【正文】 中文 3350 字 本科畢業(yè)設(shè)計(jì)（英文翻譯） 英文原文 ： Estimations For A Simple StepStress Model With Progressively TypeII Censored Data 院 系 ： 能源與環(huán)境工程學(xué)院 專業(yè)年級(jí)： 機(jī)械設(shè)計(jì)制造及其自動(dòng)化 2020 級(jí) 學(xué)生姓名： 學(xué)號(hào)： 2020 年 5 月 12 日 1 International Journal of Reliability, Quality and Safety Engineering , (2020) 385–395 169。World Scienti?c Publishing Company ESTIMATIONS FOR A SIMPLE STEPSTRESS MODEL WITH PROGRESSIVELY TYPEII CENSORED DATA SHUOJYE WU? and HSIUMEI LEE Department of Statistics, Tamkang University Tamsui, Taipei 251 Taiwan ? DARHSIN CHEN Graduate Institute of Finance National Chiao Tung University Hsinchu City 300, Taiwan Received 1 January 2020 Revised 23 May 2020 With today’s 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 higherthanusual stress conditions in order to obtain failures quickly. This study discusses the point and interval estimations of parameters on the simple stepstress model in accelerated life testing with progressive type II censoring. An exponential failure time distribution with mean life that is a loglinear function of stress and a cumulative exposure 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. 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 higherthanusual stress conditions 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, step stress, and random stress. Nelson (Ref. 10, Chap. 1) discussed their advantages and disadvantages. In stepstress 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 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 stepstress ALT uses only two stress levels and we call simple stepstress ALT. The statistical inference in this simple stepstress 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 。 In ALT, tests are often stopped before all units fail. The estimate from the censored data are less accurate than those from plete data. However, this is more than o?set by the reduced test time and expense. One of the most mon censoring schemes is type II censoring. A type II censored sample has observed only the m(1≤m≤n) smallest observations 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 points 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 promise is sought 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 going 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 mth failure is observed and the remaining 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 censoring, and if 12rr??… 0mr??, thennm? which corresponds to the plete 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 exposure model. In , 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 . A numerical data set is studied to illustrate the inferential procedure in . 2. Model and Assumptions Let us consider the following simple stepstress accelerated lifetesting 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 those that fail