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JSRI 2019, 16(1): 165-209 Back to browse issues page
Estimation of Reliability of Stress-strength for a Kumaraswamy Distribution based on Progressively Censored Sample‎
Akram Kohansal *1, Ramin Kazemi
1- , kohansal@sci.ikiu.ac.ir
Abstract:   (180 Views)
‎The estimation of R=P(X<Y) in the case that X and Y are two independent Kumaraswamy distributed random variables with different parameters for progressively Type-II censored samples is studied‎. ‎First assuming the same second shape parameters of two distributions‎, ‎the maximum likelihood estimation and different confidence intervals are considered‎. ‎Moreover‎, ‎in case the second shape parameters of two distributions are known‎, ‎MLE‎, ‎UMVUE‎, ‎Bayes estimation of R and confidence intervals are derived‎. ‎Finally‎, ‎the Maximum Likelihood and Bayes estimations of R in general case are obtained‎. ‎Performance comparisons of different methods are carried out utilizing Monte Carlo simulations‎. ‎Besides‎, ‎the proposed approach is employed for reliability analysis on a real strength-stress dataset to demonstrate its application‎.
 
Keywords: Kumaraswamy distribution, Progressive Type-II censoring, Bayesian estimator, Confidence interval, Monte Carlo simulation, Maximum likelihood estimator.‎
Full-Text [PDF 1036 kb]   (40 Downloads)    
Type of Study: Research | Subject: General
Received: 2020/05/14 | Accepted: 2020/10/13 | Published: 2019/09/19
References
1. Ahmad‎, ‎K.E.‎, ‎Fakhry‎, ‎M.E‎. ‎and Jaheen‎, ‎Z.F‎. ‎(1997)‎. ‎Empirical Bayes Estimation of P(Y < X) and Characterization of Burr-Type X Model‎. Journal of Statistical Planning and Inference‎, 64‎, ‎297-308‎. [DOI:10.1016/S0378-3758(97)00038-4]
2. Ahmadi‎, ‎K‎. ‎and Ghafouri‎, ‎S‎. ‎(2019)‎. ‎Reliability Estimation in a Multicomponent Stress-strength Model under Generalized Half-normal Distribution based on Progressive Type-II Censoring‎. Journal of Statistical Computation and Simulation‎, 89‎, ‎2505-2548‎. [DOI:10.1080/00949655.2019.1624750]
3. Asgharzadeh‎, ‎A.‎, ‎Valiollahi‎, ‎R‎. ‎and Raqab‎, ‎M.Z‎. ‎(2011)‎. ‎Stress-strength Reliability of Weibull Distribution based on Progressively Censored Samples‎. SORT‎, 35‎, ‎103-124‎.
4. Badar‎, ‎M.G‎. ‎and Priest‎, ‎A.M‎. ‎(1982)‎. ‎Statistical Aspects of Fiber and Bundle Strength in Hybrid Composites‎, ‎in‎: Progress in Science and Engineering Composites‎, ‎Hayashi‎, ‎T.‎, ‎Kawata‎, ‎K‎. ‎and Umekawa‎, ‎S‎. ‎Eds.‎, ‎Tokyo‎. ‎1129-1136‎, ‎ICCM-IV‎.
5. Balakrishnan‎, ‎N‎. ‎and Aggarwala‎, ‎R‎. ‎(2000)‎. Progressive Censoring‎: ‎Theory‎, ‎Methods and Applications‎. ‎Birkhauser‎, ‎Boston‎.
6. Baklizi‎, ‎A‎. ‎(2007)‎. ‎Inference about the Mean Difference of Two Non-normal Populations based on Independent‎ ‎Samples‎: ‎a Comparative Study‎. Journal of Statistical Computation and Simulation‎, 77‎, ‎613-623‎. [DOI:10.1080/10629360600569501]
7. Birnbaum‎, ‎Z.W‎. ‎(1956)‎. ‎On a Use of Mann-Whitney Statistics‎. Proceedings of the Third Berkley Symposium in Mathematics‎, ‎Statistics and Probability‎, 1‎, ‎13-17‎. [DOI:10.1525/9780520313880-005]
8. Cao‎, ‎J.H‎. ‎and Cheng‎, ‎K‎. ‎(2006)‎. An Introduction to the Reliability Mathematics‎. ‎Beijing‎: ‎Higher Education Press‎.
9. Chen‎, ‎M.H‎. ‎and Shao‎, ‎Q.M‎. ‎(1999)‎. ‎Monte Carlo Estimation of Bayesian Credible and HPD Intervals‎. Journal of Computational and Graphical Statistics‎, 8‎, ‎69-92‎. [DOI:10.1080/10618600.1999.10474802]
10. Efron‎, ‎B‎. ‎(1982)‎. ‎The Jackknife‎, ‎the Bootstrap and Other Re-sampling Plans‎. Philadelphia‎, ‎PA‎: ‎SIAM‎, ‎CBMSNSF Regional Conference Series in Applied Mathematics‎, 34‎.
11. Gradshteyn‎, ‎I.S‎. ‎and Ryzhik‎, ‎I‎. ‎M‎. ‎(1994)‎. Table of Integrals‎, ‎Series‎, ‎and Products‎. ‎5th ed.‎, ‎Academic Press‎, ‎Boston‎, ‎MA‎.
12. Hall‎, ‎P‎. ‎(1988)‎. ‎Theoretical Comparison of Bootstrap Confidence Intervals‎. Annals of Statistics‎, 16‎, ‎927-953‎. [DOI:10.1214/aos/1176350944]
13. Johnson‎, ‎N.L.‎, ‎Kotz‎, ‎S‎. ‎and Balakrishnan‎, ‎N‎. ‎(1994)‎. Continuous Univariate Distributions‎. ‎2nd ed.‎, ‎Wiley‎, ‎NewYork‎.
14. Jones‎, ‎M‎. ‎C‎. ‎(2009)‎. ‎Kumaraswamy's Distribution‎: ‎A beta-type Distribution with Some Tractability Advantages‎. Statistical Methodology‎, 6‎, ‎70-81‎. [DOI:10.1016/j.stamet.2008.04.001]
15. Kotz‎, ‎S.‎, ‎Lumelskii‎, ‎Y‎. ‎and Pensky‎, ‎M‎. ‎(2003)‎. The Stress-strength Model and Its Generalization‎: ‎Theory and Applications‎. ‎World Scientific‎, ‎Singapore‎.
16. Kundu‎, ‎D‎. ‎and Gupta‎, ‎R.D‎. ‎(2006)‎. ‎Estimation of P[Y DOI:10.1109/TR.2006.874918]
17. Lemonte‎, ‎A.J‎. ‎(2011)‎. ‎Improved Point Estimation for the Kumaraswamy Distribution‎. Journal of Statistical Computation and Simulation‎, 81‎, ‎1971-1982‎. [DOI:10.1080/00949655.2010.511621]
18. Li‎, ‎J‎. ‎and Fine‎, ‎J.P‎. ‎(2010)‎. ‎Weighted Area under the Receiver Operating Characteristic Curve and Its Application to Gene Selection‎. Journal of the Royal Statistical Society‎: ‎Series C (Applied Statistics)‎, 59‎, ‎673-692‎. [DOI:10.1111/j.1467-9876.2010.00713.x]
19. Li‎, ‎J‎. ‎and Ma‎, ‎S‎. ‎(2011)‎. ‎Time-dependent ROC Analysis under Diverse Censoring Patterns‎. Statistics in Medicine‎, 30‎, ‎1266-1277‎. [DOI:10.1002/sim.4178]
20. Lindley‎, ‎D.V‎. ‎(1980)‎. ‎Approximate Bayesian Methods‎. Trabajos de Estadistica‎, 3‎, ‎281-288‎.
21. Mirjalili‎, ‎S.M.‎, ‎Torabi‎, ‎H.‎, ‎Nadeb‎, ‎H‎. ‎and Bafekri‎, ‎S.F‎. ‎(2016)‎. ‎Stress-strength Reliability of Exponential Distribution based on Type-I Progressively Hybrid Censored Samples‎. Journal of Statistical Research of Iran‎, 13‎, ‎89-105‎. [DOI:10.18869/acadpub.jsri.13.1.5]
22. Mitnik‎, ‎P.A‎. ‎(2013)‎. ‎New Properties of the Kumaraswamy Distribution‎. Communications in Statistics‎ - ‎Theory and Methods‎, 42‎, ‎741-755‎. [DOI:10.1080/03610926.2011.581782]
23. Nadar‎, ‎M.‎, ‎Papadopoulos‎, ‎A‎. ‎and Kizilaslan‎, ‎F‎. ‎(2013)‎. ‎Statistical Analysis for Kumaraswamy's Distribution based on Record Data‎. Statistical Papers‎, 54‎, ‎355-369‎. [DOI:10.1007/s00362-012-0432-7]
24. Nadar‎, ‎M.‎, ‎Kizilaslan‎, ‎F‎. ‎and Papadopoulos‎, ‎A‎. ‎(2014)‎. ‎Classical and Bayesian Estimation of P(YDOI:10.1080/00949655.2012.750658]
25. Nadar‎, ‎M‎. ‎and Kizilaslan‎, ‎F‎. ‎(2014)‎. ‎Classical and Bayesian Estimation of P(XDOI:10.1007/s00362-013-0526-x]
26. Raqab‎, ‎M.Z‎. ‎and Kundu‎, ‎D‎. ‎(2005)‎. ‎Comparison of Different Estimators of P(Y < X) for a Scaled Burr Type X Distribution‎. Communications in Statistics‎ - ‎Simulation and Computation‎, 34‎, ‎465-483‎. [DOI:10.1081/SAC-200055741]
27. Shoaee‎, ‎S‎. ‎and Khorram‎, ‎E‎. ‎(2015)‎. ‎Stress-strength Reliability of a two-parameter Bathtub-Shaped Lifetime Distribution based on Progressively Censored Samples‎. Communications in Statistics‎ - ‎Theory and Methods‎, 44‎, ‎5306-5328‎. [DOI:10.1080/03610926.2013.821485]
28. Surles‎, ‎J.G‎. ‎and Padgett‎, ‎W.J‎. ‎(1998)‎. ‎Inference for P(Y < X) in the Burr Type X Model‎. Journal of Applied Statistical Sciences‎, 7‎, ‎225-238‎.
29. Surles‎, ‎J.G‎. ‎and Padgett‎, ‎W.J‎. ‎(2001)‎. ‎Inference for Reliability and Stress-strength for a Scaled Burr-type X Distribution‎. Lifetime Data Analysis‎, 7‎, ‎187-200‎.
30. Wang‎, ‎B.X.‎, ‎Wang‎, ‎X.K‎. ‎and Yu‎, ‎K‎. ‎(2016)‎. ‎Inference on the Kumaraswamy Distribution‎. Communications in Statistics‎ - ‎Theory and Methods‎. Accepted. DOI‎: ‎10.1080/03610926.2015.1032425‎.
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kohansal A, Kazemi R. Estimation of Reliability of Stress-strength for a Kumaraswamy Distribution based on Progressively Censored Sample‎. JSRI. 2019; 16 (1) :165-209
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