1、 PDF外文：http:/ 3350 字 本科毕业设计（英文翻译） 英文原文 ： Estimations For A Simple Step-Stress Model With Progressively Type-II Censored Data 院 系 ：
2、; 能源与环境工程学院 专业年级： 机械设计制造及其自动化 2008 级 学生姓名： 学号： &nbs
3、p;2012 年 5 月 12 日 1 International Journal of Reliability, Quality and Safety Engineering Vol.12, No.5(2005) 385395 World Scientic Publishing Company
4、; ESTIMATIONS FOR A SIMPLE STEP-STRESS MODEL WITH PROGRESSIVELY TYPE-II CENSORED DATA SHUO-JYE WU and HSIU-MEI LEE Department of Statistics, Tamkang University Tamsui, Taipei 251 Taiwan shuostat.tku.edu.tw DAR-HSIN CHEN Graduate Institute of Finance National Chiao Tung
5、 University Hsinchu City 300, Taiwan Received 1 January 2005 Revised 23 May 2005 With todays high technology, some life tests result in no or very few failures by the end of test. In such cases, an approach is to do life test at higher-than-usual stress conditions in order to obtain fai
6、lures quickly. This study discusses the point and interval estimations of parameters on the simple step-stress model in accelerated life testing with progressive type II censoring. An exponential failure time distribution with mean life that is a log-linear function of stress and a cumulative exposu
7、re model are considered. We derive the maximum likelihood estimators of the model parameters. Confidenc eintervals for the model parameters are established by using pivotal quantity and can be applied to any sample size. A numerical example is investigated to illustrate the proposed methods.
8、 Keywords: Accelerated life test； confidence interval； exponential distribution； maximum likelihood method； pivotal quantity； progressive type II censoring. 1. Introduction Accelerated life test (ALT) is often used for reliability analysis. Test units are run at higher-than-usual stress conditi
9、ons in order to obtain failures quickly. A model relating life length to stress is fitted to the accelerated failure times and then extrapolated to estimate the failure time distribution under usual conditions. The stress loading in an ALT can be applied various ways. They include constant stress, s
10、tep stress, and random stress. Nelson (Ref. 10, Chap. 1) discussed their advantages and disadvantages. In step-stress scheme, a test unit is subjected to successively higher levels of stress. A test unit starts at a specified low stress for a specified length of time. If it does not fail, stress on
11、it is raised and held a specified time. The stress is thus increased step by step until the test unit fails. Generally all test units go through the same specified pattern of stress levels and test times. The simplest step-stress ALT uses only two stress levels and we call simple step-stress ALT. Th
12、e statistical inference in this simple step-stress ALT has been investigated by several authors such as Tang et al.， 11Khamis and Higgins， 6Xiong， 12 Yeo and Tang， 2 13Gouno， 5McSorley et al.， 8 Dharmadhikari and Rahman， 4 and Alhadeed and Yang.1。 In ALT, tests are often stopped before a
13、ll units fail. The estimate from the censored data are less accurate than those from complete data. However, this is more than oset by the reduced test time and expense. One of the most common censoring schemes is type II censoring. A type II censored sample has observed only the m(1mn) smallest obs
14、ervations in a random sample of n units. If an experimenter desires to remove live units at points other than the nal termination point of the life test, the above described scheme will not be of use to the experimenter. Type II censoring does not allow for units to be removed from the test at the p
15、oints other than the nal termination point. However, this allowance will be desirable, as in the case of accidental breakage of test units, in which the loss of units at points other than the termination point may be unavoidable. Intermediate removal may also be desirable when a compromise is sought
16、 between time consumption and the observation of some extreme values. These reasons lead us into the area of progressive censoring. Consider an experiment in which n independent units are placed on a test at time zero, and the failure times of these units are recorded. Suppose that m failures are go
17、ing to be observed. When the rst failure is observed, 1r of the surviving units are randomly selected and removed. At the second observed failure, 2r of the surviving units are randomly selected and removed. This experiment stops at the time when the m-th failure is observed and the rema
18、ining 12mr n r r 1mrm surviving units are all removed. The m ordered observed failure times are called progressively type II censored order statistics of size m from a sample of size n with censoring scheme ( 1,., mrr). Note that if 12rr 1 0mr , then mr n m which corresponds to the type II cen
19、soring, and if 12rr 0mr, thennm which corresponds to the complete sample. In this study, we consider point and interval estimations for the simple stepstress ALT with (1) progressive type II censoring, (2) an exponential failure time distribution at a constant stress, and (3) the cumulative ex
20、posure model. In Sec.2, we describe the model and some necessary assumptions. We use the maximum likelihood method to obtain the point estimators of the model parameters in Sec. 3. The confidence intervals for the model parameters are derived in Sec.4. A numerical data set is studied to illustrate t
21、he inferential procedure in Sec.5. 2. Model and Assumptions Let us consider the following simple step-stress accelerated life-testing scheme with progressive type II censoring: Suppose n randomly selected units are simultaneously placed on a life test at stress setting 1v ； the failure times of thos
22、e that fail in a time interval 0, are observed and some surviving units are removed when a failure occurs； starting from time , the non-removed surviving units are put to a different stress setting 2v 12()vv ； the failure times of those that fail are observed and some surviving units are remov
23、ed when a failure occurs； at the time of the mth failure, the life test is stopped. For any stress, the failure time distribution of the test unit is an exponential distribution. At stress level iv , the mean life of a test unit is a log-linear function of stress. That is, 01lo g iiv ， 1,2.i
24、 (1) Here the 0 and 1 are unknown parameters. The log-linear function is a common choice for the life-stress relationship since it includes both the power-law and the Arrhenius-relation as special cases. Furthermore, failures occur according to a cumulative exposure model. That
