| This thesis is concerned with the analysis of lifetime and reliability of the products in Weibull distribution case.For the data obtained from the test with stopping time,i.e.type I censored data,how to obtain the accurate lower confidence limits of reliability and conditional reliability when the lifetime follows Weibull distribution is one of not well solved,widespread concerned and important problem in the reliability engineering practice.There exist some approximation methods based on the large sample theory to tackle with such problem.But for Assessing the reliability of high reliability products we usually get the small or medium size sample,these methods based on the large sample theory does not work well.Based on the theory of ordering method in the sample space,for prearranged confidence level,with arbitrary sample size(not less than 2),[1](see [2] also)give the estimation and the accurate lower confidence limit of the reliability as well as its effective calculating method.Based on the work of [1],we developed a new ordering function and solved the problem to calculate the accurate lower confidence limit of the conditional reliability,especially,if the sample size is small.The main results are as follows:For prespecified confidence level,with arbitrary sample size(not less than 2),we give the accurate lower confidence limits of conditional reliability for Weibull distribution as well as its effective calculating method for the no failure Type I censored data.For prespecified confidence level,with arbitrary sample size(not less than 2),we give the accurate point estimation and lower confidence limit of conditional reliability for Weibull distribution as well as its effective calculating method under Type I censoring in the case of one or more failure.An approximate lower confidence limit for conditional reliability is also given.We not only provide theoretical method,but also work out corresponding C++computing program. |
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