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Abstract: With the help of relative entropy theory, norm theory, and bootstrap methodology, a new hypothesis testing method is proposed to verify reliability with a three-parameter Weibull distribution. Based on the relative difference information of the experimental value vector to the theoretical value vector of reliability, six criteria of the minimum weighted relative entropy norm are established to extract the optimal information vector of the Weibull parameters in the reliability experiment of product lifetime. The rejection region used in the hypothesis testing is deduced via the area of intersection set of the estimated truth-value function and its confidence interval function of the three-parameter Weibull distribution. The case studies of simulation lifetime, helicopter component failure, and ceramic material failure indicate that the proposed method is able to reflect the practical situation of the reliability experiment.

[1]Abbasi, B., Niaki, S.T.A., Khalife, M.A., Faize, Y., 2011. A hybrid variable neighborhood search and simulated annealing algorithm to estimate the three parameters of the Weibull distribution. Exp. Syst. Appl., 38(1):700-708.

[2]Bartkute-Norkuniene, V., Sakalauskas, L., 2011. Consistent estimator of the shape parameter of three-dimensional Weibull distribution. Commun. Stat. Theory Meth., 40(16):2985-2996.

[3]Basu, A., Manda, A., Pardo, L., 2010. Hypothesis testing for two discrete populations based on the Hellinger distance. Stat. Prob. Lett., 80(3-4):206-214.

[4]Chatterjee, S., Bandopadhyay, S., 2012. Reliability estimation using a genetic algorithm-based artificial neural network: an application to a load-haul-dump machine. Exp. Syst. Appl., 39(12):10943-10951.

[5]Deng, J., Gu, D.S., Li, X.B., 2004. Parameters and quantile estimation for fatigue life distribution using probability weighted moments. Chin. J. Comput. Mech., 21(5):609-613 (in Chinese).

[6]de Santis, F., 2004. Statistical evidence and sample size determination for Bayesian hypothesis testing. J. Stat. Plan. Infer., 124(1):121-144.

[7]Duffy, S.F., Palko, J.L., Gyekenyesi, J.P., 1993. Structural reliability analysis of laminated CMC components. J. Eng. Gas Turb. Power, 115(1):103-108.

[8]Efron, B., 1979. Bootstrap methods. Ann. Stat., 7(1):1-36.

[9]El-Adll, M.E., 2011. Predicting future lifetime based on random number of three parameters Weibull distribution. Math. Comput. Simul., 81(9):1842-1854.

[10]Ennis, D.M., Ennis, J.M., 2010. Equivalence hypothesis testing. Food Qual. Pref. 21(3):253-256.

[11]Feng, D.C., Chen, F., Xu, W.L., 2012. Learning robust principal components from L1-norm maximization. J. Zhejiang Univ.-Sci. C (Comput. & Electron.), 13(12):901-908.

[12]Harris, T.A., 1991. Rolling Bearing Analysis (3rd Ed.). John Wiley & Sons, New York.

[13]Jiang, R.Y., Zuo, M.J., 1999. Reliability Model and Application. China Machine Press, Beijing (in Chinese).

[14]Johnson, L.G., 1970. Theory and Technique of Variation Research. Elsevier, New York.

[15]Kaplan, E.L., Meier, P., 1958. Nonparametric estimation from incomplete observations. J. Am. Stat. Assoc., 53(282):457-481.

[16]Konishi, Y., Nishiyama, Y., 2009. Hypothesis testing in rank-size rule regression. Math. Comput. Simul., 79(9):2869-2878.

[17]Kula, K.S., Apaydin, A., 2009. Hypotheses testing for fuzzy robust regression parameters. Chaos Solit. Fract., 42(4):2129-2134.

[18]Lee, J., Pan, R., 2012. Bayesian analysis of step-stress accelerated life test with exponential distribution. Qual. Rel. Eng. Int., 28(3):353-361.

[19]Li, Q., Liu, S.L., Pan, X.H., Zheng, S.Y., 2012. A new method for studying the 3D transient flow of misaligned journal bearings in flexible rotor-bearing systems. J. Zhejiang Univ.-Sci. A (Appl. Phys. & Eng.), 13(4):293-310.

[20]Luxhoj, T.J., Shyur, H.J., 1995. Reliability curve fitting for aging helicopter components. Rel. Eng. Syst. Safety, 48(3):229-234.

[21]Martin, M.A., 2007. Bootstrap hypothesis testing for some common statistical problems: a critical evaluation of size and power properties. Comput. Stat. Data Anal., 51(12):6321-6342.

[22]Nelson, W., 1990. Accelerated Testing: Statistical Models, Test Plans and Data Analysis. John Wiley & Sons, New York.

[23]Niesłony, A., Ruzicka, M., Papuga, J., Hodr, A., Balda, M., Svoboda, J., 2012. Fatigue life prediction for broad-band multiaxial loading with various PSD curve shapes. Int. J. Fatigue, 44:74-88.

[24]Pierce, D.M., Zeyen, B., Huigens, B.M., Fitzgerald, A.M., 2011. Predicting the failure probability of device features in MEMS. IEEE Trans. Dev. Mat. Rel., 11(3):433-441.

[25]Prawoto, Y., Dillon, B., 2012. Failure analysis and life assessment of coating: the use of mixed mode stress intensity factors in coating and other surface engineering life assessment. J. Fail. Anal. Prev., 12(2):190-197.

[26]Qian, L.F., 2012. The Fisher information matrix for a three-parameter exponentiated Weibull distribution under type II censoring. Stat. Methodol., 9(3):320-329.

[27]Shafieezadeh, A., Ellingwood, B.R., 2012. Confidence intervals for reliability indices using likelihood ratio statistics. Struct. Safety, 38:48-55.

[28]Tan, P., He, W.T., Lin, J., Zhao, H.M., Chu, J., 2011. Design and reliability, availability, maintainability, and safety analysis of a high availability quadruple vital computer system. J. Zhejiang Univ.-Sci. A (Appl. Phys. & Eng.), 12(12):926-935.

[29]Toasa Caiza, P.D., Ummenhofer, T., 2011. General probability weighted moments for the three-parameter Weibull distribution and their application in S-N curves modeling. Int. J. Fatigue, 33(12):1533-1538.

[30]Woodbury, A.D., 2004. A FORTRAN program to produce minimum relative entropy distributions. Comput. Geosci., 30(1):131-138.

[31]Woodbury, A.D., Ulrych, T.J., 1998. Minimum relative entropy and probabilistic inversion in groundwater hydrology. Stoch. Hydrol. Hydraul., 12(5):317-358.

[32]Xia, X.T., 2012. Forecasting method for product reliability along with performance data. J. Fail. Anal. Prev., 12(5):532-540.

[33]Xia, X.T., Chen, J.F., 2011. Fuzzy hypothesis testing and time series analysis of rolling bearing quality. J. Test. Eval., 39(6):1144-1151.

[34]Zhang, Y., Zheng, Y.M., Yang, M., Li, H., Jin, Z.H., 2012. Design and implementation of the highly-reliable, low-cost housekeeping system in the ZDPS-1A pico-satellite. J. Zhejiang Univ.-Sci. C (Comput. & Electron.), 13(2):83-89.

[35]Zhao, X.P., Lu, Z.Z., Wang, W.H., 2010. A practical and effective method for estimating confidence limits of population percentile and reliability of three-parameter Weibull distribution on probability weighted moment. J. Northw. Polytechn. Univ., 38(3):470-475 (in Chinese).