| I . With the development of science and technology , the manufacturer and the clients hope to obtain all kinds of information of the product reliability under conditions with using less time and testing cost .Because bobtailed life test can not adapt to this need ,this comes in the accelerated life test(ALT).Weibull distribution is common in reliability.So we always estimate the unknown parameters of the Weibull distribution by constant stress accelerated life test(CSALT) and stepwise stress accelerated life test (SSALT) and progressive stress accelerated life test (PSALT).Former articles([l] ~ [5]) all estimated parameters by single CSALT,SSALT or PSALT,however,under CSALT or PSALT at least need two different stress level sets ,this will increase time and cost .At the same time the statistical analysis under the ALT is based on a more important assumption:the failure mechanism bears no relation with the stress level . But under PSALT,as the stress level is increasing with time ,in order to obtain more failure data,the stress level maybe exceeds the reasonable range .For the aforesaid reasons, in the second chapter ,this article estimates some parameters in the two-parameters Weibull distribution by the hybrid ALT method,and gives the inverse moment estimator for the shape parameter,at the same time the confidence interval of the accelerated coefficient is given . In order to check the validity of this method ,this article stochastically simulates a sample at last.Basic Researching Problem :Assume the life time follows the two-parameter Weibull distribution under a stress V,then under the hybrid ALT ,the cumulative distribution of T isof c and u respectively ,which lead to the only solutions of c and u. The estimators of c and u from (2.2.3) and (2.2.4)say,rh and u, are refered to as inverse moment estimators .Thus we can get the inverse estimators : c, m. Prom(2.2.2) andwe can get the estimators d and 9.From the known inverse moment estimator ra,Give confidence level l-a,the followingsystem can be establishedThus we obtain the confidence interval of the accelerated coefficient V-V0 =At last this article testified the validity of this method by an example.Example Let c=d=l,k=l,m=2,t0 = l,sample size n=20,simulating a sample by computer :0.6774 , 0.7246, 0.8025, 0.8297, 0.9152 , 0.9733, 0.9779 , 1.0480 , 1.0594 , 1.2006, 1.2306 ,1.3891,1.4043, 1.4066 ,1.4133 ,1.4384 ,1.4653 ,1.4729 ,1.7384 , 2.1451Prom theorem 2.2.3 ,we obtain the inverse moment estimators m = 2.0199, c = 0.8763.Prom (2.2.5) and (2.2.6),we get the resolution =1.5653, d=1.2125. From (2.2.7) and (2.2.8),we obtain the 90 percent confidence interval of c : (0.5721,1.2232).II .As we all known ,there is a bound for the increasing of the stress level ,the failure mechanism will change when excessing the determinate bound. For this stress level should not increase too much ,however that will have an influence on the efficiency of the tests.In order to make testing time be shortened to an acceptable level ,we have to use the second accelerated stress(for example ,voltage),and apply accelerated technique to it ,so the double stress ALT is produced.Recent years statistical analysis under both stress accelerated soft ware has undergone a quick development .Article[7]studied the parameters estimators of Weibull distribution by double stress modeling. Article[8jstudied BLIE problems of Weibull distribution under both stress constant stress ALT.In order to reduce the sample size and life testing time ,this article has gived the BLIE of lognormal distribution by both stress and crossed step-stress ALT in the third chapter , and proved it is better than the former BLUE.Basic problem :Assume the life time T follows lognormal distribution,stress levels setdistribution of T under stress level (i,j) by both stress crossed and stepwise stress ALTwhere ( ) is the standard normal distribution(N(0,l)function , ij, ij2 and ij are logmean,logvariance and logarithmic standard deviate under stress level Sij respectively.The acce...
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