Inference Of Censored Data In Weibull Distribution And Its Application In Reliability Analysis

High-quality development has become the focus of China’s future development.And it is inseparable from reliability technology.Reliability is defined as the probability that a product,system,or service will perform its intended function adequately for a specified period of time,or will operate in a defined environment without failure.The application of reliability theory exists in every aspect of economic development and social life.Therefore,it is of great significance to the research of parameter estimation method in reliability analysis.In this context,first of all,based on the Weibull distribution model,a parameter estimation method is proposed for type I interval censored data.This method is based on Weibull linear transformation and LES method.An improved method PLSE method is proposed to improve the estimation efficiency of LSE method.Aiming at the problem of bias from the estimate,the paper proposes two bias-corrected methods for LSE and PLSE,called CLSE method and PCLSE method.For type II doubly censored data,a new parameter estimation method PE method is proposed.Based on the two-parameter Weibull distribution,by data transformation and data sequencing,the paper sets up equations to estimate the population parameters.On this basis,a new goodness of fit test,PG test is proposed too.Secondly,all the proposed methods are studied by Monte Carlo simulation.Based on type I interval censored data,the results show that the performance of the proposed LSE method or PLSE method is better than MLE method when the number of observation intervals is small.The effect of bias-corrected method is very good.After bias correction,the performance of CLSE or PCLSE is better than LSE and PLSE,moreover,the effect of CPLSE is the best among the three methods.Based on type II doubly censored data,the proposed PE method is superior to the MLE method in most cases,especially in the left or doubly censored schemes.In addition,the proposed PG test performs better in most cases than the other two goodness-of-fit tests.Finally,the proposed methods are applied to a real data analysis,with a group of groove ball bearing endurance data.Based on type I interval censored data,the performance of LSE,PLSE,CLSE and CPLSR methods proposed in this paper is reasonable,reliable and competitive with MLE methods.Based on type II doubly censred data,the performance of PE parameter estimation method proposed in this paper is more stable than that of MLE method under different censored ratios.In addition,the PG test proposed in this paper is competitive with KS test and CVM test.In general,it can be seen from the results of simulation study or real data analysis that several parameter estimation methods proposed in this paper for type I interval censored data and type II doubly censored data are competitive with the MLE method.Based on type II doubly censored data,the goodness of fit test method proposed in this paper is also competitive with KS test and CVM test.