In this paper,the statistical inference for system stress-strength reliability with bounded strength is discussed.When the stress and strength variables follow the three-parameter Exponentiated-Weibull distributions w...In this paper,the statistical inference for system stress-strength reliability with bounded strength is discussed.When the stress and strength variables follow the three-parameter Exponentiated-Weibull distributions with unequal scale and shape parameters,the maximum likelihood estimator(MLE)and bootstrap-p confidence interval for system reliability are derived.In addition,combining the score equations which are got by taking the first derivative of the log-likelihood function with respect to the model parameters,the modified generalized pivotal quantity for the system reliability is obtained.After that,two point estimators and a modified generalized confidence interval based on the modified generalized pivotal quantity for the system reliability are derived.Monte Carlo simulations are performed to compare the performances of the proposed point estimators and confidence intervals.Finally,a real data analysis is provided to illustrate the proposed procedures.展开更多
Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibili...Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibility, some modifications of the Weibull distribution have been made from several researches in order to best adjust the non-monotonic shapes. This paper gives a study on the performance of two specific modifications of the Weibull distribution which are the exponentiated Weibull distribution and the additive Weibull distribution.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.12101475,12101476,11901134,12061091the Soft Science Project of Xi’an under Grant No.22RKYJ0065+1 种基金the Natural Science Basic Research Program of Shaanxi under Grant Nos.2021JQ-186,2020JQ-285the Fundamental Research Funds for the Central Universities under Grant Nos.XJS210603,JGYB2222。
文摘In this paper,the statistical inference for system stress-strength reliability with bounded strength is discussed.When the stress and strength variables follow the three-parameter Exponentiated-Weibull distributions with unequal scale and shape parameters,the maximum likelihood estimator(MLE)and bootstrap-p confidence interval for system reliability are derived.In addition,combining the score equations which are got by taking the first derivative of the log-likelihood function with respect to the model parameters,the modified generalized pivotal quantity for the system reliability is obtained.After that,two point estimators and a modified generalized confidence interval based on the modified generalized pivotal quantity for the system reliability are derived.Monte Carlo simulations are performed to compare the performances of the proposed point estimators and confidence intervals.Finally,a real data analysis is provided to illustrate the proposed procedures.
文摘Proposed by the Swedish engineer and mathematician Ernst Hjalmar Waloddi Weibull (1887-1979), the Weibull distribution is a probability distribution that is widely used to model lifetime data. Because of its flexibility, some modifications of the Weibull distribution have been made from several researches in order to best adjust the non-monotonic shapes. This paper gives a study on the performance of two specific modifications of the Weibull distribution which are the exponentiated Weibull distribution and the additive Weibull distribution.
