In the literature, many works on determining inspection interval by the delay time concept generally assumed that the time of inspection span and the time of failure renewal are negligible. However, in realistic cases...In the literature, many works on determining inspection interval by the delay time concept generally assumed that the time of inspection span and the time of failure renewal are negligible. However, in realistic cases, the above time should not be neglected for both the time itself and its effect. In order to model the effect of the possible overlapping of inspection span with failure downtime on determining the optimal inspection interval, we propose a block-based inspection model for a single component-based on delay time concept. We further compare this model with the age-based model to show the practical sense. The developed models are also demonstrated by numerical examples.展开更多
The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of c...The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.展开更多
文摘In the literature, many works on determining inspection interval by the delay time concept generally assumed that the time of inspection span and the time of failure renewal are negligible. However, in realistic cases, the above time should not be neglected for both the time itself and its effect. In order to model the effect of the possible overlapping of inspection span with failure downtime on determining the optimal inspection interval, we propose a block-based inspection model for a single component-based on delay time concept. We further compare this model with the age-based model to show the practical sense. The developed models are also demonstrated by numerical examples.
基金supported by the Natural Science Foundation of China under Grant Nos.11071022,11028103,11231010,11471223,BCMIISthe Beijing Municipal Educational Commission Foundation under Grant Nos.KZ201410028030,KM201210028005Jishou University Subject in 2014(No:14JD035)
文摘The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.
