): 611-614, (1986).
  • [23] Faucher, B. and Tyson, W., “On the determination of Weibull parameters”, J. Mater. Sci. Lett., 7(11): 1199-1203, (1988).
  • [24] Birgoren, B., Ceramics and Composite Materials: New Research, New York : Nova Science Publishers, 215-235, (2006).
  • [25] Nelson, W., Applied Life Data Analysis, New York: John Wiley & Sons, (2005).
  • [26] Johnson, N.L., Kotz, S. and Balakrishnan, N., Continuous Univariate Distributions, 2nd ed. New York: Wiley, (1995).
  • [27] Murthy, D.N.P, Xie, M. and Jiang, R., Weibull Models, New York: Wiley, (2004).
  • [28] Langlois, R., “Estimation of Weibull parameters”, J. Mater. Sci. Lett., 10(18): 1049-1051, (1991).
  • [29] Gurvich, M., Dibenedetto, A. and Pegoretti, A., “Evaluation of the statistical parameters of a Weibull distribution”, J. Mater. Sci., 32(14): 3711-3716, (1997).
  • [30] Gong, J., “Determining the confidence intervals for Weibull estimators”, J. Mater. Sci. Lett., 18(17): 1405-1407, (1999).
  • [31] Gong, J., “A new probability index for estimating Weibull modulus for ceramics with the least-square method”, J. Mater. Sci. Lett., 19(10): 827-829, (2000).
  • [32] Davies, I., “Empirical correction factor for the best estimate of Weibull modulus obtained using linear least squares analysis”, J. Mater. Sci. Lett., 20(11): 997-999, (2001).
  • [33] Davies, I., “Best estimate of Weibull modulus obtained using linear least squares analysis: an improved empirical correction factor”, J. Mater. Sci. Lett., 39(4): 1441-1444, (2004).
  • [34] Griggs, J. and Zhang, Y., “Determining the confidence intervals of Weibull parameters estimated using a more precise probability estimator”, J. Mater. Sci. Lett., 22(24): 1771-1773, (2003).
  • [35] Wu, D. and Jiang, H., “Comment on “A new probability index for estimating Weibull modulus for ceramics with the least-square method”, J. Mater. Sci. Lett., 22(24):1745-1746, (2003).
  • [36] Tiryakioğlu, M., “On estimating Weibull modulus by moments and maximum likelihood methods”, J. Mater. Sci., 43(2): 793-798, (2008).
  • [37] Tiryakioğlu, M., Hudak, D., “Guidelines for two-parameter Weibull analysis for flaw-containing materials”, Metall. Mater. Trans. B., 42(6): 1130-5, (2011).
  • [38] Phan, L. and McCool, J., “Exact confidence intervals for Weibull parameters and percentiles”, P. I. Mech. Eng. O-J Ris., 223(4): 387-394, (2009).
  • [39] Menon, M.V., “Estimation of the shape and scale parameters of the Weibull distribution”, Technometrics, 5: 175-182, (1963).
  • [40] McCool, J.I., “Software for Weibull inference”, Quality Engineering, 23: 253-264, (2011).
  • [41] Bütikofera, L., Stawarczykb, B. and Roosa, M., “Two regression methods for estimation of a two-parameter Weibull distribution for reliability of dental materials”, Dent. Mater., 31: 33-50, (2015).
  • [42] Ahmed, A.O.M., Ibrahim, N.A. and Al-Kutubi, H.S., “Comparison of the Bayesian and maximum likelihood estimation for Weibull distribution”, J. Math. Stat., 6(2): 100-104, (2010).
  • [43] Alkutubi, H.S., AlShemmary E.N.A., Yasseen S.A. and Alwan Y.H., “New bayes estimator of parameter Weibull distribution using simulation study”, IJBAS, 1(3): 237-243, (2012).
  • [44] Aslam, M., Kazmi, S.M.A. and Ahmad, I., “Bayesian estimation for parameters of the Weibull distribution”, Sci.Int.(Lahore), 27(1): 259-264, (2014).
  • [45] Guure, C.B., Ibrahim, N.A. and Ahmed, A.O.M., “Bayesian estimation of two-parameter Weibull distribution using extension of Jeffreys' prior information with three loss functions”, Math. Probl. Eng., 2012(13), (2012).
  • [46] Guure, C.B. and Ibrahim, N.A., “Approximate Bayesian estimates of Weibull parameters with Lindley's method”, Sains Malaysiana, 43(9): 1433-1437, (2014).
  • [47] Jia, J., Yan, Z. and Peng, X., “A New Discrete Extended Weibull Distribution”,  IEEE Access , 7: 175474- 175486, (2019).
  • [48] Aron, A., Guo, H., Mettas, A. and Ogden D., “Improving the 1-parameter weibull: A bayesian approach”, Annual Reliability and Maintainability Symposium, 432–435, (2009).
  • [49] http://reliawiki.com/index.php/The_Weibull_Distribution. Access date: 13.05.2020.
  • [50] Simoa, N.F., Wieler, M., Feltenb, F. and Reh S., “Bayesian analysis for determination and uncertainty assessment of strength and crack growth parameters of brittle materials”, J. Eur. Ceram. Soc., 37: 1769–1777, (2017).
  • [51] Nguyen, D.L. Thai, D.K., Ngo, T.T, Tran, T.K. and Nguyen, T.T., “Weibull modulus from size effect of high-performance fiber-reinforced concrete under compression and flexure”, Constr. Build. Mater., 226 (30): 743-758, (2019).
  • [52] Ono, K., “A Simple Estimation Method of Weibull Modulus and Verification with Strength Data”, Appl. Sci., 9(8): 1575, (2019)
  • [53] Zellner, A., New developments in the applications of Bayesian methods, Amsterdam:University of Chicago Press, 211-232, (1977).
  • [54] Zellner, A., Maximum entropy and Bayesian methods, Boston: Kluwer, 17–31, (1991).
  • [55] Zellner, A., “Models, prior information and Bayesian analysis”, J. Econom., 75: 51–68, (1996).
  • [56] Berger, J.O., Statistical decision theory and Bayesian analysis, 2nd ed. New York: Springer, (2013).
  • [57] Soofi, E.S., Bayesian Analysis in Statistics and Econometrics, D.A. Berry, K.M. Chaloner, J.K. Geweke (eds).New York: Wiley, (1992).
  • [58] Skilling, J., Maximum entropy and Bayesian methods, Dordrecht:Kluwer Academic Publisher, (1989).
  • [59] LeBesnerais, G., Bercher, J.F. and Demoment, G., “A new look at entropy for solving linear inverse problems”, IEEE Trans. Inform. Theory, 45: 1565–1578, (1999).
  • [60] Soofi, E.S., “Principal information theoretic approaches”, J. Am. Stat. Assoc., 95: 1349–1353, (2000).
  • [61] Miller, D.J. and Yan, L., “Approximate maximum entropy joint feature inference consistent with arbitrary lower order probability constraints: application to statistical classification”, Neural Comput., 12: 2175– 2208, (2000).
  • [62] Green, N.R. and Campbell J., Mater. Sci. Eng. A, A137: 261-266, (1993).
  • [63] Ćurković, L., Bakić, A., Kodvanj, J. and Haramina, T., “Flexural strength of alumina ceramics: Weibull analysis”, Transactions of FAMENA, 34(1): 13-19, (2010).
  • [64] Askeland, D.R. and Fulay, P.P., Essentials of Materials Science and Engineering, 3nd ed., Canada: Cengage Learning, (2013).
  • [65] Tobias, P.A. and Trindade, D., Applied Reliability. 3nd ed., Boca Raton: CRC Press, (2011).
  • [66] Birgoren, B. and Dirikolu, M.H., “A computer simulation for estimating lower bound fracture strength of composites using Weibull distribution”, Compos. Part B-Eng., 35(3): 263-266, (2004).
  • [67] Thoman, D.R., Bain L.J. and Antle C.E., “Inferences on the parameters of theWeibull distribution”, Technometrics, 11: 445–460, (1969).
  • [68] Suen, H.K., Principles of Test Theories, New York: Routledge, (2012).
  • [69] Glasgow, L.A., Applied Mathematics for Science and Engineering, John Wiley & Sons, (2014).
  • [70] Casella, G. and Berger, R.L., Statistical Inference, 2nd ed. USA: Thomson Learning, (2002).
  • [71] Riedel, R. and Chen, I.W., Ceramics Science and Technology, John Wiley & Sons, (2011).
  • [72] Juritz, J. M., Juritz, J. W. F. and Stephens, M. A., “On the accuracy of simulated percentage points”, J. Am. Stat. Assoc., 83: 441–444, (1983).
  • [73] Dirikolu, M.H., Aktas¸ A. and Birgören, B., “Statistical analysis of fracture strength of composite materials using Weibull distribution”, Turkish J Engng Environ Sci, 26(1): 45–8, (2002).
There are 73 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Statistics
Authors

Meryem Yalçınkaya 0000-0003-4255-5656

Burak Birgören 0000-0001-9045-6092

Publication Date March 1, 2021
Published in Issue Year 2021 Volume: 34 Issue: 1

Cite

APA Yalçınkaya, M., & Birgören, B. (2021). Bayesian Confidence Interval Estimation of Weibull Modulus Under Increasing Failure Rate. Gazi University Journal of Science, 34(1), 290-309. https://doi.org/10.35378/gujs.736084
AMA Yalçınkaya M, Birgören B. Bayesian Confidence Interval Estimation of Weibull Modulus Under Increasing Failure Rate. Gazi University Journal of Science. March 2021;34(1):290-309. doi:10.35378/gujs.736084
Chicago Yalçınkaya, Meryem, and Burak Birgören. “Bayesian Confidence Interval Estimation of Weibull Modulus Under Increasing Failure Rate”. Gazi University Journal of Science 34, no. 1 (March 2021): 290-309. https://doi.org/10.35378/gujs.736084.
EndNote Yalçınkaya M, Birgören B (March 1, 2021) Bayesian Confidence Interval Estimation of Weibull Modulus Under Increasing Failure Rate. Gazi University Journal of Science 34 1 290–309.
IEEE M. Yalçınkaya and B. Birgören, “Bayesian Confidence Interval Estimation of Weibull Modulus Under Increasing Failure Rate”, Gazi University Journal of Science, vol. 34, no. 1, pp. 290–309, 2021, doi: 10.35378/gujs.736084.
ISNAD Yalçınkaya, Meryem - Birgören, Burak. “Bayesian Confidence Interval Estimation of Weibull Modulus Under Increasing Failure Rate”. Gazi University Journal of Science 34/1 (March 2021), 290-309. https://doi.org/10.35378/gujs.736084.
JAMA Yalçınkaya M, Birgören B. Bayesian Confidence Interval Estimation of Weibull Modulus Under Increasing Failure Rate. Gazi University Journal of Science. 2021;34:290–309.
MLA Yalçınkaya, Meryem and Burak Birgören. “Bayesian Confidence Interval Estimation of Weibull Modulus Under Increasing Failure Rate”. Gazi University Journal of Science, vol. 34, no. 1, 2021, pp. 290-09, doi:10.35378/gujs.736084.
Vancouver Yalçınkaya M, Birgören B. Bayesian Confidence Interval Estimation of Weibull Modulus Under Increasing Failure Rate. Gazi University Journal of Science. 2021;34(1):290-309.