Accelerated life testing for double-truncated general half normal distribution.

*(English)*Zbl 1456.62237Summary: 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.

##### MSC:

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 |

##### Keywords:

bootstrap percentile method; maximum likelihood estimation; mean squared error; Metropolis-Hastings Markov chain Monte Carlo approach; Newton-Raphson method
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\textit{H. Xin} and \textit{J.-P. Zhu}, Int. J. Inf. Manage. Sci. 31, No. 1, 35--53 (2020; Zbl 1456.62237)

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##### References:

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