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Estimating the parameters of Weibull distribution and the acceleration factor from hybrid partially accelerated life test. (English) Zbl 1252.62103
Appl. Math. Modelling 36, No. 7, 2920-2925 (2012); corrigendum ibid. 39, No. 18, 5743 (2015).
Summary: We consider the estimation of the parameters of the Weibull distribution based on hybrid censored data. The parameters are estimated by the maximum likelihood method under a step-stress partially accelerated test model. The maximum likelihood estimates (MLEs) of the unknown parameters are obtained by Newton-Raphson algorithm. Also, the approximate Fisher information matrix is obtained for constructing asymptotic confidence bounds for the model parameters. The biases and mean square errors of the maximum likelihood estimators are computed to assess their performances through a Monte Carlo simulation study.

MSC:
62N05 Reliability and life testing
62N01 Censored data models
65C05 Monte Carlo methods
62F10 Point estimation
62F25 Parametric tolerance and confidence regions
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References:
[1] Nelson, W., Accelerated life testing: statistical models, data analysis and test plans, (1990), John Wiley and sons New York
[2] P.K. Goel, Some estimation problems in the study of tampered random variables, Technical Report No. 50, Department of statistics, Carnegie-mellon university, Pittspurgh, Pennsylvania, 1971.
[3] DeGroot, M.H.; Goel, P.K., Bayesian and optimal design in partially accelerated life testing, Nav. res. logist. quart., 16, 2, 223-235, (1979) · Zbl 0422.62089
[4] Bhattacharyya, G.K.; Soejoeti, Z., A tampered failure rate model for step-stress accelerated life test, Commun. statist. theory methods, 18, 5, 1627-1643, (1989) · Zbl 0696.62356
[5] Bai, D.S.; Chung, S.W., Optimal design of partially accelerated life tests for the exponential distribution under type-I censoring, IEEE trans. reliab., 41, 3, 400-406, (1992) · Zbl 0749.62063
[6] Bai, D.S.; Chung, S.W.; Chun, Y.R., Optimal design of partially accelerated life tests for the lognormal distribution under type-I censoring, Reliab. eng. syst. safety, 40, 85-92, (1993)
[7] A.A. Abdel-Ghaly, E.H. El-Khodary, A.A. Ismail, Maximum likelihood estimation and optimal design in step partially accelerated life tests for pareto distribution using Type-I censoring, in: Proceedings of the 14th Annual Conference of Statistics and Computer Modeling in Human and Social Sciences, Faculty of Economics and Political Sciences, Cairo, University, 2002, pp. 27-40.
[8] A.A. Abdel-Ghaly, E.H. El-Khodary, A.A. Ismail, (2003a). Estimation and optimum constant-stress partially accelerated life test plans for Pareto distribution with Type-I censoring, in: Proceedings of the 38th Annual Conference of Statistics, Computer Sciences and Operation Research, ISSR, Cairo University, Egypt, pp. 49-65.
[9] A.A. Abdel-Ghaly, E.H. El-Khodary, A.A. Ismail, (2003b). Estimation and optimal design in step partially accelerated life tests for pareto distribution using Type-II censoring, in: Proceedings of the 15th annual conference on Statistics and Computer Modeling in Human and Social Sciences, Faculty of Economics and Political Science, Cairo University, Egypt, pp. 16-29.
[10] M.M. Abdel-Ghani, Investigation of some Lifetime Models under Partially Accelerated Life Tests, Ph.D. Thesis, Department of Statistics, Faculty of Economics and Political Science, Cairo University, Egypt, 1998.
[11] Abdel-Ghani, M.M., The estimation problem of the log-logistic parameters in step partially accelerated life tests using type-I censored data, Nat. rev. soc. sci., 41, 2, 1-19, (2004)
[12] A.A. Ismail, The test design and parameter estimation of pareto lifetime distribution under partially accelerated life tests, Ph.D. Thesis, Department of Statistics, Faculty of Economics & Political Science, Cairo University, Egypt, 2004.
[13] Aly, H.M.; Ismail, A.A., Optimum simple time-step stress plans for partially accelerated life testing with censoring, Far east J. theor. statist., 24, 2, 175-200, (2008) · Zbl 1327.62493
[14] Ismail, A.A.; Sarhan, A.M., Design of step-stress life test with progressively type-II censored exponential data, Int. math. forum, 4, 40, 1963-1976, (2009) · Zbl 1186.62124
[15] Ismail, A.A.; Aly, H.M., Optimal planning of failure-step stress partially accelerated life test under type-II censoring, J. statist. comput. simulat., 80, 12, 1335-1348, (2010) · Zbl 1205.62153
[16] Ismail, A.A., Bayes estimation of Gompertz distribution parameters and acceleration factor under partially accelerated life tests with type-I censoring, J. statist. comput. simulat., 80, 11, 1253-1264, (2010) · Zbl 1205.62027
[17] Cohen, A.C., Truncated and censored samples: theory and applications, (1991), Marcel Dekker · Zbl 0742.62027
[18] Ismail, M.A., Bayesian analysis of hybrid censored life tests using asymmetric loss functions, Nahda quart. J. faculty econ. polit. sci. Cairo univ., 9, 5-28, (2001)
[19] Fairbanks, K.; Madson, R.; Dykstra, R., A confidence interval for an exponential parameter from a hybrid life test, J. amer. statist. assoc., 77, 137-140, (1982) · Zbl 0504.62087
[20] Draper, N.; Guttman, I., Bayesian analysis of hybrid life tests with exponential failure times, Ann. inst. statist. math., 39, 219-225, (1987) · Zbl 0612.62134
[21] Chen, S.; Bhattacharya, G.K., Exact confidence bounds for an exponential parameter under hybrid censoring, Commun. statist. theory methods, 17, 1857-1870, (1988) · Zbl 0644.62101
[22] Ebrahimi, N., Prediction intervals for future failures in exponential distribution under hybrid censoring, IEEE trans. reliab., 41, 127-132, (1992) · Zbl 0743.62089
[23] Gupta, R.D.; Kundu, D., Hybrid censoring schemes with exponential failure distribution, Commun. statist. theory methods, 27, 12, 3065-3083, (1998) · Zbl 1008.62679
[24] Kundu, D., On hybrid censored Weibull distribution, J. statist. plan. infer., 137, 2127-2142, (2007) · Zbl 1120.62081
[25] Xie, Q, Exact inference for exponential step-stress model under different forms of censoring, ETD Collection for McMaster University. Paper AAINR28250, (2006). <http://digitalcommons.mcmaster.ca/dissertaions/AAINR28250>.
[26] Park, S.; Balakrishnan, N., On simple calculation of the Fisher information in hybrid censoring schemes, Statist. prob. lett., 79, 10, 1311-1319, (2009) · Zbl 1162.62091
[27] Zhang, S.; Zhang, Y.; Chaloner, K.; Stapleton, J.T., A copula model for bivariate hybrid censored survival data with application to the MACS study, Lifetime data anal., 16, 2, 231-249, (2010) · Zbl 1322.62295
[28] Miller, R.C., Survival analysis, (1981), John Wiley & Sons
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