[Back to Results | New Search]

Student Number 952205005 Author Bing-Yi Wu(吳秉懌) Author's Email Address No Public. Statistics This thesis had been viewed 1365 times. Download 677 times. Department Graduate Institute of Statistics Year 2007 Semester 2 Degree Master Type of Document Master's Thesis Language zh-TW.Big5 Chinese Title 群組資料指數分配加速壽命試驗之貝氏可靠度分析與最佳化設計 Date of Defense 2008-06-17 Page Count 50 Keyword accelarated life test Bayesian analysis grouped data optimal test Type-I progressive censoring Abstract Accelarated life test (ALT) is a widely used technique to reduce the experiment time. Experimenters abridge the time by placing the items at the more severe stress levels than at nomal-use contidion. Besides, in the step-stress ALT, the stress levels are gradually increasing. Also, censoring scheme is often applied when the life test is to be executed. Complete data, which record all failure times and grouped data, which only include the numbers of failure items are two types of data in life test. In this thesis, assume that the lifetime of each item follows an exponential

distribution under the single stress progressive Type-I censoring ALT with grouped data. Maximum likelihood as well as Bayesian inferences on the related parameters are developed. The traditional MLE according as the large sample properties is not precise enough since there is no large sample in reliability test. However Bayesian method would offer stable estimation when the sample size is not large. Futhermore, the search for optimal experiment time and optimal stress increment is derived, which is based on V-optimality, D-optiamlity and A-optimality.Table of Content 中文摘要i

英文摘要ii

致謝辭iii

1 緒論1

1.1 研究動機

1.2 文獻回顧

1.3 研究方法

2 型I 逐步設限階段應力加速壽命試驗推論與最佳設計7

2.1 模型介紹與統計推論

2.1.1 最大概似估計

2.1.2 貝氏推論

2.2 最佳化準則

2.2.1 V-最佳化準則

2.2.2 D-最佳化準則

2.2.3 A-最佳化準則

3 數值分析與模擬研究

3.1 最佳化試驗時間

3.2 最佳化應力增量

3.3 模擬資料研究

4 結論與展望

參考文獻Reference [1] Bai, D.S., and Kim, M.S. (1993) Optimum simple step-stress accelerated life

tests for weibull distribution and type I censoring. Naval Research Logistics 40,

193-210.

[2] Bai, D.S., Kim, M.S. and Lee, S.H. (1989) Optimum simple step-stress accelerated

life tests with censoring. IEEE Transactions on Reliability 38, 528-532.

[3] Balakrishnan, N. and Aggarwala, R. (2000) Progressive Censoring: Theory,

Methods, and Applications. Birkhauser, Boston.

[4] Balakrishnan, N. and Han, D. (2008) Optimal step-stress testing for progressively

Type-I censored data from exponential distribution. J. Statist. Plann.

Inference to appear.

[5] Balakrishnan, N. and Sandhu, R.A. (1996) Best linear unbiased and maximum

likelihood estimation for exponential distribution under progressive type-II censored

smaples. Sankhya 58, 1-9.

[6] Berger, J.O. (1985) Statistical Decision Theory and Bayesian Analysis, 2nd edn. Springer, New York.

[7] Casella, G. and Berger, R.L. (2002) Statistical Inference, 2nd edn. Duxbury,

Pacific Grove, CA.

[8] Chib, S. and Greenberg, E. (1995) Understanding the Metropolis-Hastings algorithm.

Amer. Statist. 49, 327-335

[9] Cohen, A.C. (1963) Progressively censored samples in life testing. Technometries

5, 327-329.

[10] Cohen, A.C. and Norgaard, N.J. (1977) Progressively censored sampling in the

three-parameter gamma distribution. Technometrics 19, 333-340.

[11] Drop, J.R. and Mazzuchi, T.A. (2004) A general Bayes exponential inference

model for accelerated life test. J Stat Plan Inference 119, 55-74.

[12] Fan T.H., Wang W.L. and Balakrishnan, N. (2008) Exponential progressive

step-stress life-testing with link function based on Box-Cox transformation.

Journal of Statistical Planning and Inference 138, 2340-2354.

[13] Gibbons, D. I. and Vance, L. C. (1983) Estimators for the 2-parameter Weibull

distribution with progressively censored samples. IEEE Transactions on Reliability

32, 95-99.

[14] Gouno, E., Sen, A. and Balakrishnan, N. (2004) Optimal step-stress test under

progressive Type-I censoring. IEEE Transactions on Reliability 53, 383-393.

[15] Khamis, I.H. (1997) Optimum M-step, step-stress test with k stress variables.

Comm. Statist. Comput. Simul. 26, 1301-1313.

[16] Hastings, W.K. (1970) Monte Carlo sampling method using Makov chain and

their applications. Biometrika 57, 97-109.

[17] Jeffreys, H. (1961) Theorey of Probability, 3rd edn. Oxford University Press,

London.

[18] Khamis, I.H. and Higgins, J.J. (1998) A new model for step-stress testing. IEEE

Transactions on Reliability 47, 131-134.

[19] Mann, N.R. (1971) Best linear invariant estimation for weibull parameter under

pregressive censoring. Technometrics 13, 521-533.

[20] Meeker, W.Q. and Hann, G.J. (1985) How to plan an accelerated life test.

American Socirty for Quality Control Statistics Division 10.

[21] Miller, R. and Nelson, W. (1983) Optimum simple step stress plans for accelerated

life testing. IEEE Transactions on Reliability 32, 59-65.

[22] Nelson,W. (1980) Accelerated life testing - step-stress models and data analysis.

IEEE Transactions on Reliability 29, 103-108.

[23] Nelson, W. (1990) Accelerated Testing: Statistical Models, Test Plans, and Data

Analyses. John Wiley & Sons, New York.

[24] Robert, C.P. (2001) The Bayesian Choice : From Decision-Theoretic Foundations

to Computational Implementation. Springer, New York.

[25] Tang, L.C., Sun, Y.S., Goh, T.N. and Ong, H.L. (1996) Analysis of step-stress

accelerated-life-test data: a new approach. IEEE Transactions on Reliability

51, 69-74.

[26] Tang, L.C., Sun, Y.S., Goh, T.N. and Ong, H.L. (1999) Planning accelerated

life tests for censored two-parameter exponential distributions. Naval Research

Logistics 16, 169-186.

[27] Teng, S.L. and Yeo, K.P. (2002) A least-squares approach to analyzing lifestress

relationship instep-stress accelerated life tests. IEEE Transactions on

Reliability 51, 177-182.

[28] Thisted, R.A. (1988) Elements of Statistical Computing: NUMERICAL COMPUTATION

(Elements of Statistical Computing). Chapman & Hall/CRC.

[29] Wu, S.J. and Chang, C.T. (2003) Inference in the Pareto distribution based

on progressive Type II censoring with random removals. J. Appl. Statist 30,

163-172.

[30] Wu, S.J., Lin, Y.P. and Chen, Y.J. (2006) Planning step-stress life test with

progressively type I group-censored exponential data. Neerlandica 60, 46-56.

[31] Wong, J. S. (1993) Simultaneously estimating the three Weibull parameters

from progressively censored samples. Microelectronics and Reliability 33, 2217-

2224.

[32] Xiong, C.(1998) Inferences on a simple step-stress model with type-II censored

exponential data. IEEE Transactions on Reliability 47, 142-146.

[33] Xiong, C. and Ji, M. (2004) Analysis of grouped and censored data from stepstress

life test. IEEE Transactions on Reliability 53, 22-28.

[34] Yuen, H.K. and Tse, S.K. (1996) Parameters estimation for weibull distributed

lifetimes under progressive censoring with random removeals. Journal of Statistical

Computation and Simulation 57-71.Advisor Tsai-Hung Fan(樊采虹)

Files approve immediately

952205005.pdf Date of Submission 2008-07-06

Our service phone is (03)422-7151 Ext. 57407,E-mail is also welcomed.