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Accelerated life testing for double-truncated general half normal distribution. (English) Zbl 1456.62237
Summary: The maximum likelihood estimation method and the Bayesian estimation method using Metropolis-Hastings Markov chain Monte Carlo (M-H MCMC) approach are investigated for estimating the parameters in the accelerated life test (ALT) model when the quality characteristic of product follows a double-truncated generalized half normal (DTGHN) distribution. To overcome the complexity by applying Fisher information matrix with the maximum likelihood estimates (MLEs) to obtaining the confidence intervals (CIs) of distribution quantiles, a bootstrap percentile method is used to obtain the CIs of distribution quantiles. The estimation performance of the proposed methods is evaluated by means of Monte Carlo simulations. Simulation results show that the proposed M-H MCMC method with non-informative prior distributions outperforms the maximum likelihood estimation method to obtain reliable MLEs of the ALT model parameters for the DTGHN distribution. An example about the stress-rupture life of Kevlar 49/epoxy is used to demonstrate the applications of the proposed methods and investigate the coverage probability of the bootstrap percentile CI for the distribution median at the normal-use condition.
62N05 Reliability and life testing
62G08 Nonparametric regression and quantile regression
62G09 Nonparametric statistical resampling methods
62M05 Markov processes: estimation; hidden Markov models
62P30 Applications of statistics in engineering and industry; control charts
65C05 Monte Carlo methods
Full Text: DOI
[1] Ahmadi, K., Rezaei, M. and Yousefzadeh, F. (2015).Estimation for the generalized half-normal distribution based on progressive Type-II censoring, Journal of Statistical Computation and Simulation, Vol.85, 1128-1150. · Zbl 1457.62291
[2] Altun, E., Yousof H. M. and Hamedani, G. G. (2018).A new generalization of generalized half-normal distribution: properties and regression models, Journal of Statistical Distributions and Applications, 5:7; https://doi.org/s40488-018-0089-4. · Zbl 1420.60013
[3] Byrd, R. H., Lu, P., Nocedal, J. and Zhu, C. (1995).A limited memory algorithm for bound constrained optimization, SIAM Journal of Scientific Computing, Vol.16, 1190-1208. · Zbl 0836.65080
[4] Cooray, K. and Ananda, M. M. (2008).A generalization of the half-normal distribution with applications to lifetime data, Communications in Statistics-Theory and Methods, Vol.37, 1323-1337. · Zbl 1163.62006
[5] Cordeiro, G. M., Pescim, R. R. and Ortega, E. M. (2012).The Kumaraswamy generalized half-normal distribution for skewed positive data, Journal of Data Science, Vol.10, 195-224.
[6] Cordeiro, G. M., Alizadeh, M., Pescim, R. R. and Ortega, E. M. (2017).The odd log-logistic generalized half-normal lifetime distribution: properties and applications, Communications in StatisticsTheory and Methods, Vol.46, 4195-4214. · Zbl 1368.62025
[7] He, Q., Zha, Y., Sun, Q., Pan, Z. and Liu, T. (2017).Capacity fast prediction and residual useful life estimation of valve regulated lead acid battery, Mathematical Problem in Engineering, Article ID 7835049, 9 pages.
[8] Lawless, J. F. (2003). Statistical Models and Methods for Lifetime Data, John Wiley & Sons, NY, USA. · Zbl 1015.62093
[9] Meeker, W. Q. and Escobar, L. A. (1998). Statistical Methods for Reliability Data, John Wiley & Sons, NY, USA. · Zbl 0949.62086
[10] Nelson, W. B. (1990). Accelerated Testing: Statistical Models, Test Plans and Data Analysis, John Wiley & Sons, NJ, USA. · Zbl 0717.62089
[11] Nogales, A. G. and P´erez, P. (2015).Unbiased estimation for the general half-normal distribution, Communications in Statistics-Theory and Methods, Vol.44, 3658-3667. · Zbl 1328.62133
[12] Olmos, N. M., Varela, H., Bolfarine, H. and G´omez, H. W. (2014).An extension of the generalized half-normal distribution, Statistical Papers, Vol.55, 967-981. · Zbl 1306.62056
[13] Pescim, R. R., Ortega, E. M., Cordeiro, G. M., Alizadeh, M. (2017).A new log-location regression model: estimation, influence diagnostics and residual analysis, Journal of Applied Statistics, Vol.44, 233-252.
[14] Pewsey, A. (2002).Large-sample inference for the general half-normal distribution, Communications in Statistics-Theory and Methods, Vol.31, 1045-1054. · Zbl 1075.62533
[15] Pewsey, A. (2004).Improved likelihood based inference for the general half-normal distribution, Communications in Statistics-Theory and Methods, Vol.33, 197-204. · Zbl 1066.62035
[16] Powell, P. C. (1983). Engineering with Polymers, New York: Chapman and Hall.
[17] Srivastava, P. W. and Savita, S. (2018).An accelerated life test plan for a two-component parallel system under ramp-stress loading using masked data, International Journal of Quality and Reliability Management, Vol.35, 811-820.
[18] Wachtman, J. B. (1996). Mechanical Properties of Ceramics, New York: John Wiley & Sons, Inc, Vol.69, 265-267.
[19] Wang, W. and Kececioglu, D. B. (2000).Fitting the Weibull log-linear model to accelerated life-test data, IEEE Transactions on Reliability, Vol.49, 217-223.
[20] Wang, G., Niu, Z. and He, Z. (2015).Accelerated lifetime data analysis with a nonconstant shape parameter, Mathematical Problem in Engineering, Article ID 801465, 8 pages.
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