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JSRI 2020, 16(2): 535-557 Back to browse issues page
Weibull Analysis with Sequential Order Statistics Under a Power Trend Model for Hazard Rates with Application in Aircraft Data Analysis
Majid Hashempour *1, Mahdi Doostparastand, Elaheh Velayati Moghaddam
1- , ma.hashempour@hormozgan.ac.ir
Abstract:   (428 Views)
 

 
‎In engineering systems‎, ‎it is usually assumed that the lifetimes of components are independent and identically distributed (iid)‎. ‎But‎, ‎the failure of a component results in a higher load on the remaining components and hence causes the distribution of the surviving components to change‎. ‎For modelling this kind of system‎, ‎the theory of sequential order statistics (SOS) can be used‎.
‎Assuming Weibull distribution for lifetimes of components and conditionally proportional hazard rates model as a special case of the SOS theory‎, ‎the maximum likelihood estimates of the unknown parameters are obtained in different cases‎. ‎A new model‎, ‎denoted by PTCPHM‎, ‎as a generalization of the iid case is proposed‎, ‎and then statistical inferential methods including point and interval estimations as well as hypothesis tests‎
‎under PTCPHM are developed‎. ‎Finally‎, ‎real data on failure times of aircraft components‎, ‎due to Mann and Fertig (1973), ‎are analysed to illustrate the model and inferential methods developed here‎.
 
Keywords: Censored data, estimation, hazard function, reliability, sequential order statistics.
Full-Text [PDF 244 kb]   (86 Downloads)    
Type of Study: Research | Subject: General
Received: 2021/07/14 | Accepted: 2021/10/13 | Published: 2021/11/28
References
1. AL-Hussaini‎, ‎E.K‎. ‎(1999)‎. ‎Predicting Observable from a General Class of Distributions‎. Journal of Statistical Planning and Inference‎, 79‎, ‎79-91‎. [DOI:10.1016/S0378-3758(98)00228-6]
2. ‎Arnold‎, ‎B.C.‎, ‎Balakrishnan‎, ‎N.‎, ‎and Nagaraja‎, ‎H.N‎. ‎(2008)‎. A First Course in Order Statistics. Classic Edition‎, ‎SIAM‎, ‎Philadelphia‎‎.
3. ‎Balakrishnan‎, ‎N.‎, ‎Beutner‎, ‎E.‎, ‎and Kamps‎, ‎U‎. ‎(2008)‎. ‎Order Restricted Inference for Sequential K-out-of n Systems‎. Journal of Multivariate Analysis. 99‎, ‎1489-1502‎. [DOI:10.1016/j.jmva.2008.04.014]
4. ‎Balakrishnan‎, ‎N.‎, ‎and Kateri‎, ‎M‎. ‎(2008)‎. ‎On the Maximum Likelihood Estimation of Parameters of Weibull Distribution Based on Complete and Censored Data‎. Statistics and Probability Letters, 78‎, ‎2971-2975‎. [DOI:10.1016/j.spl.2008.05.019]
5. ‎Bedbur‎, ‎S‎. ‎(2010)‎. ‎UMPU Test Based on Sequential Order Statistics‎,Journal of Statistical Planning and Inference, 140‎, 2520-2530‎. [DOI:10.1016/j.jspi.2010.03.021]
6. ‎Billinton‎, ‎R.‎, ‎and Allan‎, ‎R‎. ‎(1992). Reliability of Engineering Systems‎: ‎Concepts and Techniques‎. ‎Second edition‎, ‎Springer-Verlag‎, ‎New York‎.
7. Casella‎, ‎C.‎, ‎and Hwang‎, ‎J.T.G‎. ‎(2012)‎. ‎Shrinkage Confidence Procedures‎. Statistical Science, 27‎, ‎51-60‎. [DOI:10.1214/10-STS319]
8. ‎Cramer‎, ‎E.‎, ‎and Kamps‎, ‎U‎. ‎(1996)‎. ‎Sequential Order Statistics and K-out-of-n Systems with Sequentially Adjusted Failure Rates‎. Annals of the Institute of Statistical Mathematics, 48‎, ‎535-549‎. [DOI:10.1007/BF00050853]
9. Cramer‎, ‎E.‎, ‎and Kamps‎, ‎U‎. ‎(1998)‎. ‎Sequential K-out-of-n Systems with Weibull Components‎. ‎Economic Quality Control‎, 13‎, ‎227-239‎.
10. ‎Cramer‎, ‎E.‎, ‎and Kamps‎, ‎U‎. ‎(2001)‎. ‎Sequential K-out-of-n Systems‎, ‎In‎: ‎N‎. ‎Balakrishnan and C.R‎. ‎Rao (Eds.)‎. Handbook of Statistic‎, ‎Vol‎. 20‎, Advances in Reliability‎, ‎301-372‎, ‎North-Holland‎, ‎Amsterdam‎. [DOI:10.1016/S0169-7161(01)20014-5]
11. Cramer‎, ‎E.‎, ‎and Kamps‎, ‎U‎. ‎(2003)‎. ‎Marginal Distributions of Sequential and Generalized Order Statistics‎. Metrika‎, 58, ‎293-310‎. [DOI:10.1007/s001840300268]
12. Johnson‎, ‎N.L.‎, ‎Kotz‎, ‎S.‎, ‎and Balakrishnan‎, ‎N‎. ‎(1994)‎. ‎Continuous Univariate Distributions-Vol‎. ‎1‎, ‎Second edition‎, ‎John Wiley and Sons‎, ‎New York‎.
13. Hashempour‎, ‎M.‎, ‎and Doostparast‎, ‎M‎. ‎(2017)‎. ‎Considered Bayesian Inference on Multiply Sequential Order Statistics from Heterogeneous Exponential Populations with GLR Test for Homogeneity‎. Communications in Statistics-Theory and Methods‎, 46‎, ‎8086-8100‎. [DOI:10.1080/03610926.2016.1175625]
14. ‎‎Kamps‎, ‎U‎. ‎(1995)‎. A Concept of Generalized Order Statistics. Teubner‎, ‎Stuttgart‎, ‎Germany‎. [DOI:10.1007/978-3-663-09196-7_2]
15. Lehmann‎, ‎E.L.‎, ‎and Casella‎, ‎G‎. ‎(1998)‎. Theory of Point Estimation. Second edition‎, ‎Springer-Verlag‎, ‎New York‎.
16. Lehmann‎, ‎E.L.‎, ‎and Romano‎, ‎J.P‎. ‎(2005)‎. Testing Statistical Hypothesis. Third edition‎, ‎Springer-Verlag‎, ‎New York‎.
17. Mann‎, ‎N.R.‎, ‎and Fertig‎, ‎K.W‎. ‎(1973)‎. ‎Tables for Obtaining Weibull Confidence Bounds and Tolerance Bounds Based on Best Linear Invariant Estimates of Parameters of the Extreme Value Distribution‎. Technometrics, 15‎, ‎87-101‎. [DOI:10.1080/00401706.1973.10489013]
18. ‎Schenk‎, ‎N.‎, ‎Burkschat‎, ‎M.‎, ‎Cramer‎, ‎E.‎, ‎and Kamps‎, ‎U‎. ‎(2011)‎. ‎Bayesian Estimation and Prediction with Multiply Type-II Censored Samples of Sequential Order Statistics from One‎- ‎and Two-Parameter Exponential Distributions‎, Journal of Statistical Planning and Inference, 141‎, ‎1575-1587‎. [DOI:10.1016/j.jspi.2010.11.009]
19. Shafay‎, ‎A.R.‎, ‎Balakrishnan‎, ‎N.‎, ‎and Sultan‎, ‎K.S‎. ‎(2012)‎. ‎Two-Sample Bayesian Prediction for Sequential Order Statistics from Exponential Distribution Based on Multiply Type-II Censored Samples‎. Journal of Statistical Computation and Simulation, 84‎, ‎526-544‎. [DOI:10.1080/00949655.2012.718779]
20. ‎Smith‎, ‎P.J‎. ‎(2002)‎. ‎Analysis of Failure and Survival Data. Chapman and Hall/CRC Press‎, ‎Boca Raton‎, ‎Florida‎.
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Hashempour M, Doostparastand M, Velayati Moghaddam E. Weibull Analysis with Sequential Order Statistics Under a Power Trend Model for Hazard Rates with Application in Aircraft Data Analysis. JSRI. 2020; 16 (2) :535-557
URL: http://jsri.srtc.ac.ir/article-1-389-en.html


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Volume 16, Issue 2 (3-2020) Back to browse issues page
مجله‌ی پژوهش‌های آماری ایران Journal of Statistical Research of Iran JSRI
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